Kyung Il-Choe
Gunter Sharp

School of Industrial and Systems Engineering
Georgia Institute of Technology

Copyright: 1991 Georgia Tech Research Corporation, Atlanta, Georgia 30332


This report is concerned with order picking in a warehousing system. Although an order pick system (OPS) contains a few basic functions, the wide spectrum of external and internal factors in order picking makes the real OPS very complicated. For analysis purposes, order picking is defined as the selective retrieval of the appropriate amounts of products from a pick (or storage) area to fill specific customer orders. Orders are usually represented by a list of stock keeping units (SKUs) or line items. The list specifies the type and retrieval quantity of each line item, along with other information such as the due date, the customer name and address, etc.

Order picking and material handling, in general, have received considerable attention since the 1970s. Kearney (1986) estimated that the overall logistics cost in the United States is 21% of the Gross National Product, and that 28% of this logistics cost is accounted for by storage and retrieval (S/R) systems. The Warehouse Education and Research Council (1986) identified order picking as the number one area for improvement in warehousing.

Recent trends in distribution and manufacturing will make order picking even more important. In distribution systems there is increasing emphasis on better delivery time and accuracy standards. In manufacturing the move to smaller lot sizes, point-of-use delivery, and cycle time reductions, make efficient order picking crucial to being competitive (Shirk 1989). Other economic factors such as marketing pressures for more diversified product lines and shorter product life cycles result in additional importance and complexity of order picking (Weber 1989). Hence, the efficiency and cost of order picking are crucial issues to a corporation in today's intensely competitive marketing arena.

1.1 A General Structure of OPS

Considering the flows of items and orders in OPS, a general structure of OPS is proposed in Figure 1 (Yoon and Sharp 1990). The general structure of OPS consists of 8 departments (or functional areas): receiving area, pallet reserve area, case pick area, item pick area, sorting area A, sorting area B, unitizing area, and shipping area. The eight departments can be functionally categorized as breakdown area or consolidation area. All possible and most likely (thick arrows) flows are represented by the appropriate types of handling unit in Figure 1.

(Reprinted from Yoon and Sharp 1990)

To appreciate the functions of each department, let us consider the flow of a hypothetical high-activity product. The product is received in pallets and stored in a pallet reserve area (e.g. the upper levels of pallet rack). It is then moved to a case pick area (e.g. lower levels of pallet rack). Individual cases are removed from the case pick area and placed in the item pick area (e.g. gravity flow rack holding cases). The pickers selectively retrieve items from the flow racks and place them on conveyors which carry the items to sorting area A. There the items of each order are contained in totes; they might then go to a unitizing area to be palletized or combined into a mixed unit load (mul), and then to shipping, or directly to shipping.

Some customers might order this high-activity product in case lots. These might be retrieved directly from the case pick area and sent to sorting area B, for sorting cases and totes. The equipment in sorting area B might be different from that in area A, which is for sorting smaller items. It is conceivable that the same equipment could be used for both purposes, either simultaneously or at a different times.

Figure 1 should not suggest that every OPS should have this structure and all the diverse flows. Instead, it shows the many possible ways that products can flow through an OPS. The question of which SKUs for which orders should flow in which ways is in realm of specifying the operational strategy. We designate this as the specification of order pick system structure.

1.2 Types of Order Pick Systems

Figure 1 also shows three types of order picking: pallet retrieval, case picking, and item picking. By focusing primarily on order profiles, OPS can be classified in four categories for analysis purposes, as shown below (Sharp, Choe, and Yoon 1990). The factors of order size (line items per order), order volume (orders per time period), and extent of advance information, results in 23 = 8 combinations when 2 levels of each factors are considered.

Precise definitions of the descriptors are not possible. It is suggested that the number of orders be compared to the number of packing/shipping lanes. If during a process cycle a packing/shipping lane can be dedicated to an order, we say there are few (F) orders. If a packing/shipping lane is to be shared by several orders during a process cycle, we say there are many orders. A high volume of orders results in additional complexity of the OPS, especially of sorting areas.

Order size can be determined by cubic volume and/or number of line items. It is suggested that a small (S) order be defined as one that contains 10 or fewer line items; a line item is a SKU requested by an order. If the quantity per line item results in a cubic volume less than 0.01 cu. m.(0.35 cu. ft.), then a small order is also limited roughly to 0.1 cu. m. (3.5 cu. ft.). A large (L) order, containing more than 10 line items, would often have a volume greater than 0.1 cu. m. In some situations a large order might fill a truck. These definitions allow for some awkward, in-between situations. We believe that the demarcation based on the number of SKUs is more important since it relates more to operating strategies than a demarcation based on cubic volume.

The difference between advance (A) information and statistical (S) information relates to the ability to process the order data for more efficient operation. In the MSS example of a stock room serving a manufacturing facility, the requirement for fast response (e.g. 20 minutes) probably would preclude the types of batching strategies used by a catalog retailer, who usually has several hours at night for data processing and a late-afternoon shipping deadline. If there is adequate time for preprocessing, we say there is advance information. Otherwise, the information is statistical.

The information availability is directly related to the control rules in the operation of the OPS, since decision making based on statistical information is often quite different from one based on advance or deterministic information. For the MSS-OPS, the primary objective of analysis is to estimate the response time by finding the stochastic behavior of the system under given statistical information. Advance information or the availability of a 'long' response time allows many opportunities for operating a system in an 'intelligent' way; for example, batching, sequencing, workload balancing, etc. Consequently, the major challenge in the OPS with advance information such as MSA-, MLA-, and FLA-OPS is how to take advantage of the advance information.

Our classification considers only 4 out of possible 8 combinations. The scenarios of a few small orders, with statistical or advance information (FSS and FSA), do not provide much incentive for analysis and are excluded. The situation of a few large orders with statistical information (FLS) is relatively unusual. The situation of many large orders with statistical information (MLS), it can be argued, can be approached with many of the same strategies as MLA-OPS. Thus, the four categories listed suffice for analysis purposes.

1.3 Purpose and Scope of Research

This report presents an outline of order picking from an analytic viewpoint. By examining thoroughly the complicated nature of OPS, the primary objective is to lay a sound base which reveals the unique features of order picking and so to systematize research efforts in the future. Previous attempts can be found in Gudehus (1973), Frazelle (1988), Goetschalckx and Ashayeri (1988), Muller (1989), and Yoon and Sharp (1990). Most of these efforts focus on some specific aspects of order picking rather than a framework. Reviews of the literature on general material handling can be found in Matson and White (1982), Ashayeri and Gelders (1985), Francis, McGinnis and White (1985), and Kusiak (1985).

For the development of a general framework of OPS, Yoon and Sharp identify seven types of factors in the design of OPS:

1. Material properties of items stored.

2. Transaction data for SKUs and orders.

3. Operational strategies for storage assignment and retrieval.

4. Specification of hardware for subsystems and design of operator work areas.

5. System requirements with respect to throughput, inventory capacity, accuracy, and system response time.

6. Constraints based on building layout and operator safety.

7. Budget constraints related to investment and total annual cost.

Instead of an itemized discussion of the issues above, we classify them into 3 categories: strategic factors, design issues, and operational issues. They, along with other issues, will be presented with an emphasis on their inter-relationships. Such discussion will be helpful in comprehending the OPS as a multifaceted system of great dimensional complexity.

The next section identifies the strategic factors of OPS and presents an OPS design procedure. Included is a discussion of the various issues involved in order picking. The third and fourth sections, along with a literature review, go into more details on the issues in the design and operation of OPS, respectively. Issues in design include the specification of OPS structure, equipment selection, determination of the space requirements, and layout. Issues in operation include storage rules, pick strategies, A/S strategies, packing/palletizing, human factors, and hardware solutions. The issues and results applicable to individual equipment type are discussed in the fifth section. Finally, the sixth section describes future research opportunities that seem to offer promise for significant efficiency gains. Some of the results here are presented in Sharp, Choe, and Yoon (1990).


A design of a system shows what we know about the system; a design procedure for a system shows what we should know about the system. Therefore, a design procedure for OPS is crucial to the identification of the issues involved in the design and operation of OPS, and also to their inter-relationships and hierarchy. We first explain the strategic factors, usually beyond of the control of the system planner, which delineate the requirements and objectives of OPS. Then, we present how to design an 'efficient' OPS to meet such requirements.

2.1 Strategic Factors of OPS

The strategic factors of OPS can be classified into three categories: system profiles, order profiles, and item profiles.

The system profiles determine the status of an OPS within the whole system and its interactions with other subsystems. In a broad sense the system profiles include the strategic planning factors of the corporate organization; in a narrow sense the system profiles include the type and number of suppliers, the type and number of customers and their service levels, etc. (Goetschalckx and Ashayeri 1988).

The supplier type can be an in-house manufacturing facility, external (domestic or overseas) manufacturing facility, or external distribution center. The major effects of suppliers are on the inventory policy and the replenishment patterns of inventories in the OPS. For example, if the supplier is an in-house manufacturing facility, the control on replenishment of the OPS might be limited by other considerations such as the efficiency of the manufacturing process. Overseas suppliers, on the other hand, usually mean long lead times and large order quantities.

The inventory policy depends on the customers as well. The customers can be wholesalers, retailers, a combination of both, or a manufacturing facility. The types and number of customers are important, since they basically determine order profiles and service levels. For example, the design and operation of a local distribution center are usually different from those of a national depot.

The order profiles include the volume of orders, the number of line items per order, the retrieval quantity of a line item per order, due dates, priority classes, and any similarities among orders. In general, the order profiles strongly influence the system design. For example, an order of a truck-load of goods, a typical one for a national distribution center, is not processed by the same type of equipment and procedure as one of a cart-load, a typical one for a local distribution center for small retailers. Another important factor of order profiles is the information availability or the response time constraint. Generally, the more time that is available before an order must be shipped, the greater the opportunity to improve efficiency by 'intelligent' control rules. Hence the design and operation of an OPS should be compatible with the information availability.

The item profiles include the number, size, weight, stackability, suitability for nesting, and environmental requirements of the SKUs. These factors must be considered in selecting equipment for S/R and handling among other issues. For example, high-security items should be stored in a closed equipment such as storage drawers, vertical carousels, or miniload AS/RS, and not in an open equipment, such as shelving. Fragile items might be damaged by a high-speed sortation system. Diversity in size and weight of items can also lead to more dimensionality and problems in using high-speed sortation. The item profiles thus restrict the compatible equipment types and their layout, and influence the total cost of the OPS.

2.2 A Systematic Design Procedure for OPS

Considerable previous work has been done on systematic and/or analytic methods for the design of 'conventional' warehouses of which a major function is pallet retrieval: e.g. Kay (1968), Gudehus (1973), Amagai (1985), Branigan (1988), Juenemann and Meister (1988), Perlmann and Bailey (1988), Park and Webster (1989a), Schulze and Westfal (1989). Some of them develop computer aided systems for the design of conventional warehouses.

The design of an OPS is a more difficult task than that of a conventional warehouse due to the greater complexity of order picking. Elliott (1986), Goetschalckx and Ashayeri (1988), Hanelt and Kryder (1989) are concerned with the design procedure especially for OPS. Elliott, and Hanelt and Kryder explain the details of OPS design by following each step of the classical engineering design process. Goetschalckx and Ashayeri present a structured approach called SYDOPS, along with a general framework of an OPS. A practical and comprehensive guide can be found in Zollinger (1982), the Naval Supply Systems Command (1985), and Carew (1989). None of these efforts, however, explicitly specifies the structure of an OPS, and none considers the flows of orders and items in the system. A number of case studies for the design of warehouses and OPS are reported in the literature, such as the Proceedings of the International Conference on Automation in Warehousing.

A design procedure by Yoon and Sharp (1990), with an emphasis on the interwoven structure of the OPS, consists of three main stages: input stage, selection stage, and evaluation stage. Their procedure is illustrated in Figure 2. First, the input stage includes the determination of strategic factors and the specification of the structure of the OPS. A data analysis phase leads to specifying the objectives, requirements, and structure of the OPS. The major outputs of this stage include a functional specification of subsystems and the flows of the items and orders in the system.

They then proceed to the selection stage, which consists of

These four design tasks must be performed together for each alternative. For example, a five aisle person-aboard S/RS with batch picking in five zones, one per aisle, will have a different information transformation of the order data into pick lists than a 20-aisle shelving system with single-order-pick strategy. Similarly, physical transformation of items depend on the equipment, the operational strategy, and the results from the input stage. The outputs of the selection stage are an explicit specification of each potential subsystem including equipment types, operational strategies, performance evaluation, cost and space requirements, etc.

The evaluation stage is concerned with the overall evaluation of subsystems from the system point of view. It consists of the following four steps:

(Reprinted from Yoon and Sharp 1990)

The first important task in the evaluation stage is subsystem reconciliation. An example is the use of a pallet rack for both the reserve storage (RS) and the pick system (PS); there must be proper balance between spaces required and time needed for each function. Another example is when single-order picking and batch picking are performed using the same equipment. A third example is the capacity matching of the sorting system with the output of the pick system. Some type of multi-criteria evaluation procedure is usually employed in the evaluation stage (Pliskin and Dori 1982). It is not unusual for the design procedure to be partially repeated. The actual implementation of the design selected requires again a considerable amount of planning and effort; this issue is beyond the scope of this research.


The design procedure for OPS reveals the issues crucial to the 'successful' design of OPS: determination of system requirements, specification of order picking system structure, selection of equipment for each subsystem, operating strategies, and determination of the physical dimensions and layout. The determination of system requirements, the upper-most level of the decision hierarchy, should be based on a comprehensive analysis of both the current status and the long-term perspective of management. Especially, the requirements should reflect possible changes of the strategic factors in the decision horizon, and also of order picking technology. See White (1988) and Hatanaka (1989) for current trends in material handling and order picking.

3.1 Specification of Subsystems and equipment Types

The specification of subsystems and equipment types usually consists of several steps as follows:

The analysis of order profiles, along with other system requirements, will reveal how many orders require pallet retrieval, case picking, and item picking, respectively, and also what quantities of which items should be provided for each type of order picking. Suzuki (1988) presents a structured method based on the so-called order pattern graph which enables a planner to identify easily the relationships among orders, SKUs, and retrieval quantities.

Based on these results we then can determine whether each type of order picking is performed by a separate system or by sharing a system with others. It is difficult to obtain the structure of the OPS by quick analysis, and few guidelines are available in the literature (Yoon and Sharp 1990). More structured methods such as group technology may be applied to the classification problem (Mutel and Anciaux 1989).

