Title: Solving a multi-echelon inventory-location problem utilising an efficient Lagrangian relaxation-based heuristic

Authors: Sanaz Khalaj Rahimi; Mehdi Seifbarghy; Davar Pishva

Addresses: Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran ' Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran ' Faculty of Asia Pacific Studies, Ritsumeikan Asia Pacific University, 1-1 Jumonjibaru, Beppu, Oita 874-8577, Japan

Abstract: This paper considers an integrated inventory-location problem in which a single product is supplied and distributed through a multi-echelon supply chain including a number of suppliers, distribution centres (DCs), and retailers. It adopts the well-known periodic review inventory control policy (R, S) at DCs. The problem is formulated as a mixed integer nonlinear programming problem and is solved utilising a Lagrangian relaxation-based heuristic. One of its main focuses is to reduce processing time, particularly when dealing with large-size problems. This is achieved via an additional step which converts the lower bound of the Lagrangian relaxation algorithm to an appropriate upper bound. Furthermore, we examine all the combinations of the constraints of the model when selecting constraints to be relaxed. The computational results confirm the efficiency of the proposed approach (i.e., an obtained average time of around 8 minutes with an optimality distance of less than 3%).

Keywords: supply chain management; location-inventory; mixed nonlinear integer programming; Lagrangian relaxation.

DOI: 10.1504/IJLSM.2023.129371

International Journal of Logistics Systems and Management, 2023 Vol.44 No.3, pp.369 - 402

Received: 28 Dec 2019
Accepted: 03 Feb 2021
Published online: 07 Mar 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article