A Decomposition Algorithm for Single and Multiobjective Integrated Market Selection and Production Planning

Wilco van den Heuvel*, Semra Aǧrali, Z. Caner Taşkin

*Corresponding author for this work

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Abstract

We study an integrated market selection and production planning problem. There is a set of markets with deterministic demand, and each market has a certain revenue that is obtained if the market's demand is satisfied throughout a planning horizon. The demand is satisfied with a production scheme that has a lot-sizing structure. The problem is to decide on which markets' demand to satisfy and plan the production simultaneously. We consider both single and multiobjective settings. The single objective problem maximizes the profit, whereas the multiobjective problem includes the maximization of the revenue and the minimization of the production cost objectives. We develop a decomposition-based exact solution algorithm for the single objective setting and show how it can be used in a proposed three-phase algorithm for the multiobjective setting. The master problem chooses a subset of markets, and the subproblem calculates an optimal production plan to satisfy the selected markets' demand. We investigate the subproblem from a cooperative game theory perspective to devise cuts and strengthen them based on lifting. We also propose a set of valid inequalities and preprocessing rules to improve the proposed algorithm. We test the efficacy of our solution method over a suite of problem instances and show that our algorithm substantially decreases solution times for all problem instances.

Original languageEnglish
Pages (from-to)1439-1453
Number of pages15
JournalINFORMS Journal on Computing
Volume35
Issue number6
DOIs
Publication statusPublished - Nov 2023

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© 2023 INFORMS.

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