In this article, we study a two-level lot-sizing problem with supplier selection (LSS), which is an NP-hard problem arising in different production planning and supply chain management applications. After presenting various formulations for LSS, and computationally comparing their strengths, we explore the polyhedral structure of one of these formulations. For this formulation, we derive several families of strong valid inequalities, and provide conditions under which they are facet-defining. We show numerically that incorporating these valid inequalities within a branch-and-cut framework leads to significant improvements in computation.
Bibliographical noteFunding Information:
The authors wish to thank the two anonymous reviewers and the associate editor for their valuable insights and suggestions that have helped improve the presentation of this article. This project is partially supported by Office of Naval Research Young Investigator Award N000141010749 and National Science Foundation grant CMMI-1200616.
- Cutting planes
- polyhedral study
- supplier selection