Multi-product joint delivery planning in a retailers’ network under resource constraints

Abstract

The main objective of the JRP (joint replenishment problem) is to build a delivery programme so as to satisfy local demands while minimising the total cost including ordering and storage costs. The classical nonlinear formulation of this problem can be seen as a multi-product and multi-site extension of the economic order quantity (EOQ) problem. If demand rates are fixed and known, the problem allows a periodic solution, in which an optimal delivery programme repeats indefinitely. In the unconstrained case, the delivery plan has two levels of periodicity: a global periodicity for the delivery sequence and a particular periodicity for each product and site. The main purpose of this paper is to combine in the same model grouping, transportation, and storage issues. Constraints on transportation capacity and routing are introduced in a linear reformulation of the problem, leading to a better coordination of delivery schedules with respect to products and sites. The superiority of the proposed method is that it provides the optimal route of delivery for each tour and permits minimisation of the maximal delivery capacity, whereas other existing methods could not offer such important features.

Keywords:

• inventory theory
• joint replenishment problem
• mixed integer linear programming
• Lagrangian relaxation
• optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Mouna Rahmouni

Mouna Rahmouni was born in Tunis, Tunisia in 1984. She received a MS degree in Control and Manufacturing from University of Tunis and is currently a Doctoral Student in Computer Science at the LSIS Laboratory of Aix-Marseille University and in Electrical Engineering at the SIME Laboratory of ENSIT in University of Tunis.

Jean-Claude Hennet

Jean-Claude Hennet is a Senior Researcher of the French Research Center (CNRS). He is a member of the LSIS Laboratory and the head of the FRIIAM Research Federation in Marseilles, France. He graduated from the Ecole Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France, in 1974, received a MS degree in Industrial Engineering from Stanford University, California (1975), a Docteur-Ingénieur degree from INSA-Toulouse in 1978 and a degree of Docteur d'Etat from University Paul Sabatier, Toulouse in 1982. His research interests are in the fields of Optimization and Game Theory applied to Manufacturing and Logistics. For more information, please visit the web site: http://www.lsis.org/hennetjc.

Farhat Fnaiech

Farhat Fnaiech (M'85, SM'01) was born in La Chebba, Tunisia, in 1955. He received the BSc degree in mechanical engineering, the MSc degree in electrical engineering, the PhD degree, and the DSc degree from the University of Tunis, Tunis, Tunisia, in 1978, 1980, 1983, and 1999, respectively. He is currently a Professor with the Ecole Superieure des Sciences and Techniques of Tunis (ESSTT). He has published more than 200 research papers in many journals and international conferences. He has been the General Chairman and member of the international board committee of many international conferences. His main interest research areas are nonlinear adaptive signal processing, nonlinear control of power electronic devices, digital signal processing, image processing, intelligent techniques, and control. His is an Associate Editor of the IEEE Transactions Industrial Electronics. He has served as IEEE Chapter committee coordination sub- committee delegate of Africa Region 8 and Vice Chair of IEEE Tunisia Section. Recently, he has been appointed as an AdCom member in the IEEE Industrial Electronics Society