The next step after specifying the structure of the OPS is to select the 'best' equipment type for each subsystem. The decision is usually associated with multiple criteria, some of which might be conflicting. The equipment selection is closely related to the total space and budget constraints and also to the layout planning of the OPS. For example, when there is a limit to the available space, the selection problem of a subsystem should be based not only on its own factors but on their effects on the total space requirements and layout. These decision problems lead indeed to a fertile, open research area.

Equipment Types for Order Picking

To facilitate our discussion, material handling equipment available for OPS is classified into four categories: S/R equipment, accumulation/sortation (A/S) equipment, handling equipment, and auxiliary equipment. This study focuses on the S/R and A/S types of equipment, which comprise the main hardware of an OPS. The handling equipment links the subsystems of the OPS. The auxiliary equipment items are a vital part of any material handling system, but they do not physically handle items.

S/R equipment is classified into three types:

The major difference between picker-to-part systems and part-to-picker systems is whether the picker has to travel to the pick location or vice versa. White (1979), and Frazelle and Sharp (1990) give brief discussions on the pros and cons of picker-to-part and part-to-picker systems. Krajacic (1988) gives a general description of the automatic item picker.

The equipment types for A/S operation include

A/S operation is not clearly separable from S/R operation, since partial and complete sorting can sometimes be done during the order pick process.

The primary function of handling equipment is to link subsystems by moving items from one to another. The major types of handling equipment are

The auxiliary equipment to support the other equipment types includes

Selection of Equipment

It is a complicated issue to determine the 'best' equipment even under well-defined requirements and specification of material handling activities. The complexity is ascribed to the great variety of factors such as the number of equipment alternatives, the multiple criteria for selection, and the inter-relationships with other subsystems. From an analytical view point, the equipment selection problem consists of three sub-issues: unit load size, equipment type, and physical dimensions.

Determining the container or the unit load size is one of the strategic issues in material handling as well as order picking. The unit load is defined as the number of items or the amount of bulk material contained in the basic handling unit of a set of material handling activities. According to Tanchoco and Agee (1981), the potential advantages of the unit load include more effective utilization of storage space, and reductions in handling, packaging, and transportation costs; its potential disadvantages include loss of the flexibility in the handling system, and labor costs and additional equipment for unitizing/de-unitizing.

The scope of previous works related to the unit load problem is very limited. Most of the results focus on certain aspects of the problem in handling pallets: Steudel (1983) for general material handling systems; Tanchoco, Davis and Wysk (1980), Grasso and Tanchoco (1983), Tanchoco et al. (1983), Emamizadeh and Knott (1986) in conjunction with inventory policies; Roll, Rosenblatt and Kadosh (1989) for a unit-load AS/RS.

Various attempts have been made for the selection of equipment type; a review on earlier works can be found in Matson and White (1982). Recently, Malmborg, Hubbard and Agee (1985) develop a computer aided procedure based on simulation and multi-attribute decision models. Houmas (1986) presents the cost and performance comparisons of various equipment types for item picking such as storage drawers, gravity flow racks, carousels, and miniload AS/RS. Assuming a warehousing system with just two different types of S/R equipment, Azadivar (1987) and (1989) develops analytical models to allocate the space to each S/R equipment type. Azadivar formulates the allocation problem as stochastic programs of which the parameters are estimated by simulation.

The limited scope of analytical models results in the development of rules-of-thumb for equipment selection. One of the criteria frequently used for such rules-of-thumb is the level of automation. Using the level of automation as the major criterion of equipment selection, Cox (1986) develops a framework, called a hierarchy of productivity ratios, to determine the suitable level of automation. Gelders and Ashayeri (1989), among others, give typical equipment types at three different levels of automation for each combination of two factors: item size and throughput requirements.

As Malmborg, Simmons and Agee (1986) suggest, the expert system approach can be applied also to equipment selection: Fisher, Farber and Kay (1988), and Matson, Swaminathan and Mellichamp (1990) for the selection of handling equipment including manual, trucks, conveyors, AGVs, and cranes; Malmborg et al. (1989) for the selection of industrial truck types. However, no expert systems for S/R equipment selection are reported in the literature.

3.2 Physical Dimensions and Layout

We discuss here two major issues associated with the specification of the physical dimensions and layout of OPS: the determination of the total space requirement and an efficient layout.

Total Space Requirements

The estimation of the total space requirement is a prime example of the degree of complexity peculiar to OPS design. The total space requirement is influenced by virtually all the issues associated with order picking. For example, a long-term perspective of business influences the physical size of buildings and other structures to meet foreseeable future demands; order profiles, item profiles, the inventory policy, and the replenishment pattern influence the OPS size; the equipment types used in the OPS influence the OPS size; operational strategies, such as the storage rule, influence the equipment size, and so the total space requirement; the layout influences the OPS size. The discussion above implies two conflicting restrictions: the space requirement cannot be precisely estimated until most details of the OPS are specified; however, the space requirement is crucial to the specification of those details.

The estimation of the space requirement consists of two major steps: estimation of peak and average (aggregate) inventory levels of items stored, and transformation from the inventory volume to the space requirement. Yang (1988) and Hall (1989) contain a literature review of the inventory packing problem, which consists of estimating the maximum level of the aggregate inventory in the system and then minimizing the peak level. Even if we can estimate the inventory volume, it is difficult to transform the inventory volume into the space requirement, especially for case and item picking. Most of results obtained so far are concerned with the space requirement for pallet retrieval only: Mullens (1981), Rosenblatt and Roll (1988), Park and Webster (1989a), Camp (1990). All the works are based on simulation.

Our discussion based on two separate steps should not imply that they are truly separable. For a conventional warehouse, Wilson (1977) demonstrates that the inventory policy and the storage rule should be determined simultaneously to minimize the total costs. The analogous problem in the unit-load AS/RS is exploited by Hodgson and Lowe (1982). Vemuganti (1987) presents an optimization model for determining the production lot size that includes all of the production, inventory, and storage space costs; however, the model does not consider handling costs. For a block stacking system, Schall and Chandra (1989) are concerned with a generalized model including the inventory packing problem, unit load size, and storage space. In fact, their model is a generalization of Tanchoco et al. (1983) by using Page and Paul (1976) on the inventory packing problem.

Layout of OPS

Planning the layout of a system certainly deserves the great attention shown in the literature (Tompkins and White 1984). With the emphasis on order picking, the layout problem of OPS has two subproblems: the layout of the system containing the OPS and the layout within the OPS. For example, the first subproblem, usually called the facility layout, is crucial to an OPS supporting a manufacturing system such as MSS-OPS; the second one to an 'independent' distribution center such as FLA-OPS.

Most results in the literature are concerned with the layout of conventional warehouses. Since the equipment in a conventional warehouse is either block stacking or pallet racks, most effort for the layout focuses on the aisle configuration, e.g. Bassan, Roll and Rosenblatt (1980). In addition, a block stacking system needs to specify the number of lanes, and the depth of each lane; see Ashayeri and Gelders (1985) and Goetschalckx and Ratliff (1987) for details.

One of crucial issues related to OPS layout is the pick versus reserve problem (P-R) problem or what the inventory policies and replenishment patterns of RS and PS are. A review can be found in Bozer (1985). The primary objective of the P-R problem is to minimize the storage, replenishment, and handling costs of both systems. It is a formidable task to find a universal solution to the P-R problem. The results obtained so far point out that solutions are far from trivial, and that the decision has significant effects on the system performance (White and Kinney 1982). Kooy (1984) and (1985) give practical methods and guidelines for real P-R problems.


As explained in the previous sections, the decisions in the design stage should reflect the effects of operational strategies. This section presents more details on operational issues.

4.1 Storage Rules

The storage rule is defined as a rule for assigning each SKU to storage locations, and the storage location assignment problem (SLAP) is a problem to find a storage rule which optimizes the objective function(s) given a detailed specification of SKUs and equipment. The primary objective of the SLAP is to minimize the average process time per S/R activity (or order). Even if the total cost of order picking may be the ultimate concern, a significant portion of the total cost is usually proportional to S/R time. Rules-of-thumb for SLAP can be roughly stated as follows:

Rule RT1 results from the ABC (or Pareto's) law which characterizes the typical distribution of S/R activity of SKUs in real OPS. Loosely translated, it states that some small percentage, say 20%, of the SKUs in the system usually represent a majority, say 80%, of S/R activity. Consequently, most design efforts should focus on the high-activity SKUs, which deserve the 'prime' locations near the I/O point.

The second rule, RT2, can be achieved by minimizing empty storage space. It can be achieved either by using a 'balanced' inventory policy, or by sharing a location with as many SKUs as possible. The S/R area is 'perfectly balanced' if the number of arriving units is equal to the number of departing units during any time period (Goetschalckx 1983). In the perfectly balanced, but unrealistic, system there is never an empty location at the end of each period. For OPS not perfectly balanced, however, RT2 leads to frequent conflicts with rule RT1. For example, contrary to RT1, RT2 may fill a location near the I/O point with a slow mover if the item is the only one to be stored at the time. Effort for solving this conflict leads to various strategies for the SLAP.

Types of Storage Policies

The storage rules widely used in industry can be classified into three major categories: floating slot storage, fixed slot storage, and hybrid storage of both. Floating slot storage basically follows RT2; fixed slot storage follows RT1; hybrid storage comprises both.

With floating slot storage many different storage locations can be assigned to a SKU over its many replenishments. A typical rule of floating slot storage is random (or randomized) storage (RANDS). RANDS, strictly following RT2, assigns an incoming item to the location closest to the I/O point among available ones, regardless of the item's storage period (or turnover rate). RANDS derives its name from the fact that the locations of SKUs, especially in unit-load AS/RS, 'appear' to be randomly distributed. It is interesting that the equivalence between the closest-open-location (COL) rule and the purely-randomized-assignment (PRA) rule is not fully addressed in the literature. The seemingly conflicting results imply that

Lim shows also that unfavorable zoning (fast movers in the back of the rack, and slow movers in the front) can occur in a model with some restricted conditions. Consequently, the equivalence between COL and PRA is still in doubt, even though it is assumed by most works in the literature.

Fixed slot storage (or dedicated storage, DEDIS) is solely based on rule RT1; each SKU has its own fixed storage location usually based on the intensity of S/R activity. The major issue in DEDIS is how to assign each storage location to which SKU, even though the optimal strategy would follow RT1 in principle. It turns out that the optimal assignment depends on various factors, which will be discussed later.

The hybrid of floating slot storage and fixed slot storage is frequently referred to as class-based storage (CLASS). First, CLASS partitions all the SKUs into several classes, and assigns a (usually fixed) area to each class. Then, RANDS is used within each class area. Partitioning of SKUs into classes may be based on S/R activity, so that fast moving SKUs are grouped as the first class stored near the I/O point. In fact, RANDS is CLASS with the single class, and DEDIS is CLASS with as many classes as the number of SKUs. Some variations are possible. For example, Lim considers a variation of CLASS, the so-called Skip-k policy, with 2 classes. Under the Skip-k policy, an incoming item of the second class is assigned to the (k+1)st open location. Lim can not distinguish an advantage of the Skip-k policy over the fixed-zone policy in the 2-class CLASS.

Comparison of Storage Rules

In general, RANDS results in high space utilization or low space requirement with the expense of increased travel time; DEDIS yields the largest savings in travel time, but usually with substantial under-utilization of space. CLASS is somewhere between RANDS and DEDIS, depending on parameters such as the number of zones and the skewness of the S/R activity distribution. The comparison above is not conclusive, since a number of factors are involved in the efficiency of each storage rule. Among the more important are the ABC skew and the operating mode of the pickers (or S/R machines).

The operating mode can be classified into three categories: single command (SC), dual command (DC), and multi command (MC). In SC operation the picker performs only one S/R activity between successive visits to the I/O point; in DC operation, 2 S/R activities; in MC operation, more than 2 S/R activities. For example, a conventional unit-load AS/RS or miniload AS/RS can do either SC or DC operation. A person-aboard S/RS and a rack system are normally operated in MC mode. The picker aboard an S/R machine or walking (or riding) through aisles of racks is usually able to do 5-25 S/R activities on a trip.

SC operation is typical in a conventional warehouse mainly for pallet retrieval. Most earlier works on the storage rule are concerned with the optimal storage rule of a conventional warehouse under DEDIS and SC operation. The most famous storage rule in that case is the cube-per-order index (COI) rule, which is attributed to Heskett (1963). The COI is the ratio of the space requirement (cube) of a SKU to its turnover rate. The COI rule ranks the items in an ascending order of the index, and then assigns them in that order to the locations nearest to the I/O point. The analytical results supporting the COI rule include Francis and White (1974), Harmatuck (1976), Kallina and Lynn (1976), Evans (1984) for SC operation; Malmborg and Bhaskaran (1987) and (1990) for DC operation; Malmborg and Bhaskaran (1989) for MC operation. For a real warehousing system, Davies, Gabbard and Reinholdt (1983) report that the COI rule increases the productivity of item picking.

The COI rule can be used also for CLASS. The major issues in CLASS include the number of classes, the shape of each class area, and the partitioning rule (i.e. a rule to assign each SKU to a class). Most works related to CLASS use the COI rule as the criterion for the partitioning rule. Schwarz, Graves and Hausman (1978), Choe and Sharp (1989), and Kim and Seidman (1990) show that CLASS yields significant savings in travel time for both SC and DC operation, and Choe and Sharp (1988) for MC operation. More specifically, Choe and Sharp develop the analytical estimators of SC and DC travel times in unit-load AS/RS, and then gives a set of partitioning rules depending upon the skewness of S/R activity among SKUs. Their results also imply that CLASS leads to shorter travel time even under MC operation in person-aboard S/RS, and that a small number of classes, say 3-5, with a few partitioning rules, can achieve most of such reductions in travel time, since the average travel time curve is quite flat near the optimal parameters.

All the results above assume that the total space requirement is independent of storage rules, which does not hold in real circumstances. Roll and Rosenblatt (1983), Rosenblatt and Roll (1984) are concerned with such effects of storage rules for port warehouses. Using simulation, they compare the space requirement of RANDS, CLASS, and DEDIS; their definitions are slightly different from ours due to the unique features of the port warehouse. Their results imply that CLASS can significantly reduce the space requirement compared to DEDIS, and that most of such reductions can be achieved by no more than 6 classes.

