Valid inequalities and extended formulations for lot-sizing and scheduling problem with sequence-dependent setups
- Authors
- Lee, Younsoo; Lee, Kyungsik
- Issue Date
- Oct-2023
- Publisher
- ELSEVIER
- Keywords
- Production; Lot -sizing and scheduling problem; Sequence -dependent setup; Valid inequality; Extended formulation
- Citation
- EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v.310, no.1, pp 201 - 216
- Pages
- 16
- Journal Title
- EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
- Volume
- 310
- Number
- 1
- Start Page
- 201
- End Page
- 216
- URI
- https://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/49590
- DOI
- 10.1016/j.ejor.2023.03.003
- ISSN
- 0377-2217
1872-6860
- Abstract
- In this paper, we propose new valid inequalities and extended formulations for the lot-sizing and schedul-ing problem with sequence-dependent setups, which are derived by investigating the single-period sub-structure of the problem. Specifically, we derive two new families of valid inequalities and identify their facet-defining conditions. Additionally, we demonstrate that these inequalities can be separated in poly-nomial time. After introducing the existing extended formulations for the problem, we provide new ex-tended formulations adapting decision variables representing the time-flow and compare the theoretical strengths of the various formulations and valid inequalities, including the proposed ones. Finally, we con-duct computational experiments to demonstrate the effectiveness of the proposed inequalities and for-mulations. The test results indicate that the proposed inequalities and extended formulations facilitate tightening the linear programming relaxation bounds.(c) 2023 Elsevier B.V. All rights reserved.
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