Replenishment planning for stochastic inventory systems with shortage cost

Rossi, Rémi;Tarim, S.A.;Hnich, B.;Prestwich, S.
(2007) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. 4th International Conference, CPAIOR 2007 — Location: Brussels, Belgium (23.May.2007)

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  • Rossi, RémiUCLouvain
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  • Tarim, S.A.
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  • Hnich, B.
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  • Prestwich, S.
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Abstract
One of the most important policies adopted in inventory control is the (R,S) policy (also known as the "replenishment cycle" policy). Under the non-stationary demand assumption the (R,S) policy takes the form (R/sub n/,S/sub n/) where R/sub n/ denotes the length of the n/sup th/ replenishment cycle, and S/sub n/ the corresponding order-up-to-level. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a CP approach able to compute optimal (R/sub n/,S/sub n/) policy parameters under stochastic demand, ordering, holding and shortage costs. The convexity of the cost-function is exploited during the search to compute bounds. We use the optimal solutions to analyze the quality of the solutions provided by an approximate MIP approach that exploits a piecewise linear approximation for the cost function.
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Rossi, R., Tarim, S. A., Hnich, B., & Prestwich, S. (2007). Replenishment planning for stochastic inventory systems with shortage cost. In Van Hentenryck, P.; Wolsey, L.; (ed.), Integration of AI and OR Techniques in Constraint Programming forCombinatorial Optimization Problems. Proceedings 4th InternationalConference, CPAIOR 2007 (p. p. 229-243). Springer-verlag. https://hdl.handle.net/2078.5/230377