Yang (1988) is the first work which explicitly considers the space requirement depending on the number of classes for unit-load AS/RS. He develops an algorithm to find an optimal partition of SKUs for CLASS to minimize the expected travel time of the S/R machine. In his case study, as the number of classes increases, the expected travel time follows a U-shaped curve with the minimum at 6-class CLASS. In other words, the expected travel time decreases until the increased space requirement resulting from the large number of classes offsets the savings in travel time.

An interesting concept for the SLAP is SKU vs. unit assignment. CLASS and DEDIS use SKU assignment. Namely, all units of a SKU are assigned to the same class in CLASS or a contiguous area in DEDIS. Contrary to SKU assignment, unit assignment is based on the expected storage time of each unit, instead of average storage time of the SKU. Goetschalckx (1983) pursues unit assignment under the name of shared storage. With floating storage, he gives several methods for considering the activity level of each unit, instead of the naive COL assignment. Goetschalckx and Ratliff (1987) develop the unit assignment rule for a block stacking system.

Another approach for the SLAP is the correlated assignment (CORAS) (Frazelle and Sharp 1989). The simple principle of CORAS can be stated as SOTAST, which stands for "SKUs Ordered Together Are Stored Together." CORAS is devised to take advantages of the correlated S/R activity which is frequently manifested in real OPS. Frazelle and Sharp report significant savings in travel time under CORAS.

Dichtl and Beeskow (1980) present a CORAS model for an OPS with MC operation. Their model first estimates the pairwise correlation among SKUs, and then assign SKUs with strong correlation to locations that are close to each other. Stern (1986) applies SOTAST to a carousel system. Considering various improvement strategies for a real warehouse, Oudheusden, Tzen and Ko (1988) implement CORAS in a person-aboard S/RS. Since the picker aboard the S/R machine can access two opposite locations at a single stop, they devise CORAS by considering pairwise correlation, and then solve the problem as a maximum weighted matching problem.

SOTAST becomes more attractive for a multi stocking system in which several different SKUs can be assigned to the same storage location. For example, a tray in a miniload AS/RS and a storage drawer in a drawer system can house more than one SKU. Consequently, multi stocking results in great complexity of the SLAP, which now has to consider the capacity constraint of each storage location on the size and sometimes on the orientation of each unit (Herrera-Cuella and Sharp 1983). Note that multi stocking has some features of the packing/palletizing problem which is discussed later.

Some equipment types may have more than one I/O point, which can be used for input only, or for output only, or for both functions. Even though most results in the literature assume a single I/O point, the extension to the multiple-I/O system is not straightforward. Few studies have been done on this issue; see Francis and White (1974) for a conventional warehouse, Waugh and Ankener (1977) for a unit-load AS/RS, and Kaylan and Medeiros (1988) for CLASS in a miniload AS/RS.

4.2 Pick Strategies

Picking line items is one of the most time-consuming and labor-intensive activities of OPS. Consequently, various strategies are used to improve the productivity of the pick process. Among them are batching, zoning, human factors, and hardware solutions.

Batching and Zoning

Batching and zoning determine which order/item is retrieved by which picker; pick sequencing determines the retrieval sequence of line items. Batching, one of the most frequently used strategies for the pick process, is designed to reduce the average travel time per order by sharing a pick tour with other orders. Batch picking is sometimes called group picking or consolidation picking. Rhea (1985) reports a successful case study in the cosmetic industry to significantly increase the system throughput by batching and other strategies as well.

There are basically two criteria for batching: the proximity of pick locations and the time window. Proximity batching assigns each order to a batch based on proximity of its S/R locations to those of other orders. The major issue in proximity batching is how to measure the proximities among orders, which implicitly assumes a pick sequencing rule to visit a set of locations. In general, the pick sequencing rule depends on the equipment type, which is the subject of the next section. The problem of obtaining an optimal proximity batching strategy can be formulated as a vehicle routing problem (VRP) but in a more complicated form; see Golden and Assad (1986) for a review on the VRP. Unfortunately, the relationship does not provide any new insights to our problem, since the VRP is already one of the most difficult problems in combinatorial optimization.

Chisman (1975) and (1977) presents two heuristics for the batching problem by considering the underlying VRP. Elsayed (1981), and Elsayed and Stern (1983) develop several heuristics for proximity batching. Their heuristics consist of two phases: first, select a 'seed' order; second, add an order at a time based on the proximity of pick locations. Platzman and Bartholdi (1985) develop a general framework for proximity batching based on the spacefilling curve, which is a simple, flexible heuristic for the traveling salesman problem; see Bartholdi and Platzman (1988b) for other applications of the heuristic. Hwang and Lee (1988a) give a batching algorithm for person-aboard S/RS. Using a measure of pairwise proximity, they consider several heuristics which are categorized as agglomerative or sequential. For the examples considered, their heuristics outperform those of Elsayed and Stern, and Hwang, Baek, and Lee (1988).

Elsayed (1988), and Elsayed and Unal (1989) consider proximity batching rules with and without due time constraints. Their simulation results for person-aboard S/RS favor a heuristic similar to those of Elsayed and Stern. Mutel and Anciaux (1989) present analytical models for batching and storage rules in a warehouse with an aisle configuration.

Using simulation, Gibson (1990) examines the effects of the following factors on travel time:

He reports that a suitable batching rule used in conjunction with CLASS yields significant reductions in average batch tour lengths; in some instances these reductions are 44%.

Under time window batching, the orders arriving during the same time interval (fixed or variable length), called a time window, are grouped as a batch. These orders are then processed simultaneously in the following stages (Quinn 1983). Time window batching requires minimal analysis effort, and still seems to achieve a significant reduction in travel time, which is a major portion of total process time. Few results with general applicability are available for time window batching (Choe 1991).

Zoning is closely related to batching, although it may be implemented with or without batching; see Sharp, Choe, and Yoon (1990) for various combinations of batching and zoning. Zoning divides the entire picking area into several zones with each picker dedicated to select the line items only in his or her zone. In some cases zones naturally correspond to each equipment type in the pick area if an OPS has several different types of S/R equipment. In other cases zones are artificially determined. The major advantages of zoning are familiarity of the picker with his or her zone and travel time reduction, because of the smaller area coverage by each picker.

Depending on the process sequence, zoning may be further classified into two types: progressive zoning and synchronized zoning. Under progressive zoning, each batch (possibly of one order) is processed only by one zone at a time; at any particular point in time each zone processes a batch that is different from the others. Hence, the batch is finished only after it sequentially visits all the zones containing its line items. Under synchronized zoning, all the zones are working on the same batch at the same time. There may be some idle times of zone pickers to wait until all the zone pickers finish the current batch. This synchronization of pickers is intended to keep the batches from being mixed, and so to lessen the complexity of the following stages such as the A/SS.

The major difference between the two types is whether a batch is split into suborders (in synchronized zoning) or not (in progressive zoning). Synchronized zoning usually gives a shorter response time at the expense of order integrity than does progressive zoning. However, synchronized zoning requires an additional system, the A/SS, to recover order integrity, while progressive zoning usually does not require such a system. It is not straightforward to compare directly one zoning type with the other. Moreover, an OPS may use both types of zoning; 'small' orders in terms of the number of zones visited are processed by progressive zoning, while large ones are processed by synchronized zoning.

Despite the significant impact of zoning on the performance of OPS, zoning has received little attention in the literature. Armstrong, Cook, and Saipe (1979) consider an OPS with proximity batching and synchronized zoning. For the FLA-OPS with both the PS and the A/SS, they formulate a mixed-integer program to minimize the total process time, and then solve the problem by Bender's decomposition method. For a rack system with item picking, Mellema and Smith (1988) evaluate the effects of various factors on system performance: storage rule, aisle configuration, and batching and zoning rules. Their simulation model shows that operation with both batching and zoning significantly increases picker utilization. However, the comparison is not conclusive, because their model does not include the A/SS, which is a direct consequence of the decision to use batching and zoning.

Choe (1991) seems to be the only analytical results with general applicability which can evaluate the efficiency of both time window batching and synchronized zoning. The results provide a quick analytical tool for a MSS-OPS with conventional racks and A/SS. The rack system is of ladder layout (no intermediate cross aisles), and pickers selects items under selective one-way traffic (pickers are not allowed to turn around in the middle of an aisle). Using a prototype example, the results indicate that time window batching can significantly increase the system capacity, and synchronized zoning with time window batching can increase it further.

Human Factors and Hardware Solutions

Aside from batching and zoning, there are many alternatives to improve the efficiency of OPS. For example, a 'good' design that provides suitable (physical and/or mental) aiding systems for humans might yield an OPS more efficient than a highly automated OPS; in some cases automation is used as a quick solution rather than the best one (Weber 1989). After considering human factors in automated warehousing systems, Yates (1989) points out that modern technology for automation in warehousing will eliminate some human factors but at the expense of introducing others. Therefore, a real OPS should be designed as an integrated system of hardware, software, and 'humanware'. Of course, this issue is not peculiar to order picking, but a fundamental question arising in most engineering applications.

For order picking Gross (1981) estimates that, depending on the type of warehouse, 30% to 40% of the labor cost can be associated with the pick operation. The author then suggests rules-of-thumb to reduce the labor cost. Falk (1983) deals with an illumination system in automated and manual warehouses. Mital (1983), Mital and Asfour (1983), and Bienkowski et al. (1986) attempt to develop a data base for determining time standards of various material handling activities such as lifting, lowering, pushing, pulling, and carrying. Armbruster (1988) presents various issues in human factors of manual OPS and suggests some designs of work environments. Lewis and Lin (1989) focus on manual lifting in the electronics industry.

Considering a real warehouse, Riaz-Kahn (1984) develops a model which gives the time standards of a human picker in a conventional warehouse with racks and aisles. The time standards consist of three components: load time, travel time, and miscellaneous time. The estimation of travel time, however, is based on a naive aisle routing rule that generates the pick tour from prenumbered storage locations.

One may use a computer aided system for order picking to simplify the tasks of human pickers (Frazelle 1988). For example, the computer aided system may provide several features as follows:

In addition to reduced labor cost, Gross (1981) and Gupta (1982) claim high accuracy resulting from such computer aided systems as their major advantage. They also report that, in some cases, the computer aided OPS with human pickers are more efficient in terms of both throughput and cost than highly automated OPS. Rhea (1985) reports a successful case study where the 'friendly' work environments for human pickers, along with the participation of employees during the design process, can dramatically improve system performance. Shirk and Bredenbeck (1987) give an example of an automated documentation system that consists of radio-linked, mobile computer terminals. Tolliver (1989) observes that, for a manual OPS, a light-directed pick system with automated data entry reduces human errors by 95%, and increases productivity by 10%.

4.3 Accumulation/Sortation Strategies

The primary objective of the A/SS is to re-establish order integrity that is lost during the pick process. The A/SS takes various forms including, at opposite ends of the spectrum, manual staging and high-volume automated sortation system. A number of articles are mainly concerned with the general treatment of the A/SS: Walsh (1979) for the components of high-volume A/SS; Emerson and Schmatz (1981) and Gupta (1982) for a kitting matrix (a manual-staging type of A/SS); Suzuki (1981) for issues in A/SS; Cox (1983) for a case study of the A/SS design; Horrey (1983) for various alternatives of A/SS.

The high-volume automated A/SS as shown in Figure 3 usually has a closed-loop conveyor, automated divert mechanisms, and accumulation lanes. This type of A/SS is of our interest, since it requires large initial and operating costs as well as space. The high-volume A/SS usually processes a wave (or batch of orders) in the following way:

1. each wave is released into the A/SS according to the wave release rule.

2. as the sensor identifies the order corresponding to an incoming (or recirculated) item, usually in a container (e.g. a tote), it assigns the item to one of the available lanes, if possible.

3. otherwise, the item yet assigned is recirculated.

A few results with general applicability have appeared in the literature. Bozer and Sharp (1985) elaborate the issues in the operation of an A/SS in which each order is pre-assigned to an accumulation lane, e.g. according to the shipping door corresponding to the order. Their A/SS can be found in FLA- and MLA-OPS. Using simulation, they evaluate the throughput of the system as a function of the induction capacity, the number of lanes, the length of lanes, the presence of a recirculation loop, and the control system.

(Reprinted from Yoon and Sharp 1990)

Bozer, Quiroz, and Sharp (1988) then study a different type of A/SS which processes a batch in which the number of orders is greater than the number of lanes. A typical example of this A/SS is the sorting area A of the MSS-OPS shown in Figure 1. In this case the throughput of the system is determined mainly by the number of recirculations. Their simulation, which focuses on the lane assignment strategy and the wave release strategy, shows that incidental assignment achieves the greatest throughput among the assignment rules considered. Under incidental assignment, the sensor assigns any incoming item (belonging to an order yet assigned) into one of the available lanes, regardless of any other considerations.

Few analytical results are reported in the literature. Murphy and Stohr (1978) develop analytical models for a sortation process such as the check processing system of a bank, which however is not applicable to our A/SS. Santana and Platzman (1979) formulate a Markov decision process for the A/SS with many accumulation lanes and one packer, which is not applicable to most real A/SS either. Regarding recirculation as the major bottleneck of A/S operation, Choe (1991) develop a quick, rough method to determine the mean and variance of A/S times. It is indeed a formidable task to develop an analytical model which is able to describe the movement of recirculated items on the loop conveyor and the releasing pattern of items into the A/SS.

The analysis of A/SS itself is of interest also because it is related to a number of problems arising in other areas, such as the kitting operation in electronics assembly (Sellers and Nof 1986), and postal sortation (Vrgoc and Ceric 1988). Bozer, Quiroz, and Sharp point out the similarity to the operation of an AGV system with a single, closed-loop path (Bartholdi and Platzman 1989), and information retrieval from computer drum storage (Fuller 1977). In addition, the features of the A/SS are similar to the retrial queue (Yang and Templeton 1987), and the random coverage problem (Yadin and Zacks 1982).

4.4 Packing/Palletizing

Palletizing or packing is a common material handling activity in the OPS. Obviously, it is the major activity in the shipping area. A less obvious palletizing problem occurs in the multiple stocking problem and the inventory packing problem as mentioned earlier. Our discussion here is confined to the practical palletizing problem (PPP): find an optimal loading rule to palletize a set of (3-dimensional) items into a set of (3-dimensional) containers such as pallets or boxes. The objective function of the PPP is either to maximize the volume utilization of a pallet or to minimize the total number of pallets used for a given set of items. The resulting pallet should be capable of enduring some physical forces and constraints during its handling and transportation.

