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The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands

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Abstract

We develop an algorithm to compute an optimal Q(s,S) policy for the joint replenishment problem when demands follow a compound correlated Poisson process. It is a non-trivial generalization of the work by Nielsen and Larsen (2005). We make some numerical analyses on two-item problems where we compare the optimal Q(s,S) policy to the optimal uncoordinated (s,S) policies. The results indicate that the more negative the correlation the less advantageous it is to coordinate. Therefore, in some cases the degree of correlation determines whether to apply the coordinated Q(s,S) policy or the uncoordinated (s,S) policies. Finally, we compare the Q(s,S) policy and the closely connected P(s,S) policy. Here we explain why the Q(s,S) policy is a better choice if item-demands are correlated.

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  • Larsen, Christian, 2007. "The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands," CORAL Working Papers L-2007-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbls:2007-001
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    1. S G Johansen & P Melchiors, 2003. "Can-order policy for the periodic-review joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 283-290, March.
    2. Edward Ignall, 1969. "Optimal Continuous Review Policies for Two Product Inventory Systems with Joint Setup Costs," Management Science, INFORMS, vol. 15(5), pages 278-283, January.
    3. K. Ohno & T. Ishigaki, 2001. "A multi-item continuous review inventory system with compound Poisson demands," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 147-165, April.
    4. Melchiors, Philip, 2002. "Calculating can-order policies for the joint replenishment problem by the compensation approach," European Journal of Operational Research, Elsevier, vol. 141(3), pages 587-595, September.
    5. Wildeman, R.E. & Frenk, J.B.G. & Dekker, R., 1997. "An efficient optimal solution method for the joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 99(2), pages 433-444, June.
    6. Nielsen, Christina & Larsen, Christian, 2005. "An analytical study of the Q(s,S) policy applied to the joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 163(3), pages 721-732, June.
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    Cited by:

    1. Kjeldsen, Karina Hjortshøj, 2008. "Classification of routing and scheduling problems in liner shipping," CORAL Working Papers L-2008-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.

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    Keywords

    joint replenishment problem; compound correlated Poisson process;

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