Multi-Period Profit-Oriented Location Routing Problem in Multi-User Warehouses with Backordering and Order Acceptance: A Relax-Fix-Optimize Heuristic

Mohammed Rida Ech-Charrat (), Najlae Zhani (), Kaoutar Chargui and Tarik Zouadi ()
Additional contact information
Mohammed Rida Ech-Charrat: ENSATE, University of Abdelmalek Essaadi, Tetouan, Morocco
Najlae Zhani: Rabat Business School, BEAR Lab, International University of Rabat, Technopolis Shore, Rocade 11100, Sala Al Jadida, Morocco
Kaoutar Chargui: Rabat Business School, BEAR Lab, International University of Rabat, Technopolis Shore, Rocade 11100, Sala Al Jadida, Morocco
Tarik Zouadi: Rabat Business School, BEAR Lab, International University of Rabat, Technopolis Shore, Rocade 11100, Sala Al Jadida, Morocco

Asia-Pacific Journal of Operational Research (APJOR), 2025, vol. 42, issue 03, 1-25

Abstract: This paper addresses profit maximization in location routing problem (LRP) where backordering is allowed and serving all customers is not mandatory. The problem is motivated by the practical case of distribution companies using temporary multi-user warehouses to serve their customers. We propose a multi-period novel mixed integer linear programming (MILP) model for the problem where demand is price sensitive. The model seeks to find optimal locations of warehouses over the planning horizon, set of orders to serve, to backorder or to reject, and routing decisions giving optimal profit. The commercial solver (CPLEX) is used to solve the model on small instances. For medium and large instances, we propose a solution approach that incorporates the Relax and Fix (R&F), Fix and Optimize (F&O) procedures combined with local search heuristics. Computational experiments and economic analysis show the relevance of the proposed approach and the impact of parameters on generated profit.

Keywords: Location routing problem; backordering; profit maximization; price-sensitive demand; mixed linear integer programming; relax and fix; fix-and-optimize; local search (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595924500180
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:42:y:2025:i:03:n:s0217595924500180

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595924500180

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().