## ABSTRACT

ABSTRACT In today’s global business environment, an effective and reliable supply chain substantially increases a company’s competitive advantage. Supply chain management has played a crucial role in a business’s success. Optimization has been sought to model and solve many of these supply chain problems. However, as the size of the optimization model grows, the difficulty of finding the optimal or near-optimal solution typically grows exponentially. Nested partitions is one of the algorithms developed to tackle these large-scale optimization problems. In this chapter, the nested partitions method, and its implementation in two critical supply chain problems, are reviewed. One problem is the intermodal hub location problem, a special case of facility location problems, and the other is the multilevel capacitated

CONTENTS

5.1 Introduction ................................................................................................ 124 5.1.1 Supply Chain and Supply Chain Management ......................... 124 5.1.2 Supply Chain Optimization ......................................................... 126

5.2 Nested Partitions and Large-Scale Optimization ................................. 128 5.2.1 Large-Scale Discrete Optimization ............................................. 128 5.2.2 Nested Partitions Overview ......................................................... 129

5.3 Nested Partitions for Facility Location ................................................... 133 5.3.1 Mathematical Model ...................................................................... 133 5.3.2 Hybrid NP and Mathematical Programming Algorithm ........ 135

5.3.2.1 Sampling........................................................................... 136 5.3.2.2 Calculating the Promising Index .................................. 137 5.3.2.3 Partitioning, Backtracking, and Stopping ................... 137

5.3.3 Computational Results .................................................................. 138 5.4 Nested Partitions for Production Planning ........................................... 139

5.4.1 Mathematical Model ...................................................................... 140 5.4.2 Lower and Upper Bound Guided Nested Partitions ................ 142 5.4.3 Computational Results .................................................................. 144

5.5 Conclusions ................................................................................................. 145 References ............................................................................................................. 146

lot-sizing problem with backlogging, a complex problem in production planning. The computational results show that the hybrid nested partitions approaches are superior to standard mathematical programming and specialized heuristic approaches, and thus provide an effective alternative in enhancing supply chain performance.