In fact, the PPP is a complicated 3-dimensional version of a classical optimization problem, the bin packing problem (BPP). The BPP can be defined as either a 1-dimensional problem (1-BPP) by 1-dimensional items and containers, or a 2-dimensional problem (2-BPP) in a similar manner. The 1-BPP can be applied to the storage problem of computer files in computer memory; the 2-BPP to a cutting-stock problem which maximizes the number of 'small' items taken away from 'large' material sheets. The BPP has received considerable attention in the literature; see Coffman, Garey, and Johnson (1984), and Tsai, Malstrom, and Meeks (1988) for literature reviews.

Since even the 1-BPP is (NP-) hard, most research attempts have been directed to obtaining a fast, good heuristic for the PPP. Hodgson (1982) classifies the PPP into two categories: the manufacturer's PPP (M-PPP) and the distributor's PPP (D-PPP). In the M-PPP the manufacturer palletizes identical products to identical pallets which are shipped in turn by standardized trucks. The M-PPP is usually used for a long-term plan to maximize the volume utilization of a pallet, and so to minimize the handling and transportation costs. On the other hand, the D-PPP packs various items of a customer order into possibly more than one pallet. Consequently, the D-PPP varies with each customer order, and must be solved quickly to be applicable for daily and hourly operation.

Few results for the PPP have appeared in the literature. It is remarkable that palletizing itself is one of the most common activities performed in warehouses and distribution centers, but analytical results are very limited, probably due to the apparent complexity of the problem. See Schreiner (1986), Szielasko (1988), and Roach and Hunt (1988) for case studies of palletizing systems in industry. In general, heuristics for the PPP are based on two concepts; layer building and column building. Layer building is a bottom-to-top method to build a pallet by stacking a 'horizontal' layer of items on the top of others. The pattern in a layer then can be solved by the 2-BPP; e.g. Smith and de Cani (1980), and Dowsland (1987). Column building is a side-to-side method to construct and place the columns or stacks side by side.

George and Robinson (1980) is an early article which explicitly deals with the D-PPP. Instead of developing an optimization model, they present a heuristic model containing rules-of-thumb. Their rules employ layer building along with other considerations in real palletizing operation. For the 2-BPP, Hodgson (1982) develop a heuristic based on a dynamic program. By refining the heuristic (Hodgson, Hughes, and Martin-Vega 1983), Carlo et al. (1985) implement a generalized heuristic for the D-PPP in a personal computer.

Using an interactive simulation model, Kulick (1982) attempts to find a loading pattern of the M-PPP. He suggests using an interlocking pattern (turning 180 degrees from the layer below using the same pattern) so that the resulting pallet can resist the physical forces and stresses during handling and transportation. For a similar problem, Carpenter and Dowsland (1985) develop a layer-building method with a heuristic by Bischoff and Dowsland (1982) for finding a pattern in each layer. They find that palletizing by a 'single-minded' layer heuristic may not be suitable for practical use. They suggest some additional stability criteria for practical considerations in handling and transportation.

Puls and Tanchoco (1986), Penington and Tanchoco (1988) are concerned with a prototype robotic palletizer for the M-PPP. The unique feature of their heuristic is that it incorporates the physical limitation of robots. For example, they devise a loading sequence of a pallet so that the gripper of the robot cannot interfere with the boxes already on the pallet.

Han, Knott, and Egbelu (1989) develop an L-pattern heuristic for the M-PPP, a hybrid of layer and column building, which places the base layer on the pallet, and then stacks boxes by column building. In order to determine the detailed pattern within a layer they use a dynamic program similar to that of Steudel (1979) for the 2-BPP. Their heuristic yields better performance than does a conventional method (by the General Services Administration 1966) in terms of volume utilization.


Issues in the design and operation of each equipment type include the following aspects:

Some of the issues such as storage rule, batching, and zoning, have been explained in the previous section. This section is concerned with issues peculiar to each equipment type, including racks, storage drawers, AS/RS, carousels, etc.

5.1 Racks and Storage Drawers

Racks and storage drawers are the oldest and still the most popular equipment type for order picking. There are various types of racks such as pallet racks, gravity flow racks, bin shelving, etc. The major advantages of a rack system include low initial and maintenance costs; its major disadvantages include the difficulties in storing high-security items. Storage drawers, usually limited to storage of small parts, may yield high space utilization and security as well. However, both equipment types become inefficient for retrieval in a large pick area. Despite the popularity of these equipment types, few studies have appeared in the literature.

Bassan, Roll, and Rosenblatt (1980), and Rosenblatt and Roll (1984), along with some earlier works, are concerned with the aisle layout of a conventional warehouse. Their results are limited for pallet retrieval under SC operation. Rosenblatt and Roll develop a procedure by considering simultaneously the layout, storage policies, and space requirements. Malmborg and Deutch (1988) present a model to evaluate aisle layout under DC operation.

Few results are available for the aisle layout under MC operation. This is partly due to the complexity of travel time estimation involving the notorious traveling salesman problem inherent to aisle routing. Mayer (1961) is one of the earlier works for the estimation of travel time in a conventional warehouse with racks and aisles. The aisle configuration is of the ladder type, in which the layout consists of multiple parallel aisles without intermediate cross aisles. He deals with only SC and DC travel time. Kunder and Gudehus (1975) develop approximations for MC travel time in the same layout under three simple aisle routing heuristics. In their model the travel time estimation is a function of the number of pick locations which are assumed to be uniformly distributed.

For the pick sequencing problem under MC operation, Ratliff and Rosenthal (1983) give an efficient algorithm to find a shortest path to visit a set of pick locations in a ladder layout. No probabilistic analysis of this problem is reported in the literature. Goetschalckx and Ratliff (1988a) extend the previous problem to one with wide aisles. A wide aisle is roughly defined as an aisle of more than 3.7 m (or 12 ft.) width. For a system with wide aisles, one must find the travel sequence from one aisle to another and also find the pick sequence within a wide aisle. For a ride-and-pick system with the same configuration, Goetschalckx and Ratliff (1988b) consider a clustering method to give a set of pick locations to be visited at each vehicle stop, since the travel time from one side to the other within the same aisle is no longer negligible.

Finding an optimal path in a general layout is a formidable task, since the underlying traveling salesman problem is notoriously difficult to solve exactly in a reasonable computing time. For a general layout, Bartholdi and Platzman (1988a) develop a simple heuristic based on the spacefilling curve. Their heuristic requires minimal effort for implementation and is flexible enough for dynamic environments where the pick sequencing problems may change even as they are being solved. Its performance, however, depends on the efficiency of the underlying spacefilling curve, which should be custom-designed for each application.

One of the important issues related to aisle routing is that the picker should stack the items as he or she picks them. Especially for a pick-to-pack system (a system in which the picker has to make the selected items ready for shipping as he or she returns to the I/O point at the end of each tour), an optimal path should be based not only on the shortest travel time, but also on the minimum packing time (usually by minimizing the number of re-packing operations). Donaldson (1989) reports an expert system, called WHEEL, with both routing and packing considerations which also provides information for control and management. The OPS for which the system is installed has a general layout with 'dead-end' aisles and SKUs with limited stackability.

Another issue in the OPS with an aisle configuration is traffic congestion. Easily overlooked in the literature, the aisle configuration in conjunction with the types of vehicles commonly used might result in severe congestion. For example, Ottjes and Hoogenes (1988) develop a simulation model to estimate system throughput for a heavy traffic system.

Recently, automation technology has been applied to the S/R operation in OPS, which has been one of the major tasks of humans. Although this type of automation is limited so far to pallet retrieval, the AGVs with S/R devices for handling pallets can successfully substitute for human pickers. Menon, Kapoor, and Blackman (1988) present a design model for an AGV system applied to a pallet-retrieval warehouse with racks and aisles.

For gravity flow racks, Houmas (1986) gives a regression model for cost analysis. The resulting cost equation has four terms depending on the depth and length of the shelf frame, the number of lanes, and the number of shelves. Nepola (1985) presents a case study for a large-scale gravity flow rack system in the dairy industry. O'Brien (1986) reports a real example of a single-aisle gravity flow rack system, which is used for high-activity items. For the design of the system the author examines various strategies such as layout, replenishment cycle, and storage rule.

Storage drawers have received less attention. Herrera-Cuellar and Sharp (1983) develop an algorithm that minimizes the cost of the drawers and cabinets used. Their procedure employs a regression model for cost analysis, a rectangle packing heuristic, and a two-step heuristic for the 2-BPP, and produces the detailed storage location assignment of each SKU as well as the total number of drawers and cabinets.

5.2 Automated Storage and Retrieval Systems

In general, automated storage and retrieval systems can be classified into three types: unit-load AS/RS, miniload AS/RS, and person-aboard S/RS. This classification is not exhaustive. For example, the storage rack of the AS/RS may be more than one lane deep (Shieh 1985, Szielasko 1988); the S/R machine can carry more than one pallet at the same time (Rizo-Patron, Bozer, and McGinnis 1983, Jaikumar and Solomon 1986); the S/R machine can visit more than one lane (Hwang and Ko 1988, Schmidt 1989, Baumbach et al. 1989, Park and Webster 1989b).

The major advantages of this automated equipment (except the person-aboard S/RS) include the precision, accuracy, and speed in S/R activity. The AS/RS becomes an attractive alternative when the space available is limited; the AS/RS requires minimal floor space because items can be stored much higher than in conventional equipment types. The disadvantages of the AS/RS, like other sophisticated systems, include high initial and maintenance costs, and significant engineering and design efforts.

Unit-Load AS/RS

The unit-load AS/RS has received the greatest attention in the literature among various types of AS/RS. Since the operation of a unit-load AS/RS is typically limited to SC and DC operation, the problems associated with its design and operation seem less complicated.

Design of unit-load AS/RS: Practical guidelines for the design and installation of unit-load AS/RS can be found in White (1980), Zollinger (1982), Bafna (1983), and Bafna and Solt (1983). In addition, Zollinger gives a general cost model; Bafna and Solt present a 'rough' estimator of the size of the pallet rack. Bailey (1985) focuses on the cost comparison of AS/RS with manual S/R systems. According to the cost comparison, the AS/RS might not be justified unless its operational and managerial advantages are considered.

The approaches for the design of unit-load AS/RS can be analytical models or computer aided systems. In most analytical approaches the S/R machine travel time is the basic quantity for evaluating system performance, such as the maximum throughput of the system, the response time of an order, and the utilization rate of the S/R machine. Hausman, Schwarz, and Graves (1976) obtain an expected SC travel time for the square-in-time rack with CLASS; Graves, Hausman, and Schwarz (1977) obtain an expected DC travel time for the square-in-time rack; Bozer and White (1984) give the expected SC and DC travel times for racks of general shape with RANDS; Choe and Sharp (1989) develop estimators for the SC and DC travel times in general racks with CLASS. Rosenblatt and Eynan (1989) explore the structure of SC travel time in the square-in-time rack (given by Hausman, Schwarz, and Graves) to find a fast algorithm for an optimal partitioning rule. Their model deals with SC travel time only.

Karasawa, Nakayama, and Dohi (1980) give an analytical model for the design of the unit-load AS/RS. Using a non-linear mixed integer programming formulation, their model determines the number of S/R machines, the desired speed of a S/R machine, and the size of a rack, under the throughput and space constraints. However, their scope is limited, since only SC operation with RANDS is permitted.

For a similar problem, Ashayeri, Gelders, and Wassenhove (1985) develop an analytical model to determine the number of aisles and the configuration of an aisle. The objective function is the total life-time cost including the costs of S/R machines, racks, building, buffer space, land, maintenance, and order picking labor. For the throughput estimation they use a rough approximation of DC travel time in RANDS.

Illingworth and Sharp (1988) present an optimization model to overcome some of the drawbacks of previous models, such as the limited consideration of the effects of operating decisions on system throughput. For example, their model can evaluate the effects of DC operation in CLASS. They solve the resulting nonlinear program by a search procedure.

Azadivar (1986) focuses on the buffer space in front of the AS/RS rather than the AS/RS itself. The author formulates a stochastic program to find the maximum throughput with constraints such as the buffer size of incoming pallets and the response time of retrieval orders. Some of the parameters in the problem are estimated by simulation. Those results can be applied to the design of the buffer space.

High equipment costs of the unit-load AS/RS may not be justified for a system with low S/R activity requirements. In this case Hwang and Ko (1988) suggest a multi-aisle unit-load AS/RS where the number of S/R machines are fewer than the number of aisles. They develop travel time estimators, a procedure for specifying the parameters of CLASS, and the number of S/R machines to meet the throughput requirement.

For an overcrowded unit-load AS/RS, Hackman and Rosenblatt (1990) formulate a storage allocation problem which determines what quantities of which items should be assigned to the AS/RS. The unassigned items are stored in a secondary storage area. Their heuristic yields less cost for handling the overflows than does the COI rule applied to that problem.

Due to the limited scope of an analytical approach, a number of attempts have been made to develop a computer aided system for the design of unit-load AS/RS. The major advantage of this approach, mainly with simulation modules, is its ability to represent all the details of the system, such as the interface of the AS/RS and other subsystems (e.g. in- and out-bound conveyors), and the performance evaluation of the AS/RS in dynamic environments. Aside from general-purpose simulation languages, the following computer aided systems are developed for AS/RS and other material handling systems: e.g. Ulgen and Elayat (1981), Ashayeri, Gelders, and Looy (1983), Bailey (1983), Carson et al. (1983), Perry, Hoover, and Freeman (1983) and (1984), Raghunath, Perry, and Cullinane (1986), Ashayeri and Gelders (1989).

Control of unit-load AS/RS: Obviously, DC operation of the S/R machine seems more efficient than SC operation. The gains from DC operation, however, depend on the efficiency of order sequencing to determine the pair of storage and retrieval locations on the same DC trip. For the unit-load AS/RS, re-sequencing of storage orders (or incoming pallets) is usually difficult, while re-sequencing of retrieval order is much easier (retrieval orders are nothing more than messages). Therefore, the order sequencing problem attempts to find a retrieval order well matched with a given storage location. Note that in SC operation, sequencing of retrieval orders is identical to sequencing jobs on a single machine, which is a well-known problem in scheduling theory (Kusiak, Hawaleshka, and Cormier 1985).

