Chapter 6

Mixed-Integer Optimization Approaches for Deterministic and Stochastic Inventory Management

Simge Küçükyavuz
Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210, kucukyavuz.2@osu.edu

Abstract
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 mixedinteger 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 lotsizing problems.

Keywords: lot sizing; service levels; extended formulations; cutting planes; convex hull

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Citation information:

Küçükyavuz, S. Mixed-integer optimization approaches for deterministic and stochastic inventory management. J. Geunes, ed. INFORMS TutORials in Operations Research, Vol. 8. INFORMS, Hanover, MD, pp. 90--105.