H. Milton Stewart School of Industrial and Systems Engineering

Georgia Institute of Technology

765 Ferst Drive NW

Atlanta, GA 30332

Office: Groseclose 427

atoriello

I am an assistant professor in Industrial Engineering at Georgia Tech. I am interested in the theory and applications of supply chain and logistics models primarily involving transportation and inventory decisions, and in related optimization topics. The methodologies I use to study these problems include linear, mixed-integer and dynamic programming.

My CV. (Last updated May 29, 2014.)

**Submitted or Under Review**

- M. Poremba* and A. Toriello. A Dynamic Programming-Based Branch-and-Bound Heuristic for Traveling Salesman Problems. Submitted 2014.

We propose a branch-and-bound heuristic for the TSP and its variants based on applying branch-and-bound techniques to the DP formulation.

- L. Rademacher, A. Toriello and J.P. Vielma. On Blocking and Anti-Blocking Polyhedra in Infinite Dimensions. Submitted 2014.

We study the natural extensions of blocking and anti-blocking polyhedra to arbitrary dimensions and give sufficient conditions for complementary slackness and integrality of extreme points.

- A. Toriello. Equivalence of an Approximate Linear Programming Bound with the Held-Karp Bound for the Traveling Salesman Problem. Working paper, 2014.

We show that an

*approximate linear programming*(ALP) bound for the TSP, introduced in earlier work, is equivalent to the well-known Held-Karp bound. We then show how the ALP bound can be extended to several TSP variants. - W. Hu*, M.S. Lavieri, A. Toriello and X. Liu. Strategic Health Workforce Planning. Submitted 2014.

We propose an infinite linear programming model for long-term workforce planning of a single worker type, e.g. nurses, in a large health care system. We give a series of conditions a system of this kind should satisfy, and use them to prove the optimality of a natural lookahead policy.

Honorable Mention, INFORMS SPPSN Best Paper Award, 2013. - J. Woodruff, W.B. Haskell and A. Toriello.
*Optimized Financial Systems*Helps Customers Meet their Personal Finance Goals with Optimization. Submitted 2013.

We explain how

*Optimized Financial Systems*uses customers' financial information and actuarial data in an optimization model to give recommendations on investments and tax planning, particularly focused on individual retirement arrangements (IRAs).

**Published or Accepted**

- A. Toriello, W.B. Haskell and M. Poremba*. A Dynamic Traveling Salesman Problem with Stochastic Arc Costs. To appear in
*Operations Research*, 2014.

We propose a TSP with stochastic arc costs in which the salesman can observe outgoing arc costs at every city before choosing where to go next. We use approximate linear programming to tractably bound the problem and construct high-quality policies.

- C. Nguyen*, M. Dessouky and A. Toriello. Consolidation Strategies for the Delivery of Perishable Products.
*Transportation Research Part E: Logistics and Transportation Review*. 69:108-121, 2014.

We study an agricultural supply chain with stochastic demand for perishable goods, where several suppliers can save on transportation costs by consolidating shipments, and propose a simple look-ahead heuristic.

- A. Toriello. Optimal Toll Design: A Lower Bound Framework for the Asymmetric Traveling Salesman Problem.
*Mathematical Programming*. 144:247-264, 2014.

We propose a framework of lower bounds for the asymmetric TSP based on approximating the dynamic programming formulation. We then introduce an exact reformulation that generates a family of polynomially-solvable, successively tighter lower bounds. We show that the base member of this family yields a bound greater than or equal to the well-known Held-Karp bound.

- A. Toriello and N.A. Uhan. Dynamic Cost Allocation for Economic Lot Sizing Games.
*Operations Research Letters*. 42:82-84, 2014.

For lot sizing situations in which multiple retailers or producers can pool orders, we construct allocations dynamically over time so that costs are met as they are incurred and no one has the incentive to defect at any point.

- A. Toriello and N.A. Uhan. On Traveling Salesman Games with Asymmetric Costs.
*Operations Research*, 61:1429-1434, 2013. (Technical note.)

We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. Using a variant of the Held-Karp relaxation and its dual, we construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem.

- C. Nguyen*, A. Toriello, M. Dessouky and J. Moore. Evaluation of Transportation Practices in the California Cut Flower Industry.
*Interfaces*. 43:182-193, 2013.

