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Periodic review (s, S) policies for joint replenishment inventory systems

Article Abstract:

A new class of policies is proposed for the joint replenishment problem (JRP) with stochastic demand. JRP is an inventory control problem observed in multiitem, joint replenishment inventory systems where replenishments can be coordinated. The proposed policy, called P(s, S) policy, entails the review of the inventory of each item at fixed and constant time intervals. Computation of the (s, S) policy for each of these items is based on the assumption that the item carries the minor and not the major setup cost. The P(s, S) policy involves more computations than the periodic policies of Atkins and Iyogun (1988), but these additional computational requirements should not be too burdensome due to recent advances in algorithms for computation of (s, S) policies. In addition, the practical implementation of the new policy should not present any problem.

Analysis, Stochastic processes

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A Dynamic Programming Algorithm For Joint Replenishment Under General Order Cost Functions

Article Abstract:

The multi-item joint replenishment problem is generalized to allow ordering costs to be dependent on the specific items jointly supplied. A fixed cycle approach is examined in which all the items of a group are always jointly replenished. A dynamic programming algorithm is developed for partitioning the items into groups, each with its own fixed cycle time, resulting in an optimal fixed cycle replenishment policy.

Management science, Algorithm, Dynamic programming, Production, Inventory Control

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Comment on "a dynamic programming algorithm for joint replenishment under general order cost functions."

Article Abstract:

Rosenblatt and Kaspi's proposed Dynamic Programming algorithm for an optimum partition problem is demonstrated to be incorrect. An alternative Dynamic Programming algorithm is offered for the problem. The alternative algorithm is not guaranteed to provide an optimal solution, and should be considered to be heuristic.

Partitions (Mathematics)

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