The Cost Allocation Problem for the First Order Interaction Joint Replenishment Model

Shoshana Anily () and Moshe Haviv ()
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Shoshana Anily: Recanati School of Management, Tel Aviv University, Tel Aviv 69978, Israel
Moshe Haviv: Department of Statistics, The Hebrew University of Jerusalem, Jerusalem 91905, Israel

Operations Research, 2007, vol. 55, issue 2, 292-302

Abstract: We consider an infinite-horizon deterministic joint replenishment problem with first order interaction. Under this model, the setup transportation/reorder cost associated with a group of retailers placing an order at the same time equals some group-independent major setup cost plus retailer-dependent minor setup costs. In addition, each retailer is associated with a retailer-dependent holding-cost rate. The structure of optimal replenishment policies is not known, thus research has focused on optimal power-of-two (POT) policies. Following this convention, we consider the cost allocation problem of an optimal POT policy among the various retailers. For this sake, we define a characteristic function that assigns to any subset of retailers the average-time total cost of an optimal POT policy for replenishing the retailers in the subset, under the assumption that these are the only existing retailers. We show that the resulting transferable utility cooperative game with this characteristic function is concave. In particular, it is a totally balanced game, namely, this game and any of its subgames have nonempty core sets. Finally, we give an example for a core allocation and prove that there are infinitely many core allocations.

Keywords: inventory/production; infinite-horizon; deterministic; multiretailer; lot-sizing; games; cooperative (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (27)

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