We evaluate the California cut flower industry’s current transportation practices and investigate the feasibility and cost of establishing a shipping consolidation center in Oxnard, California.

- D. Papageorgiou, A. Toriello, G. Nemhauser and M. Savelsbergh. Fixed-Charge Transportation with Product Blending.
*Transportation Science*. 46:281-295, 2012.

We introduce a fixed-charge transportation problem with linear product blending and give a polyhedral analysis. Applications include transportation problems in the petrochemical, energy and agriculture industries.

- A. Toriello and J.P. Vielma. Fitting a Continuous Piecewise Linear Function.
*European Journal of Operational Research*. 219:86-95, 2012.

We study models for piecewise linear data fitting (regression), including new mixed-binary models with variable regions. Applications include approximate inventory valuation.

- A. Toriello and G. Nemhauser. The Value Function of an Infinite-Horizon Single-Item Lot-Sizing Problem.
*Operations Research Letters*. 40:12-14, 2012.

We characterize the value function of a discounted, infinite-horizon variant of the single-item production lot-sizing problem and show that it inherits several structural properties from finite mixed-integer program value functions.

- A. Toriello, G. Nemhauser and M. Savelsbergh. Decomposing Inventory Routing Problems with Approximate Value Functions.
*Naval Research Logistics*. 57:718-727, 2010.

We introduce a time decomposition for inventory routing problems that depends on approximately valuing inventories at suppliers and consumers. Computational experiments use maritime inventory routing instances.

- F. Kılınç-Karzan, A. Toriello, S. Ahmed, G. Nemhauser and M. Savelsbergh. Approximating the Stability Region for Binary Mixed-Integer Programs.
*Operations Research Letters*. 37:250-254, 2009.

We develop an algorithm to calculate how stable a solution to a binary mixed-integer program is with respect to cost changes. Applications include real-time decision making scenarios, such as iterative combinatorial auctions.

**Miscellaneous**

- A. Toriello. Time Decomposition of Multi-Period Supply Chain Models. Ph.D. Thesis. Georgia Institute of Technology, December 2010.
- A. Toriello. A Brief Lecture on Submodular Functions.

* Indicates supervised student co-author.

- The One-Dimensional Dynamic Dispatch Waves Problem.

International Conference on Logistics and Maritime Systems (LOGMS). Rotterdam, the Netherlands. August, 2014.

- Dynamic Linear Production Games under Uncertainty.

Operations/Management Science Workshop. Booth School of Business, University of Chicago. Chicago, Illinois. December, 2013.

- Cooperative Traveling Salesman Games with Asymmetric Costs.

Department of Industrial and Operations Engineering, University of Michigan. Ann Arbor, Michigan. November, 2013.

- Equivalence of Two TSP Bounds.

INFORMS Annual Meeting. Minneapolis, Minnesota. October, 2013.

- On Traveling Salesman Games with Asymmetric Costs.

DOS Seminar Series. Stewart School of Industrial and Systems Engineering, Georgia Tech. Atlanta, Georgia. September, 2013.

- Dynamic Programming Approximations for Traveling Salesman Problems.

Tutte Seminar Series. Department of Combinatorics and Optimization, University of Waterloo. Waterloo, Ontario. May, 2013.

- Associate Editor, Optimization Methods and Software.
- Program Committee, LAGOS 2013.

VII Latin American Algorithms, Graphs and Optimization Symposium. Playa del Carmen, Mexico. April, 2013

**ISyE 3133 - Engineering Optimization**

- Spring 2009

**ISyE 4301 - Supply Chain Economics**

- Spring 2014

**ISyE 7203 - Logistics Systems Engineering**

- Fall 2013, Fall 2014

**ISE 330 - Introduction to Operations Research: Deterministic Models (USC)**

- Fall 2010, Fall 2012

**ISE 532 - Network Flows (USC)**

- Fall 2011, Spring 2012, Spring 2013

Shabbir Ahmed, Christiane Barz, Dan Dadush, Maged Dessouky, Alan Erera, Ricardo Fukasawa, Will Haskell, Fatma Kılınç-Karzan, Mariel Lavieri, Jim Moore, George Nemhauser, Dimitri Papageorgiou, Luis Rademacher, Martin Savelsbergh, Nelson Uhan, Juan Pablo Vielma, Joshua Woodruff.