TY - JOUR
T1 - The cost allocation problem for the first order interaction joint replenishment model
AU - Anily, Shoshana
AU - Haviv, Moshe
PY - 2007/3
Y1 - 2007/3
N2 - 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.
AB - 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.
KW - Deterministic
KW - Games: cooperative
KW - Inventory/production: infinite-horizon
KW - Lot-sizing
KW - Multiretailer
UR - http://www.scopus.com/inward/record.url?scp=34247492208&partnerID=8YFLogxK
U2 - 10.1287/opre.1060.0346
DO - 10.1287/opre.1060.0346
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AN - SCOPUS:34247492208
SN - 0030-364X
VL - 55
SP - 292
EP - 302
JO - Operations Research
JF - Operations Research
IS - 2
ER -