Han et al. (1987) examine two heuristics for the order sequencing problem: the nearest-neighbor heuristic and the shortest-leg heuristic. In their examples the nearest-neighbor heuristic increases the throughput by about 15%. Seidmann (1988) is also concerned with the same retrieval sequencing problem but in dynamic environments. Using an artificial intelligence approach, the so-called state-operator framework, he presents a dynamic adaptive control scheme to determine the pair of storage and retrieval locations in real-time operation. Dagli and Wasti (1989) develop a dynamic control scheme for the order sequencing problem in a unit-load AS/RS for perishable items.

The interface with other subsystems are crucial to the performance of the whole system. For a conveyor-fed AS/RS, Sharp, Kittel, and Hollender (1989) evaluate the effect of various factors on system performance. The factors considered include storage rule, conveyor configuration, buffer size, S/R machine velocities, and workload imbalance among subsystems. Everton (1989) and Takakuwa (1989) deal with the interface problem which determines the best configuration among various alternatives of conveyor- and/or AGV- fed AS/RS.

Workload equalization seems an effective control strategy for the system in dynamic environments, especially with high fluctuation in order volume; that fluctuation is quite common in real systems. Jaikumar and Solomon (1985) solve the workload equalization problem to utilize the S/R machines during the light-workload period by relocating some pallets closer to the I/O for the heavy-workload period.

One may try to evaluate the effectiveness of those issues by considering them simultaneously rather than by separating one from others. This approach makes it possible to show the interactions among various strategies, but only by simulation. Considering a real warehouse, Waugh and Ankener (1977) evaluate the effects of various factors on the performance of unit-load AS/RS. According to their results, the issues shown below are crucial to system efficiency:

Schwarz, Graves, and Hausman (1978) report similar results, that CLASS with DC operation can significantly increases the system throughput, and also that the stochastic behavior of a unit-load AS/RS is similar to that of a single-server queue.

Linn and Wysk (1987), similar to the previous approach, examine the dynamic performance of unit-load AS/RS with seasonal fluctuations in order volume. They focus on the dwell rule, the retrieval order sequencing, the method of forecasting order volume, and storage rule. Their simulation result imply that

Linn and Wysk (1990) then develop an expert system to control the AS/RS. First, they classify the domain knowledge into two types: strategic knowledge and tactical knowledge. The issues above fall into strategic knowledge; other issues such as rules for overflows and/or machine failures into tactical knowledge. They develop a rule-based expert system based on results available in the literature.

Miniload AS/RS

The major difference between the miniload and unit-load AS/RS is the size of units to be handled. In the miniload AS/RS the unit of each SKU is usually so small that each storage location can contain more than one unit. A typical retrieval quantity of a line item is less than the number of units stored in a storage location, and so the container extracted for picking is usually re-stored after the retrieval of the appropriate quantity. In this case the miniload AS/RS may have more than one pick position at the I/O point so that the S/R machine does not have to wait until the picker finishes the current S/R activity. Some miniload AS/RS may be equipped with 'remote' order pickers and/or workstations connected by a conveyor delivery system. Other variations of miniload AS/RS can be found as in the case of unit-load AS/RS.

Zollinger (1982) seems to be the only study for cost analysis of miniload AS/RS. The container and rack costs are separated from the S/R machine cost, and total costs depend on container size, weight of SKUs, height of the rack, height of the S/R machine, and the controller.

Because of the similarity to unit-load AS/RS, most results for unit-load AS/RS can be applied to miniload AS/RS, although this may not yield any new insights for miniload AS/RS. For example, the estimators of SC and DC travel times in the unit-load AS/RS with RANDS are still valid in the miniload AS/RS with the same storage rule; however, the total time of a DC cycle in the miniload AS/RS with two pick locations should include the 'possible' idle time of the S/R machine due to the imbalance of pick and travel times. Bengtson and Gomez (1988), and Pulat and Pulat (1988) develop simulation models for miniload AS/RS. Bozer and White (1988), and Sharp et al. (1988) present models for the design of miniload AS/RS. Both models are capable of evaluating the interactions between the picker and the S/R machine.

Using simulation, Medeiros, Enscore, and Smith (1986) consider the storage rule in a single-aisle miniload AS/RS with two pick positions. In their example they observe that CLASS with 2 classes increases the system throughput by about 10%, and that CLASS with more than three classes has a negligible additional effect on throughput.

For a single-aisle miniload AS/RS with two pick positions, Foley and Frazelle (1990) develop analytical expressions for the distribution of DC travel time and system throughput in a square-in-time rack with RANDS. Their formulae give the maximum throughput in closed form when the pick time is deterministic or exponential.

The miniload AS/RS is widely used for central storage of work-in-process (WIP) inventory in a manufacturing system. Cobbin (1986) shows a simulation model for such miniload AS/RS, which is sometimes referred to as the tote stacker. Using a miniload AS/RS with a single S/R machine and 8 workstations, Kaylan and Medeiros (1988) show that CLASS works significantly better for high WIP level, and that the zone configuration in CLASS is crucial to such efficiency gains. These applications to manufacturing are not of our major interest.

Person-Aboard S/RS

The unique feature of the person-aboard S/RS, a semi-automated system, is that the picker aboard the S/R machine is able to perform many S/R jobs between successive visits to the I/O point. Subsequently, the pick sequencing problem to find a shortest path to visit a set of S/R locations is crucial to the efficiency of the person-aboard S/RS.

This pick sequencing problem turns out to be a variation of the traveling salesman problem (TSP) with the Chevychev norm, since the machine travel time follows the Chevychev norm; see Lawler et al. (1985) for a comprehensive treatment of the TSP. The following results for the pick sequencing problem have appeared in the literature: Bozer (1985), Elsayed and Unal (1989) for expected travel time; Bozer, Schorn, and Sharp (1985), Bachers, Dangelmaier, and Warnecke (1988), Goetschalckx and Ratliff (1988c), Guenove and Raeside (1989) for comparison of various heuristics. Summarizing, several heuristics for the construction and improvement of a pick sequence are good enough for practical use; the length of resulting paths from those heuristics is quite often close (within 5%) to the optimal length.

Oudheusden, Tzen, and Ko (1988) examine various strategies for person-aboard S/RS such as pick sequencing and storage rule. As mentioned earlier, they apply the CORAS to find a pair of SKUs which is stored in opposite locations across the aisle. They then consider assigning the pairs within an aisle under DEDIS. Extracting the set of representative orders and tours from historical data, they formulate the SLAP as a set partitioning problem. In order to solve the problem, they use a two-phase heuristic; first, obtain an exact optimal solution of that problem but with a smaller representative set; second, use a 2-opt (or pairwise-interchange) procedure to solve the larger problem. Applying their procedure to a real person-aboard S/RS, they report significant savings in travel time.

5.3 Carousels

The carousel is a relatively old technology in material handling, and yet it has applications to various areas such as order picking (Lombardi 1985, Kobuki 1987), WIP storage in a manufacturing system (Bagadia 1982, Fredrick 1982), and kitting operations (Engwall 1985). The carousel brings the line items before the picker by rotating the shelves with containers (e.g. totes). Depending the direction of rotation, carousels are categorized as horizontal carousels, vertical carousels, or rotary racks. The horizontal and vertical carousels rotate carriers, consisting of shelves, to position the appropriate container at the I/O point in horizontal (clockwise or counter-clockwise) and vertical (upward or downward) direction, respectively. The rotary rack consists of several tracks (group of shelves as a rotation unit) which are able to rotate in different directions from each other (Tielker 1989).

In general, carousels offer good space utilization and high throughput (Weiss 1980). The vertical carousel usually exposes only one level of shelves at a time and provides excellent item protection and security but at higher costs; see Bredenbeck, Shirk and Majure (1989) for an example. While the rotary rack is the least common and most expensive type, its major advantage is a significant reduction in picker idle time and the feasibility of multiple I/O points.

Most studies in the literature focus on the horizontal carousel, since it is the most common type; fortunately, most results for the horizontal carousel (except cost analysis) are directly applicable to the vertical carousel. The unique circular structure of the carousel requires a different treatment from those for another equipment types.

Mardix and Sharp (1985) analyze the cost structure of horizontal carousels. Their analysis shows that the equipment cost mainly depends on the weight capacity, number of containers, and the number of levels (or height of the carousel). They then proceed to a performance analysis focusing on the workload balancing problem to maximize picker utilization. Assuming a uniform and independent distribution of S/R locations, their simulation and analytical results imply that

Generalizing their models, Bulla (1987) and Sharp et al. (1990) develop a design procedure that considers various operating factors.

Based on the previous cost analysis, Hwang and Lee (1988b) present a constrained optimization model for the determination of system size to minimize the life-time cost of a single carousel system. They develop an approximation of rotation time with an assumption that the S/R locations are uniformly and independently distributed over the carousel. Their approximation method is similar to one in Han and McGinnis (1986). In addition to travel time estimation, Han and McGinnis consider an order sequencing problem similar to one of Han et al. (1987) for the unit-load AS/RS.

The results presented so far assume that an order requests only one line item. Thus, those results are not compatible with order picking, where most orders request more than one line item. In this situation the pick sequencing problem becomes important to efficient operation of the carousel system. Bartholdi and Platzman (1986) examine a pick sequencing problem in a single carousel system. They present an optimal algorithm, along with several heuristics of which the performance becomes quite close to the optimal one with heavy workload. A similar problem is considered by Stern (1986). In addition to pick sequencing, he presents a Markovian model (similar to one by Mardix and Sharp) to evaluate system performance, and a heuristic for storage location assignment based on SOTAST.

The pick sequencing problem with both horizontal rotation time of the shelves and vertical moving time of the (robot) picker is treated by Wen and Chang (1988). Wen, Lin, and Chang (1989) then extend the problem to a double carousel system. Modifying the heuristics in Wen and Chang, they show that simple heuristics can yield a significant increase in throughput.

The SLAP for the carousel system has a unique feature that the relative distance of a storage location to the I/O point varies as the carousel rotates. In other words, there is no location 'close' to the I/O point which can be easily identified in other equipment types. Consequently, the performance of a storage rule in the carousel system is directly related to the pick sequencing rule used.

Let us consider a simpler problem, that is, the SLAP in a single carousel system with a single level of shelves. Here we do not need to consider the vertical travel time of the picker, and there is no interference associated with that time component. Then, the following storage rule, the so-called 'organ pipe arrangement' for a single-level carousel with FCFS order retrieval, minimizes the expected total rotation time of an order regardless if its size, the number of line items, is fixed or random (Lim, Bartholdi, and Platzman 1985):

1. sort the SKUs in decreasing order of S/R activity frequency.

2. store the most 'popular' SKU anywhere on the carousel.

3. assign subsequent SKUs to alternating positions to the left and the right of the first SKU.

The organ pipe arrangement derives its name from the fact that the resulting bar chart depicting the S/R frequency of each SKU resembles organ pipes. In fact, this storage rule is developed for a specific type of computer information storage systems, called a linear storage system (Hardy, Littlewood, and Polya 1952, Bergmans 1972).

A 2-dimensional extension of the problem for a typical multi-level carousel, unfortunately, is not straightforward. The 2-dimensional problem is (NP-) hard (Bergmans 1972), and does not even have an asymptotically optimal heuristic storage rule based solely on the ranking of S/R activity (Karp, McKeller, and Wong 1975). A review of the results for computer information storage can be found in Wong (1980). Lim, Bartholdi, and Platzman explore several extensions of the organ pipe arrangement to the multi-level carousel. In general, questions on the optimal storage rule for carousels mostly remain unanswered.

The system where a picker operates more than one carousel is of particular interest because of the apparent gains in productivity. The analysis of such multi-carousel systems, however, becomes more complicated by the interaction among carousels and the picker. For example, one carousel becomes idle if the picker is still working on the other at the time that the carousel positions a container at the I/O point. Moreover, the picker usually require some transition time to move from one carousel to the other. These situations are often referred to as 'machine interference'. It is a common phenomenon where an operator is in charge of more than one machine.

The machine interference problem has received considerable attention in the literature; see Stecke and Aronson (1985) for a review. For example, Koenisberg (1986), and Kim and Koenisberg (1987) present applications of the machine interference problem to a carousel system. The operation of a multi-carousel system is still a research area with significant potential.

The carousel system is also frequently used for a central storage of WIP inventory. In this case the carousel system is usually linked to workstations by conveyors. Such a system is studied by Koenisberg and Mamer (1982). They develop an approximate queueing model for the performance evaluation of the entire manufacturing system. In their model the machine interference problem is applied to the performance evaluation of the carousel system as a subsystem.

Buley and Knott (1986) elaborate the basic design issues for a rotary rack. As the results for the multi-carousel system suggest, the rotary rack with as many tracks as the number of levels might cost too much, yet yield little rewards in system performance. Buley and Knott solve a simpler version of the problem which determines the number of tracks to meet a constraint on picker idle time.

For a rotary rack with as many tracks as the number of levels, Han, McGinnis, and White (1988) develop travel time estimators and study the order sequencing problem by extending the work of Han and McGinnis (1986).

5.4 Other Equipment Types

The discussion so far has focused on the S/R equipment types. Although other equipment types are just as important to OPS as the S/R equipment type, those are beyond the scope of this research. We mention here some results relevant to order picking.

Handling equipment is as crucial to OPS as arteries are to the body. In our point of view, the major issues in handling equipment are associated with the layout of the OPS and the interface with each S/R equipment. General issues in handling equipment include the selection of equipment type, the determination of vehicle fleet size, and control rules such as dispatching rule: see Muth and White (1979) for an overview on conveyors, Mueller (1983) for an overview on AGV systems, Bode (1988) for an overview on industrial trucks, and Kulwiec (1985) for overviews and practical guidelines on various equipment types.

Auxiliary equipment types, such as identification systems, controllers/sensors, and data transfer systems, provide information transfer crucial to the efficient management of OPS, although they do not physically handle items: see Naval Supply Systems Command (1985) for an overview and specifications of auxiliary equipment type, and Rylander (1987) and Lacagnina (1989) for identification and control systems.


The major objective of this report is the presentation of a general analysis framework for the design and operation of an OPS with an emphasis on item picking. Elaborating a systematic design procedure of the OPS, one may view the subject as a multifaceted system of great dimensional complexity, and identify various issues and their interwoven structure.

Analytical approaches for the design of OPS seemingly fail to give satisfactory answers to a complicated real case. Moreover, it is not likely in the foreseeable future that one can develop a universal, analytical model which leads to an efficient design of real OPS. On the other hand, the use of non-analytical approaches is also limited. For example, the simulation approach is clearly not able to address all the possible alternatives during the design process. The expert system approach is questionable because of the lack of sufficient domain knowledge (Permann and Bailey 1988). Consequently, an approach with great potential is to develop a computer aided system which combines analytical models, simulation models, human expert knowledge, and the planner's insights (Yoon and Sharp 1990). The major task of this approach would be the specification of which knowledge source is more suitable for which decision in the design process.

