4OR-Q J Oper Res DOI 10.1007/s10288-017-0362-2 RESEARCH PAPER The inventory replenishment planning and staggering problem: a bi-objective approach Fayez F. Boctor 1 · Marie-Claude Bolduc 1 Received: 7 April 2016 / Revised: 17 October 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract To the best of our knowledge, this paper is the first one to suggest formu- lating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions. Keywords Evolutionary algorithms · Multi-criteria decision making · Pareto optimization · Inventory management · Heuristics Mathematics Subject Classification 90B05 · 90B50 1 Introduction The inventory replenishment planning problem is a central problem in the area of sup- ply chain management. It involves two important decisions: The lot sizing decision or the determination of the quantities to order, and the determination of replenishment dates (or schedule). Several objectives may be taken into consideration in making these B Fayez F. Boctor fayez.boctor@fsa.ulaval.ca 1 Centre interuniversitaire de recherché sur les réseaux d’entreprises, la logistique et le transport (CIRRELT), Faculté des sciences de l’administration, Université Laval, Quebec City, Canada 123