A fundamental problem arising in every supply chain is how to determine order lot sizes and inventory levels to meet customer demands with high service levels while maintaining low costs. This problem is challenging both theoretically and computationally. It includes concave costs representing economies-of-scale. It is dynamic and subject to uncertainty in demands, costs, and lead times. In addition, service-level restrictions may result in chance constraints. In this tutorial, we survey recent mixed-integer optimization models and methods for various lot-sizing and inventory control problems. We consider problems when demand is dynamic and deterministic, and when demand is random, following a discrete and finite nonstationary distribution over a finite planning horizon. We use polyhedral combinatorics to develop cutting planes to tighten the original mixed-integer formulations. In addition, we show how a polynomial dynamic program to solve a subproblem can be used to develop a strong extended formulation. We summarize computational experiments that illustrate the effectiveness of these methods in solving difficult capacitated multi-item order lot-sizing problems.
|Original language||English (US)|
|Title of host publication||INFORMS TutORials in Operations Research|
|Number of pages||16|
|State||Published - 2014|