The performance evaluation of operating strategies is a fertile area for investigation. Questions related to storage assignment, batching and zoning strategies, order and pick sequencing rules, etc., need to be addressed. Sortation and palletizing strategies have received little attention, despite their importance. Also, an efficient information management system corresponding to the resulting operating scheme is crucial to their implementation and further improvement in practice.

Another important issue in the operation of OPS is the evaluation of operating strategies in dynamic environments, and also the development of dynamic operating schemes. For example, instead of one-time storage assignment, one may develop a dynamic control scheme for stock reallocation, dynamic stocking, and workload equalization. Stock reallocation is frequently required in modern warehouses because of the shorter life cycle and diversification of products. Dynamic stocking for an item pick system is the method of stocking only those SKUs that will be selected during the next shift. Workload equalization will be crucial to OPS with high fluctuation in order volume.

The performance characteristics of individual equipment types such as AS/RS and carousel have been addressed in many studies. However, some newer, higher throughput devices, such as rotary racks, automatic item picker, and multi-shuttle miniload AS/RS, have not been fully examined. Moreover, it is certain that the number of new equipment types will keep growing. In addition, some older equipment types such as a rack system with multi-command operation certainly need more attention.

Another equipment-related area that offers potential is the design of work stations for pickers and for packers. Work station improvements in conjunction with computer aided order picking can improve productivity by a factor of two and more. Packing often requires as much labor as picking, which points to a potential area of research. Even for a sophisticated and automated OPS, the human factors and human-machine interface should be carefully designed in order to achieve successful systems.


Amagai, K. 1985. TAKENAKA Plan/Design Service Procedure for Physical Distribution Facilities. Proc. of the 6th International Conference on Automation in Warehousing, 77-84.

Armbruster, R. 1988. Ergonomics in Warehousing. Proc. of the 9th International Conference on Automation in Warehousing, 283-293.

Armstrong, R. D., W. D. Cook and A. L. Saipe. 1979. Optimal Batching in a Semi-Automated Order Picking System. J. Opl. Res. Soc. 30, 711-720.

Ashayeri, J., and L. F. Gelders. 1985. Warehouse Design Optimization. Euro J. O. R. 21, 285-294.

Ashayeri, J., and L. F. Gelders. 1989. Simulation Program Generator for AS/RS Systems. Proc. of the 10th International Conference on Automation in Warehousing, 211-219.

Ashayeri, J., L. F. Gelders and P. M. van Looy. 1983. A Simulation Package for Automated Warehouses. Matl. Flow 1, 189-198.

Ashayeri, J., L. Gelders and L. van Wassenhove. 1985. A Microcomputer-Based Optimisation Model for the Design of Automated Warehouses. Int. J. Prod. Res. 23, 825-839.

Azadivar, F. 1986. Maximization of the Throughput of a Computerized Automated Warehousing System Under System Constraints. Int. J. Prod. Res. 24, 551-556.

Azadivar, F. 1987. Minimum-Cost Modular Design of Automated Warehousing Systems. Matl. Flow 4, 177-188.

Azadivar, F. 1989. Optimum Allocation of Resources between the Random Access and Rack Storage Spaces in an Automated Warehousing Systems. Int. J. Prod. Res. 27, 119-131.

Bachers, R., W. Dangelmaier and H. J. Warnecke. 1988. Selection and Use of Order-Picking Strategies in a High-Bay Warehouse. Matl. Flow 4, 233-245.

Bafna, K. M. 1983. Procedures for Investigating AS/RS Feasibility and Suitability Are Outlined for IEs. Ind. Eng. 15, June, 60-66.

Bafna, K. M., and F. R. Solt. 1983. Procedures Given for Determining AS/RS System Size and Preparing Specs. Ind. Eng. 15, August, 76-81.

Bagadia, K. S. 1982. Carousel System and Distribution Concept Applied to Tool Cribs. Proc. of the 1982 Annual IIE Conference, 211-213.

Bailey, M. 1983. Computer-Aided Design for Automated Warehouses. Proc. of the 5th International Conference on Automation in Warehousing, 113-126.

Bailey, M. 1985. Economic Modelling of AS/RS. Proc. of the 6th International Conference on Automation in Warehousing, 45-55.

Bartholdi, III., J. J., and L. K. Platzman. 1986. Retrieval Strategies for a Carousel Conveyor. IIE Trans. 19, 166-173.

Bartholdi, III., J. J., and L. K. Platzman. 1988a. Design of Efficient Bin-Numbering Schemes for Warehouses, Matl. Flow 4, 247-254.

Bartholdi, III, J. J., and L. K. Platzman. 1988b. Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space. Mgmt. Sci. 34, 291-305.

Bartholdi, III, J. J., and L. K. Platzman. 1989. Decentralized Control of Automated Guided Vehicles on a Single Loop. IIE Trans. 21, 76-81.

Bassan, Y., Y. Roll and M. J. Rosenblatt. 1980. Internal Layout Design of a Warehouse. AIIE Trans. 12, 317-322.

Baumbach, J., V. Englert, J. C. Ammons and R. Schmidt. 1989. Design and Analysis of the Satellite Storage and Retrieval System (SS/RS). Presented at the Material Handling Focus '89, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Bengtson, N. M., and R. J. Gomez. 1988. Why a Single Aisle Miniload System Is Not Simple to Model. Proc. of the 1988 Winter Simulation Conference, 603-608.

Bergmans, P. P. 1972. Minimizing Expected Travel Time on Geometrical Patterns by Optimal Probability Rearrangements. Info. & Cont. 20, 331-350.

Bienkowski, T. L., S. S. Asfour, S. W. Waly and A. M. Genaidy. 1986. A Comprehensive Data Base for the Design of Manual Material Handling. Proc. of the 8th Annual Conference on Computers and Industrial Engineering, 351-354.

Bischoff, E., and W. B. Dowsland. 1982. An Application of the Micro to Product Design and Distribution. J. Opl. Res. Soc. 33, 271-280.

Bode, W. 1988. Industrial Trucks within Centralized Material Flow Systems. Matl. Flow 4, 225-232.

Bozer, Y. A. 1985. Optimizing Throughput Performance in Designing Order Picking Systems. Ph.D. Dissertation. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.

Bozer, Y. A., M. A. Quiroz and G. P. Sharp. 1987. Simulation for Automated Accumulation and Sortation Systems. Unpublished Report, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Bozer, Y. A., M. A. Quiroz and G. P. Sharp. 1988. An Evaluation of Alternative Control Strategies and Design Issues for Automated Accumulation and Sortation Systems. Matl. Flow 4, 265-282.

Bozer, Y. A., E. C. Schorn and G. P. Sharp. 1985. An Evaluation of Heuristics for In-the-Aisle Order Picking. Report TR-85-15, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Bozer, Y. A., and G. P. Sharp. 1985. An Empirical Evaluation of a General Purpose Automated Order Accumulation and Sortation System Used in Batch Picking. Matl. Flow 2, 111-131.

Bozer, Y. A., and J. A. White. 1984. Travel Time Models for Automated Storage/Retrieval Systems. IIE Trans. 16, 329-338.

Bozer, Y. A., and J. A. White. 1988. Design and Performance Models for End-Of-Aisle Order Picking Systems. Report TR-87-08, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Branigan, M. J. 1988. Visual Interactive Simulation for Automated Warehouse Design. Proc. of the 9th International Conference on Automation in Warehousing, 157-167.

Bredenbeck, J. E., W. T. Shirk and J. C. Majure. 1989. Small Parts Handling Needs Are Met by Installing a Vertical Storage System. Ind. Eng. 21, July, 34-38.

Buley, D. T., and K. Knott. 1986. Designing Vertical Carousels to Maximize Operator Utiliztion. Proc. of the 8th Annual Conference on Computers and Inustrial Engineering, 271-275.

Bulla, T. L. C. 1987. Efficient Carousel Configurations for Work-In-Process Storage. Report TD-86-12, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Camp, R. E. 1990. Storage Requirements Are Determined Through the Use of Simulation. Ind. Eng. 22, March, 44-48.

Carew, V. 1989. The Navy's Warehouse Utilization Program. Presented at the Material Handling Focus '89, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Carlo, H., T. J. Hodgson, L. A. Martin-Vega and E. R. Stern. 1985. MICRO-IPLS: Pallet Loading on a Microcomputer. Comp. Ind. Eng. 9, 29-34.

Carpenter, H., and W. B. Dowsland. 1985. Practical Considerations of the Pallet-Loading Problem. J. Opl. Res. Soc. 36, 489-497.

Carson, Jr., J. S., C. H. Wysowski, W. A. Johnson and N. Wilson. 1983. A GPSS Model of a Unit Load AS/R System and Shipping Department. Proc. of the 1983 Winter Simulation Conference, 193-196.

Chisman, J. A. 1975. The Clustered Traveling Salesman Problem. Comp. Opns. Res. 2, 115-119.

Chisman, J. A. 1977. Optimizing the Shipping Function. J. Ind. Eng. 9, 38-41.

Choe, K. 1991. Aisle-Based Order Pick Systems with Batching, Zoning, and Sorting. Unpublished Ph.D. Dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.

Choe, K., and G. P. Sharp. 1988. Class-Based Storage with Multi-Command Operation. Report TR-88-08, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Choe, K., and G. P. Sharp. 1989. Class-Based Storage in a Unit-Load AS/RS. Report TR-89-08, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Cobbin, P. 1986. Modeling Tote Stacker Operation as a WIP Storage Device. Proc. of the 1986 Winter Simulation Conference, 597-605.

Coffman, E. G., Jr., M. R. Garey and D. S. Johnson. 1984. Approximation Algorithms for Bin-Packing - An Updated Survey. Algorithm Design for Computer System Design, G. Ausiello, M. Lucertini and P. Serafini (Eds.), Springer-Verlag, New York, 49-106.

Cox, B. 1983. Using Standard Data and CAD Techniques to Design an Automated Parcel Sorting Facility. Proc. of the 5th International Conference on Automation in Warehousing, 149-157.

Cox, B. 1986. Determining Economic Levels of Automation by Using a Hierarchy of Productivity Ratios Techniques. Proc. of the 7th International Conference on Automation in Warehousing, 39-49.

Dagli, C. H., and S. N. Wasti. 1989. Intelligent Operations Planning in Automatic Storage and Retrieval. Proc. of the 1989 IIE Integrated Systems Conference and Society for Integrated Manufacturing Conference, 511-516.

Davies, A. L., M. C. Gabbard and E. F. Reinholdt. 1983. Storage Method Saves Space and Labor in Open-Package-Area Picking Operations. Ind. Eng., 15, June, 68-74.

Dichtl, E., and W. Beeskow. 1980. Optimal Allocation of Commodities in Warehouses by Means of Multi-Dimensional Scaling (in German). Zeitschrift Optns. Res. 24, B51-B64.

Donaldson, T. 1989. KODAK's Expert System for Order Picking. Presented at the Material Handling Focus '89, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Dowsland, K. A. 1987. A Combined Data-Base and Algorithmic Approach to the Pallet-Loading Problem. J. Opl. Res. Soc. 38, 341-345.

Elliott, K. A. 1986. Designing Warehousing Systems. Presented at the 36th Annual Material Handling Short Course, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Elsayed, E. A. 1981. Algorithms for Optimal Material Handling in Automatic Warehousing Systems. Int. J. Prod. Res. 19, 525-535.

Elsayed, E. A. 1988. Order Batching Algorithms for AS/R Interlaving Systems with/without Due Time Constraints. Presented at the Material Handling Focus '88, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Elsayed, E. A., and R. G. Stern. 1983. Computerized Algorithms for Order Processing in Automated Warehousing Systems. Int. J. Prod. Res. 21, 579-586.

Elsayed, E. A., and O. I. Unal. 1989. Order Batching Algorithms and Travel-Time Estimation for Automated Storage/Retrieval Systems. Int. J. Prod. Res. 27, 1097-1114.

Emamizadeh, B., and K. Knott. 1986. Matching Unit Load and Inventory Systems. Proc. of the 8th Annual Conference on Computers and Industrial Engineering, 105-108.

Emerson, C. R., and D. S. Schmatz. 1981. Results of Modeling an Automated Warehouse System. Ind. Eng. 13, August, 28-33.

Engwall, R. L. 1985. Automated Material Handling in Electronic Assembly. Prsented at the Annual Material Handling Users Conference, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Evans, J. R. 1984. The Factored Transportation Problem. Mgmt. Sci. 30, 1021-1024.

Everton, J. G. 1989. Improving Automated Storage/Retrieval System Performance Through the Use of Advanced Simulation Systems. Proc. of the 10th International Conference on Automation in Warehousing, 37-41.

Falk, N. 1983. Warehouse Lighting - It Costs or Pays: An Energy Management Approach. Proc. of the 5th International Conference on Automation in Warehousing, 219-224.

Fisher, E. L., J. B. Farber and M. G. Kay. 1988. MATHES: An Expert System for Material Handling Equipment Selection. Eng. Cost. Prod. Econo. 14, 297-310.

Foley, R. D., and E. H. Frazelle. 1990. Analytical Results for Miniload Throughput and the Distribution of Dual Command Travel Time. to appear in IIE Trans.

Francis, R. L., L. F. McGinnis and J. A. White. 1983. Locational Analysis. Euro. J. O. R. 12, 220-252.

Francis, R. L., and J. A. White. 1974. Facility Layout and Location: An Analytical Approach. Prentice Hall, Englewood Cliffs, New Jersey.

Frazelle, E. H. 1988. Small Parts Order Picking: Equipment and Strategy. Report OP-88-01, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Frazelle, E. A., and G. P. Sharp. 1989. Correlated Assignment Strategy Can Improve Any Order-Picking Operation. Ind. Eng. 21, April, 33-37.

Frazelle, E. H., and G. P. Sharp. 1988. How to Design, Operate, Select, and Improve Order Picking Systems. Presented at the Order Picking Workshop, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Fredrick, C. 1982. Our Automatic Carousels Slash Manufacturing Time. Mod. Matl. Handl. June.

Fuller, S. H. 1972. An Optimal Drum Scheduling Algorithm. IEEE Trans. Comp. C21, 1153-1165.

