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RESEARCH ARTICLE

Multiple item economic lot sizing problem with inventory dependent demand

Duru Balpınarlı1 ,  Mehmet Önal1*
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1 Department of Industrial Engineering, Özyeğin University, Çekmeköy, İstanbul, Türkiye
IJOCTA, 1676 https://doi.org/10.36922/ijocta.1676
Submitted: 5 September 2024 | Accepted: 5 February 2025 | Published: 20 March 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

We consider a multiple item Economic Lot Sizing problem where the demands for items depend on their stock quantities. The objective is to find a production plan such that the resulting stock levels (and hence demands) maximize total profit over a finite planning horizon. The single item version of this problem has been studied in the literature, and a polynomial time algorithm has been proposed when there are no bounds on production. It has also been proven that the single item version is NP-hard even when there are constant (i.e., time-invariant) finite capacities on production. We extend this single item model by considering multiple items and production capacities. We propose a Lagrangian relaxation method to find an initial solution to the problem. This solution is a hybrid solution obtained by combining two distinct solutions generated in the process of solving the Lagrangian dual problem. Starting with this initial solution, we then implement a Tabu Search algorithm to find better solutions. The performance of the proposed solution method is compared with the performance of a standard commercial software that works on a mixed integer programming formulation of the problem. We show that our solution approach finds better solutions within a predetermined time limit in general.

Keywords
Economic lot-sizing
Inventory dependent demand
Lagrangian relaxation
Tabu search algorithm
Funding
The work was supported by the Scientific and National Research Council of Turkey (T¨UB˙ITAK) under grant no. 119M278.
Conflict of interest
The authors declare that they have no conflict of interest regarding the publication of this article.
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