Table of ContentsLogistics Systems Design: Layout Models Layout Models Overview Program Classification Layout Models Overview Conceptual Block Layout Quadratic Assignment Problem Quadratic Assignment Formulation Quadratic Set Packing Problem Quadratic Set Packing Formulation Linear Assignment Problem Linear Assignment Formulation Factoring Condition Simplification Aisles Characteristics Aisle and Station Graph Layout Models Overview Relationship Diagram Dual Planar Diagram and Layout Maximum Planar Subgraph Problem Deltahedron Heuristic Hexagonal Adjacency Graph Hexagonal Adjacency Graph Heuristic Hexagonal Adjacency Graph Upper Bound Formulation Perimeter Specified Adjacency Matching Graph Perimeter Specified Adjacency Matching Formulation Layout Models Overview Block Layout With Shape Constraints Variables Illustration Shape Constraints Perimeter Complexity Factor Shape Ratio versus Perimeter Complexity Factor Tiny Layout Example: Department Data Tiny Layout Example: Building Data Discrete Formulation: Assignment Constraints Discrete Formulation: Boundary Coordinates Discrete Formulation: Centroid Equations Discrete Formulation: Rectilinear Distance Objective Discrete Formulation: Distance to Outside Objective Discrete Formulation: Distance to Outside Objective Discrete Formulation: Building and Shape Constraints Rectilinear Distance Objective: Positive Relation Rectilinear Distance Objective: Negative Relation Distance for Negative Relation Variable Transformation Distance to Outside Objective: Negative Relation Distance to Outside Objective: Positive Relation Distance to Outside: Variable Transformation Continuous Formulation: Building and Shape Constraints Continuous Formulation: Non-Overlap Constraints Perimeter Length And Area Constraints Minimum Area Based on Perimeter Constraint Tompkins with Max Shape Factor = 2 Area Shrinkage with MIP (MSF = 2) Area Shrinkage with MIP (MSF = 3) Piecewise Linear Approximation of Area Constraint Continuous Formulation: Area Support Constraints Tompkins with Area Constraints, Shape Factor = 2 Optimal Continuous Solution for Tiny Layout (S = 3) Shape Penalty Relaxation Simulated Annealing for Shape Relaxation: Small Cases Simulated Annealing for Shape Relaxation: Intermediate Cases Simulated Annealing for Shape Relaxation: Large Cases Dual Decomposition (Lagrangean Relaxation) Primal (Benders) Decomposition Primal Formulation for the Subproblem Dual Formulation for the Subproblem Dual Extreme Point Formulation of the Subproblem Primal Master Problem |
Author: Marc Goetschalckx
Email: marc.goetschalckx@isye.gatech.edu Home Page: www.isye.gatech.edu/~mgoetsch/index.html Other information: |