Gelders, L., and J. Ashayeri. 1989. Lessons Learned from Automation: Theory versus Practice. Proc. of the 10th International Conference on Automation in Warehousing, 15-20.

General Services Administration. 1966. Warehouse Operations. U.S. Government Printing Office, Washington, D.C.

George, J. A., and D. F. Robinson. 1980. A Heuristic for Packing Boxes into a Container. Comp. Opns. Res. 7, 147-156.

Gibson, D. R. 1990. Order Batching Procedures. Report TD-90-05, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Goetschalckx, M. 1983. Storage and Retrieval Policies for Efficient Order Picking Operations. Ph.D. Dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.

Goetschalckx, M., and J. Ashayeri. 1988. Classification and Design of Order Picking Systems. Report TR-88-14, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Goetschalckx, M., and H. D. Ratliff. 1987. Optimal Lane Depth for Single and Multiple Products in Block Stacking Storage Systems. Report TR-87-01, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Goetschalckx, M., and H. D. Ratliff. 1988a. Order Picking in an Aisle. IIE Trans. 20, 53-62.

Goetschalckx, M., and H. D. Ratliff. 1988b. An Efficient Algorithm to Cluster Order Picking Items in a Wide Aisle. Eng. Cost. Prod. Econo. 13, 263-271.

Goetschalckx, M., and H. D. Ratliff. 1988c. Sequencing Picking Operations in a Man-Aboard Order Picking System. Matl. Flow 4, 255-263.

Golden, B. L., and A. A. Assad. 1986. Perspectives on Vehicle Routing: Exciting New Developments. Opns. Res. 34, 803-810.

Grasso, E. T., and J. M. A. Tanchoco. 1983. Unit Load and Material Handling Considerations in Material Requirements Planning Systems. Matl. Flow 1, 79-87.

Graves, S. C., W. H. Hausman and L. B. Schwarz. 1977. Storage-Retrieval Interleaving in Automatic Warehousing Systems. Mgmt. Sci. 23, 935-945.

Gross, J. G. 1981. Picking Methods May Provide Key to Lower Cost Warehouse Plans. Ind. Eng. 13, June, 50-54.

Gudehus, T. 1973. Principles of Order Picking: Operations in Distribution and Warehousing Systems (in German), W. Girardet, Essen, West Germany.

Guenove, M., and R. Raeside. 1989. Real Time Optimization of Man on Board Order Picking. Proc. of the 10th International Conference on Automation in Warehousing, 89-93.

Gupta, N. K. 1982. Kitting Matrix Adds Accuracy to Small Part Picking System. Ind. Eng. 14, January, 35-38.

Hackman, S. T., and M. J. Rosenblatt. 1990. Allocating Items to an Automated Storage and Retrieval System. IIE Trans. 22, 7-14.

Hall, N. G. 1989. The Inventory Packing Problem. Nav. Res. Log. 36, 399-418.

Han, C. P., K. Knott and P. J. Egbelu. 1989. A Heuristic Approach to the Three-Dimensional Cargo-Loading Problem. Int. J. Prod. Res. 27, 757-774.

Han, M. -H., and L. F. McGinnis. 1986. Automated Work-in-Process Carousels: Modeling and Analysis. Report TR-86-06, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Han, M. -H., L. F. McGinnis, J. S. Shieh and J. A. White. 1987. On Sequencing Retrievals in an Automated Storage/Retrieval System. IIE Trans, 19, 56-66.

Han, M. -H., L. F. McGinnis and J. A. White. 1988. Analysis of Rotary Rack Operation. Matl. Flow 4, 283-293.

Hanelt, H., and K. D. Kryder. 1989. Designs-Phasing of Computer Integrated Automated Distribution Centers to Benefit Corporate Growth. Proc. of the 10th International Conference on Automation in Warehousing, 53-62.

Hardy, G. H., J. E. Littlewood and G. Polya. 1952. Inequalities, Cambridge University, Cambridge, UK.

Harmatuck, D. J. 1976. A Comparison of Two Approaches to Stock Location. Logis. Transp. Rev. 12, 282-285.

Hatanaka, S. 1989. Recent Technical Trends of Automated Storage Systems in Japan. Proc. of the 10th International Conference on Automation in Warehousing, 23-28.

Hausman, W. H., L. B. Schwarz and S. C. Graves. 1976. Optimal Storage Assignment in Automatic Warehousing Systems. Mgmt. Sci. 22, 629-638.

Herrera-Cuellar, A., and G. P. Sharp. 1983. Modular Drawer Storage Systems: A Design Procedure. Report TR-83-08, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Heskett, J. L. 1963. Cube-Per-Order Index - A Key to Warehouse Stock Location. Transp. Distn. Mgmt. 3, 27-31.

Hodgson, T. J. 1982. A Combined Approach to the Pallet Loading Problem. IIE Trans. 14, 175-182.

Hodgson, T. J., D. S. Hughes and L. A. Martin-Vega. 1983. A Note on a Combined Approach to the Pallet Loading Problem. IIE Trans. 15, 268-271.

Hodgson, T. J., and T. J. Lowe. 1982. Production Lot Sizing with Material-Handling Cost Considerations. IIE Trans. 14, 44-51.

Horrey, R. J. 1983. Sortation Systems: From Push to High-Speed Fully Automated Applications. Proc. of the 5th International Conference on Automation in Warehousing, 77-83.

Houmas, C. G. 1986. Comparing Small Parts Storage Systems. Report TD-86-04, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Hwang, H., W. Baek and M.-K. Lee. 1988. Clustering Algorithms for Order Picking in an Automated Storage and Retrieval System. Int. J. Prod. Res. 26, 189-201.

Hwang, H., and C. S. Ko. 1988. A Study on Multi-Aisle System Served by a Single Storage/Retrieval Machine, Int. J. Prod. Res. 26, 1727-1737.

Hwang, H., and M.-K. Lee. 1988a. Order Batching Algorithms for a Man-on-Board Automated Storage and Retrieval System. Eng. Cost. Prod. Econo. 13, 285-294.

Hwang, H., and M. -K. Lee. 1988b. An Approach in the Design of a Unit-Load Automated Carousel System. Eng. Opt. 13, 197-210.

Illingworth, L., and G. P. Sharp. 1988. Comparative Analysis of Unit-Load Storage Systems Using a PC-Based Program. Report TR-86-18, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Jaikumar, R., and M. M. Solomon. 1985. Dynamic Operational Policies in an Automated Warehouse. Report 85-44, Northeastern University.

Jaikumar, R., and M. M. Solomon. 1986. Real-Time Control of Multiple Command Cycle Storage-Retrieval Warehousing Systems. Proc. of the 7th International Conference on Automation in Warehousing, 155-158.

Juenemann, R., and F. Meister. 1988. Rational Warehouse Planning - EDP-Supported. Matl. Flow 4, 217-223.

Kallina, C., and J. Lynn. 1976. Appilication of the Cube-Per-Order Index Rule for Stock Location in a Distribution Warehouse. Interfaces 7, 37-46.

Karasawa, Y., H. Nakayama and S. Dohi. 1980. Trade-off Analysis for Optimal Design of Automated Warehouses. Int. J. Sys. Sci. 11, 567-576.

Karp, P. M., A. C. McKeller and C. K. Wong. 1975. Near Optimal Solutions to a Two-Dimensional Placement Problem. SIAM J. Comp. 4, 271-286.

Kay, E. 1968. A Mathematical Model for Handling in a Warehouse. Pergamon Press, Oxford.

Kaylan, A., and D. J. Medeiros. 1988. Analysis of Storage Policies for Miniload AS/RS. Eng. Cost. Prod. Econo. 13, 311-318.

Kearney, A. T. 1984. Measuring and Improving Productivity in Physical Distribution. National Council of Physical Distribution Management, Oak Brooks, Illinois.

Kim, J., and A. Seidman. 1990. Storage Assignment Policies in Automatic/Retrieval Systems. Working Paper, School of Business Administration, University of Rochester.

Kim, W. B., and E. Koenisberg. 1987. The efficiency of Two Groups of N Machines Served by a Single Robot. J. Opl. Res. Soc. 38, 523-538.

Kibuki, M. 1987. Piece Picking Using a Carousel System. Proc. of the 8th International Conference on Automation in Warehousing, 283-293.

Koenisberg, E. 1986. Analysis of the Efficiency of Carousel and Tote-Stacker Performance. Proc. of the 7th International Conference on Automation in Warehousing, 363-373.

Koenisberg, E., and J. Mamer. 1982. The Analysis of Production Systems. Int. J. Prod. Res. 20, 1-16.

Kooy, E. D. 1984. Comparison of Order Picking Methods. Working Paper, Pillsbury Co.

Kooy, E. D. 1985. Proposed Method of Determining the Best Order Picking System. Working Paper, Pillsbury Co.

Krajacic, P. 1988. The Intelligent Picking Machine for Sensitive Products. Proc. of the 9th International Conference on Automation in Warehousing, 91-98.

Kulick, A. 1982. Interlocking Pallet Pattern Simulation Program. Ind. Eng. 14, September, 22-24.

Kulkarni, V. G., and S. P. Sethi. 1989. Deterministic Retrial Times are Optimal in Queues with Forbidden States. INFOR. 27, 374-386.

Kulwiec, R. A. (Ed.) 1985. Materials Handling Handbook, 2nd Ed. John Wiley & Sons, New York.

Kunder, R., and Gudehus, T. 1975. Mean Time for Collecting Items from a Rectangular System of Shelves (in German). Zeitschrift Optns. Res. 19, B53-B72.

Kusiak, A. 1985. Material Handling in Flexible Manufacturing Systems. Matl. Flow. 2, 79-95.

Kusiak, A., O. Hawaleshka and G. Cormier. 1985. Order Picking Policies in Automated Storage Systems. Proc. of the 6th International Conference on Automation in Warehousing, 239-248.

Lacagnina, M. 1989. Next Generation Identification and Control Systems. Presented at the Material Handling Focus '89, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Lawler, E. L., J. K. Lenstra, A. H. G. Rinnoy Kan and D. B. Shmoys (Eds.) 1985. The Traveling Salesman Problem. John Wiley & Sons, New York.

Lewis, D. A., and R. Lin. 1989. Materials Handling in the Electronics Industry: The Same Old Problems. Eng. Cost. Prod. Econo. 16, 111-116.

Lim, S. 1990. Zoning in Storage Systems. Ph.D. Dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.

Lim, W. K., J. J. Bartholdi, III. and L. K. Platzman. 1985. Storage Schemes for Carousel Conveyors Under Real Time Control. Report TR-85-10, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Linn, R. J., and R. A. Wysk. 1987. An Analysis of Control Strategies for an Automated Storage/ Retrieval System. INFOR. 25, 66-82.

Linn, R. J., and R. A. Wysk. 1990. An Expert System Framework for Automated Storage and Retrieval System Control. Comp. Ind. Eng. 18, 37-48.

Lombardi, R. 1985. Implementation of a Carousel Storage and Retrieval System: Visual Graphics Case Study. Automated Material Handling and Storage, Auerbach Publishers, Pennsauken, New Jersey.

Malmborg, C. J., and K. Bhaskaran. 1987. On the Optimality of the Cube Per Order Index for Conventional Warehouse with Dual Command Cycles. Matl. Flow 4, 169-175.

Malmborg, C. J., and K. Bhaskaran. 1989. Optimal Storage Assignment for Multiaddress Warehousing Systems. IEEE Trans. Sys. Man Cyber. 19, 197-205.

Malmborg, C. J., and K. Bhaskaran. 1990. A Revised Proof of Optimality for the Cube-Per-Order Index for Stored Item Location. Appl. Math. Model. 14, 87-95.

Malmborg, C. J., and S. J. Deutch. 1988. A Stock Location Model for Dual Address Order Picking Systems. IIE Trans. 20, 44-52.

Malmborg, C. J., H. B. Hubbard and M. H. Agee. 1985. Network Simulation Approaches to Material Handling Equipment. Proc. of the 7th Annual Conference on Computers and Industrial Engineering, 144-148.

Malmborg, C. J., B. Krishnakumar, G. R. Simons and M. H. Agee. 1989. EXIT: A PC-Based Expert System for Industrial Truck Selection. Int. J. Prod. Res. 27, 927-941.

Malmborg, C. J., G. R. Simmons and M. H. Agee. 1986. Knowledge Engineering Approaches to Material Handling Specification. Proc. of the 1986 Fall IE Conference, 148-151.

Mardix, I., and G. P. Sharp. 1985. Cost and Efficiency Analysis of the Carousel Storage System. Report TR-85-08, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Matson, J. O., S. R. Swaminathan and J. M. Mellichamp. 1990. Knowledge-Based Material Handling Equipment Selection. Proc. of the 1990 International Industrial Engineering Conference, 212-217.

Matson, J. O., and J. A. White. 1982. Operational Research and Material Handling. Euro. J. O. R. 11, 309-318.

Mayer, Jr., H. E. 1961. Storage and Retrieval of Material. Western Elect. Engr. 5, 42-48.

Medeiros, D. J., E. E. Enscore, Jr. and A. D. Smith. 1986. Performance Analysis of Miniload Systems. Proc. of the 1986 Winter Simulation Conference, 606-612.

Mellema, P. M., and C. A. Smith. 1988. Simulation Analysis of Narrow-Aisle Order Selection Systems. Proc. of the 1988 Winter Simulation Conference, 597-602.

Menon, S. R., S. G. Kapoor and R. B. Blackmon. 1988. Navigation Planning for Mobile Robotic Devices in Modular Warehouses. Int. J. Adv. Mfg. Tech. 3, 47-62.

Mital, A. 1983. Generalized Model Structure for Evaluating/Designing Manual Material Handling Jobs. Int. J. Prod. Res. 21, 401-412.

Mital, A., and S. S. Ashfour. 1983. Material Handling Capacity of Workers. Matl. Flow 1, 89-100.

Mullens, M. A. 1981. Use a Computer to Determine the Size of a New Warehouse, Particularly in Storage and Retrieval Areas. Ind. Eng. 13, June, 24-32.

Muller, D. J. 1989. AS/RS and Warehouse Modelling. Proc. of the 1989 Winter Simulation Conference, 802-810.

Mueller, T. 1983. Automated Guided Vehicles. Springer-Verlag, New York.

Murphy, F. H., and E. A. Stohr. 1978. A Mathematical Programming Approach to the Scheduling of Sorting Operations. Nav. Res. Log. Qt. 25, 155-167.

