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The Inventory Replenishment Planning and Staggering Problem Revisited
Fayez F. Boctor
Marie-Claude Bolduc

May 2012

CIRRELT-2012-19

Document de travail également publié par la Faculté des sciences de l’administration de l’Université Laval, sous le numéro FSA-2012-002.

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Université de Montréal
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Montréal (Québec)
Canada H3C 3J7
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Université Laval
2325, de la Terrasse, bureau 2642
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Télécopie : 418 656-2624

www.cirrelt.ca

The Inventory Replenishment Planning and Staggering
Problem Revisited
Fayez F. Boctor*, Marie-Claude Bolduc
Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation
(CIRRELT) and Department of Operations and Decision Systems, 2325, de la Terrasse,
Université Laval, Québec, Canada G1V 0A6

Abstract. This paper reconsiders the inventory replenishment problem and emphasises the fact that it is a multi-objective problem where, in addition to minimizing the sum of order and inventory holding costs, we should optimize the usage of storage resources.
The paper proposes a mathematical formulation of the problem, suggests two heuristic solution approaches, and assesses their performance.
Keywords. Inventory replenishment planning and staggering, lot sizing, heuristics.
Acknowledgements. This research work was partially supported by grants OPG0036509 from the Natural Sciences and Engineering Research Council of Canada (NSERC), and by a grant from Université Laval. This support is gratefully acknowledged.

Results and views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect those of CIRRELT.
Les résultats et opinions contenus dans cette publication ne reflètent pas nécessairement la position du
CIRRELT et n



References: Anily S., 1991, Multi-item replenishment and storage problem (MIRSP): heuristics and bounds, Operations Research, 39, 233-243. Boctor F. F., 2010, Offsetting inventory replenishment cycles to minimize storage space, European Journal of Operational Research, 203, 321-325. Deb K., A. Pratap, S. Agarwal and T. Meyarivan, 2002, A fast and elitist multi-objective Genetic algorithm: NSGA-II, IEEE Transactions on evolutionary computation, 6, Gallego G., D. Shaw, and D. Simchi-Levi, 1992.The complexity of the staggering problem and other classical inventory problems, Operations Research Letters 12, Gallego G., M. Queyranne, and D. Simchi-Levi, 1996, Single resource multi-item inventory systems, Operations Research, 44, 580-595. Goyal S.K., 1978, A note on Multi-production inventory situation with one restriction, Journal of Operational Research Society, 29, 269-271. Hall N. G., 1998, A comparison of inventory replenishment heuristics for minimizing maximum storage, American Journal of Mathematical and Management Sciences Hariga M.A. and P.L. Jackson, 1995, Time variant lot sizing models for the warehouse scheduling problem, IIE Transaction 27, 162-170. Kasprzak E., and K. Lewis, 2001, Pareto Analysis in Multiobjective Optimization Using the Colinearity Theorem and Scaling Method, Structural and Multidisciplinary Optimization, Konak A., D.W. Coit and A.E. Smith, 2006, Multi-objective optimization using Genetic Algorithms: A Tutorial, Reliability Engineering and System Safety, 91, 992-1007. Marler R.T. and J.S. Arora, 2004, Survey of multi-objective optimization methods for engineering, Structural and Multidisciplinary Optimization, 26, 369-395. Murthy N.N., W. C. Benton and P. A. Rubin, 2003, Offsetting inventory cycles of items sharing storage, European Journal of Operational Research, 150, 304-319. Page E. and R.J. Paul, 1976, Multi-production inventory situation with one restriction, Journal of Operational Research Society 27, 815-834. Rosenblatt M.J. and U.G. Rothblum, 1990, On the Single Resource Capacity Problem for Multi-Item Inventory Systems, Operations Research, 38, 686-693. Teo C.P., J. Ou and K. Tan, 1998, Multi-Item Inventory Staggering Problems: Heuristics and Bounds, Proceedings of the ninth annual ACM-SIAM symposium on discrete algorithms, 1998, 584-593. Van Veldhuizen D.A. and G.B. Lamont, 2000, Multi-objective evolutionary algorithms: Analyzing the state of the art, Evolutionary Computation, 8, 125-147. Zitzler E., K. Deb and L. Thiele, 2000, Comparison of Multi objective evolutionary algorithms: Empirical results, Evolutionary Computation, 8, 173-195. Zitzler E., M. Laumanns and L. Thiele, 2001, SPEA 2: Improving the strength Pareto evolutionary algorithm, TIK report 103, Swiss Federal Institute of Technology, Zoller K., 1977, Deterministic multi-item inventory systems with limited capacity, Management Science, 24, 451-455.

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