Mutel, B., and D. Anciaux. 1989. Study of Storage and Picking Policies of Items in Large Delivery-Type Warehouse. Proc. of the 10th International Conference on Automation in Warehousing, Dallas, Texas.

Muth, E. J., and J. A. White. 1979. Conveyor Theory: A Survey. AIIE Trans. 11, 270-277.

Naval Supply Systems Command. 1985. Warehouse Modernization and Layout Planning Guide. NAVSUP Publication 529, Naval Publication and Forms Center, Philadelphia, Pennsylvania.

Nepola, K. 1985. Automated Warehouse System for Carts and Dollies. Proc. of the 6th International Conference on Automation in Warehousing, 85-91.

O'Brien, J. W. 1986. Pharmaceutical Distribution Improved Order Picking. Proc. of the 1986 Fall IE Conference, 476-480.

Ottjes, J. A., and E. Hoogenes. 1988. Order Picking and Traffic Simulation in Distribution Centres. Int. J. Prod. Dist. Mfg. Mgmt. 18, 14-21.

van Oudheusden, D. L., Y. -J. J. Tzen and H. -T. Ko. 1988. Improving Storage and Order Picking in a Person-on-Board AS/R System: A Case Study. Eng. Cost. Prod. Econo. 13, 273-283.

Page, E., and R. J. Paul. 1976. Multi-Product Inventory Situations with One Restriction. Opns. Res. Qt. 27, 816-833.

Park, B. C. 1988. Closest Open Location Rule in AS/RS. Working Paper, Department of Industrial Engineering, Keimyung University, Taegu, Korea.

Park, B. C., and L. Platzman. 1987. Distribution of the Closest Available Location in Automated Storage and Retrieval Systems. Working Paper, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.

Park, Y. H., and D. B. Webster. 1989a. Modelling of Three-Dimensional Warehouse Systems. Int. J. Prod. Res. 27, 985-1003.

Park, Y. H., and D. B. Webster. 1989b. Design of Class-Based Racks for Minimizing Travel Time in a Three-Dimensional Storage System. Int. J. Prod. Res. 27, 1589-1601.

Penington, R. A., and J. M. A. Tanchoco. 1988. Robotic Palletization of Multiple Box Sizes. Int. J. Prod. Res. 26, 95-105.

Perlmann, A. M., and M. Bailey. 1988. Warehouse Logistic Systems - A CAD Model. Eng. Cost. Prod. Econo. 13, 229-237.

Perry, R. F., S. F. Hoover and D. R. Freeman. 1983. Design of an Automated Storage/Retrieval System Using Simulation Modeling. Proc. of the 5th International Conference on Automation in Warehousing, 57-66.

Perry, R. F., S. V. Hoover and D. R. Freeman. 1984. An Optimal-Seeking Approach to the Design of Automated Storage/Retrieval Systems. Proc. of the 1984 Winter Simulation Conference. 349-354.

Platzman, L. K., and J. J. Bartholdi, III. 1985. A Minimal Technology Method for Order Batching and Sequencing. Report TR-85-04, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Pliskin, J. S., and D. Dori. 1982. Ranking Alternative Warehouse Area Assignments: A Multiattribute Approach. IIE Trans. 14, 19-26.

Pulat, B. M., and P. S. Pulat. 1988. Performance Analysis of Automatic Storage and Retrieval Systems - A Comparative Approach. Proc. of the 1988 Winter Simulation Conference, 591-596.

Puls, F. M., and J. M. A. Tanchoco. 1986. Robotic Implementation of Pallet Loading Patterns. Int. J. Prod. Res. 24, 635-646.

Quinn, E. B. 1983. Simulation of Order Processing Waves. Presented at the Material Handling Focus '83, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Raghunath, S., R. Perry and T. Cullinane. 1986. Interactive Simulation Modeling of Automated Storage Retrieval Systems. Proc. of the 1986 Winter Simualtion Conference, 613-620.

Ratliff, H. D., and A. S. Rosenthal. 1983. Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem. Opns. Res. 31, 507-521.

Rhea, N. W. 1985. New Clairol Product: Instant Productivity in the Warehouse. Matl. Handl. Eng. July, 89-92.

Riaz-Kahn, M. 1984. An Efficiency Measurement Model for a Computerized Warehousing System. Int. J. Prod. Res. 22, 443-452.

Rizo-Patron, A., Y. A. Bozer and L. F. McGinnis. 1983. Analytic and Simulation Models for Advanced Automated Storage/Retrieval Systems. Report TR-82-04, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Roach, B., and K. Hunt. 1988. Finished Goods Sortation and Palletizing in the Cigarette Industry. Proc. of the 9th International Conference on Automation in Warehousing, 221-239.

Roll, Y., and M. J. Rosenblatt. 1983. Random versus Grouped Storage Policies and Their Effect on Warehouse Capacity. Matl. Flow 1, 199-205.

Roll, Y., M. J. Rosenblatt and D. Kadosh. 1989. Determining the Size of a Warehouse Container. Int. J. Prod. Res. 27, 1693-1704.

Rosenblatt, M. J., and A. Eynan. 1989. Deriving the Optimal Boundaries for Class-Based Automatic Storage/Retrieval Systems. Mgmt. Sci. 35, 1519-1524.

Rosenblatt, M. J., and Y. Roll. 1984. Warehouse Design with Storage Policy Considerations. Int. J. Prod. Res. 22, 809-821.

Rosenblatt, M. J., and Y. Roll. 1988. Warehouse Capacity in a Stochastic Environment. Int. J. Prod. Res. 26, 1847-1851.

Rylander, R. 1987. Data Collection Within the Automated Warehouse. Proc. of the 8th International Conference on Automation in Warehousing, 323-329.

Santana, J. L., and L. K. Platzman. 1979. Real-Time Scheduling of an "Open Warehouse" Sorter-Palletizer System. Proc. of the 18th IEEE Conference on Decision and Control, 537-539.

Schall, S., and J. Chandra. 1989. Multiple Product Inventory Policies with Unit Load and Storage Space Considerations. Eng. Cost. Prod. Econo. 16, 245-256.

Schreiner, R. M. 1986. A Microcomputer-Based Pallet Layout System to Evaluate and Improve Storage Space Utilization. Proc. of the 8th Computers and Industrial Engineering, 87-90.

Schmidt, R. 1989. The Design of Satellite Storage and Retrieval Systems with Random Access. Proc. of the 10th International Conference on Automation in Warehousing, 159-164.

Schulze, L., and U. Westfal. 1989. Computer Aided Warehouse Planning. Proc. of the 10th International Conference on Automation in Warehousing, 45-49.

Schwarz, L. B., S. C. Graves and W. H. Hausman. 1978. Scheduling Policies for Automatic Warehousing Systems: Simulation Results. AIIE Trans. 10, 260-270.

Seidmann, A. 1988. Intelligent Control Schemes for Automated Storage and Retrieval Systems. Int. J. Prod. Res. 26, 931-952.

Sellers, C. J., and S. Y. Nof. 1986. Part Kitting in Robotic Facilities. Matl. Flow 3, 163-174.

Sharp, G. P. 1990. Intelligent Batching in Order Picking. Presented at the 40th Annual Material Handling Short Course, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Sharp, G. P., K. Choe and C. S. Yoon. 1990. Small Parts Order Picking: Analysis Framework and Selected Results. Report OP-90-04, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Sharp, G. P., J. Eckert, D. Gibson, C. G. Houmas and I. Mardix. 1990. Order Picking Using Horizontal Carousels. Report TR-89-01, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Sharp, G. P., E. H. Frazelle, R. D. Foley and D. R. Gibson. 1988. Analysis and Configuration of Miniload AS/RS. Working Paper, Material Handling Research Center, Georgia Institute of Technology, Atlanata, Georgia.

Sharp, G. P., R. Kittel and K. J. Hollender. 1989. Factors Affecting Productivity of a Pallet AS/RS. Proc. of the 10th International Conference on Automation in Warehousing, 105-111.

Shieh, J. S. 1985. On the Analysis of Selected Automated Storage and Retrieval Systems. Ph.D. Dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.

Shirk, W. T. 1989. Material Flow Controls in a JIT Environment. Presented at the Material Handling Focus '89, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Shirk, W. T., and J. E. Bredenbeck. 1987. Portable Terminals Boost Efficiency at AT&T. Matl. Hand. Eng. July.

Smith, D., and P. de Cani. 1980. An Algorithm to Optimize the Layout of Boxes on Pallets. J. Opl. Res. Soc. 31, 573-578.

Stecke, K. E., and J. E. Aronson. 1985. Review of Operator/Machine Interference Models. Int. J. Prod. Res. 23, 129-151.

Stern, H. I. 1986. Parts Location and Optimal Picking Rules for a Carousel Conveyor Automatic Storage and Retrieval System. Proc. of the 7th International Conference on Automation in Warehousing, 377-385.

Steudel, H. J. 1979. Generating Pallet Loading Patterns: A Special Case of the Two-Dimensional Cutting Stock Problem. Mgmt. Sci. 25, 997-1004.

Steudel, H. J. 1983. Determination of Economic Pallet Size for In-Plant Handling. Matl. Flow 1, 71-76.

Stone, H. S., and S. H. Fuller. 1973. On the Near Optimality of the Shortest-Latency-Time-First Drum Scheduling Discipline. Comm. ACM. 16, 352-353.

Suzuki, J. 1981. The Application and Suggestion of Sorting Machine in Japan. Proc. of the 4th International Conference on Automation in Warehousing, Tokyo, Japan.

Suzuki, S. 1988. Order Pattern Graph Assists Order Picking System Design. Proc. of the 9th International Conference on Automation in Warehousing, 113-124.

Szielasko, K. 1988. Future-Oriented Distribution Centres with Automated Order Picking in High Performance Systems. Proc. of the 9th International Conference on Automation in Warehousing, 67-84.

Takakuwa, S. 1989. Module Modeling and Economic Optimization for Large-Scale AS/RS. Proc. of the 1989 Winter Simulation Conference, 795-801.

Tanchoco, J. M. A., and M. H. Agee. 1981. Plan Unit Loads to Interact with All Components of Warehouse System. Ind. Eng. 13, June, 36-48.

Tanchoco, J. M. A., R. P. Davis, P. J. Egbelu and R. A. Wysk. 1983. Economic Unit Loads (EUL) for Multi-Product Inventory Systems with Limited Storage Space. Matl. Flow 1, 141-148.

Tanchoco, J. M. A., R. P. Davis and R. A. Wysk. 1980. Economic Order Quantities Based on Unit-Load and Material Handling Considerations. Decis. Sci. 11, 514-521.

Tielker, U. G. 1989. Classification and Trends of Order Picking Techniques. Proc. of the 10th International Conference on Automation in Warehousing, 97-102.

Tolliver, R. 1989. Order Picking Basics at Avon Products. Presented at the Material Handling Focus '89, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Tompkins, J. A., and J. A. White. 1984. Facilities Planning. John Wiley & Sons, New York.

Tsai, R. D., E. M. Malstrom and H. D. Meeks. 1988. A Two-Dimensional Palletizing Procedure for Warehouse Loading Operations. IIE Trans. 20, 418-425.

Ulgen, O. M., and H. Elayat. 1981. GENSAWS: A General Simulator for Automatic Warehousing Systems. Proc. of the 6th International Conference on Automation in Warehousing, Novi Sad, Yugoslavia.

Vemuganti, R. R. 1987. The Maximum Value of Inventory and Shortages in Production Lot Size Systems. IIE Trans. 19, 404-411.

Vrgoc, M., and V. Ceric. 1988. Investigation and Design of Parcel Sorting Systems in Postal Centres by Simulation. Comp. in Ind. 10, 137-145.

Walsh, P. 1979. Carton Sortation in the Distribution Warehouse. Proc. of the 3th International Conference on Automation in Warehousing, 15-28.

Warehouse Education and Research Council. 1986. Survey. Oak Brooks, Illinois.

Waugh, R. M., and R. A. Ankener. 1977. Simulation of an Automated Stacker Storage System. Proc. of the 1977 Winter Simulation Conference, 769-776.

Weber, H. 1989. The Humanistic Approach to Optimize Logistic Concepts. Proc. of the 10th International Conference on Automation in Warehousing, 319-325.

Weiss, D. J. 1980. Computer Controlled Carousels. Proc. of the 3th International Conference on Automation in Warehousing, Stratford, UK.

Wen, U. -P., and D. -T. Chang. 1988. Picking Rules for a Carousel Conveyor in an Automated Warehouse. Omega 16, 145-151.

Wen, W. -P., J. T. Lin and D. -T Chang. 1989. Order Picking for a Two-Carousel-Single-Server System in an Automated Warehouse. Proc. of the 10th International Conference on Automation in Warehousing, 65-70.

White, J. A. 1979. Picker to the Pick Face or Picking Face to the Picker. Mod. Matl. Handling September, 19.

White, J. A. 1980. Auditing AS/R Systems after Installation. Ind. Eng. 12, June, 20-21.

White, J. A. 1988. The Evolution of Materials Handling in Warehousing. Proc. of the 9th International Conference on Automation in Warehousing, 33-50.

White, J. A., and H. D. Kinney. 1982. Storage and Warehousing. Handbook of Industrial Engineering. G. Salvendy (ed.), John Wiley & Sons, New York.

Wilson, H. G. 1977. Order Quantity, Product Popularity, and the Location of Stock in a Warehouse. AIIE Trans. 9, 230-237.

Wong, C. K. 1980. Minimizing Expected Head Movement in One-Dimensional and Two-Dimensional Mass Storage System. Comp. Surveys 12, 167-178.

Yadin, M., and S. Zacks. 1982. Random Coverage of a Circle with Applications to a Shadowing Problem. J. Appl. Prob. 19, 562-577.

Yang, M. H. 1988. Analysis and Optimization of Class-Based Dedicated Storage Systems. Report TD-88-07, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Yang, T., and J. G. C. Templeton. 1987. A Survey on Retrial Queues. Queueing Systems 2, 201-233.

Yates, B. D. 1989. No Room for Automations in the Automated Warehouse. Proc. of the 10th International Conference on Automation in Warehousing, 149-154.

Yoon, C. S., and G. P. Sharp. 1990. Development of an Intelligent Workstation for Order Pick System Analysis and Design. Working Paper, Material Handling Research Center, Georgia Institute of Technology, Atlanta, Georgia.

Zollinger, H. A. 1982. Planning, Evaluating and Estimating Storage Systems. Presented at the 1st Annual Simulation Winter Seminar, Institute of Matrial Management, Orlando, Florida.