Periodic review and joint replenishment in stochastic demand environments

In this paper we consider periodic review systems under stochastic demands. First, we study the single product periodic review problem and propose a simple solution procedure which is near optimal. Then, given the existence of this simple procedure, we study the joint replenishment problem for multiple items under stochastic demands and suggest simple heuristics which provide very good results. We find the simple procedures combined with the robustness of the cost function to be very attractive in other applications which require coordination of cycle times under stochastic demands.

[1]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[2]  Joseph L. Balintfy,et al.  On a Basic Class of Multi-Item Inventory Problems , 1964 .

[3]  Raymond P. Lutz,et al.  Decision rules for inventory management , 1967 .

[4]  S. Goyal.  Determination of Economic Packaging Frequency for Items Jointly Replenished , 1973 .

[5]  E. Silver.  A control system for coordinated inventory replenishment , 1974 .

[6]  S. Goyal.  Determination of Optimum Packaging Frequency of Items Jointly Replenished , 1974 .

[7]  E. Silver.  A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand , 1976 .

[8]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[9]  Samuel D. Conte,et al.  Elementary Numerical Analysis , 1980 .

[10]  Edward A. Silver,et al.  Establishing reorder points in the (S,c,s) coordinated control system under compound Poisson demand , 1981 .

[11]  Meir J. Rosenblatt,et al.  An Improvement of Silver's Algorithm for the Joint Replenishment Problem , 1983 .

[12]  A. Federgruen,et al.  Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands , 1984 .

[13]  W. Maxwell,et al.  The Joint Replenishment Problem with a Powers-of-Two Restriction , 1985 .

[14]  R. Roundy.  98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems , 1985 .

[15]  Robin O. Roundy,et al.  Planning Shipping Intervals in Multi-Item, One-Warehouse, Multi-Retailer Distribution Systems , 1987 .

[16]  Robin Roundy,et al.  A 98%-Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production / Inventory System , 1986, Math. Oper. Res..

[17]  Paul Iyogun,et al.  A heuristic with lower bound performance guarantee for the multi-product dynamic lot-size problem , 1988 .

[18]  Derek A. Atkins,et al.  Periodic Versus Can-Order Policies for Coordinated Multi-Item Inventory Systems , 1988 .

[19]  A. Federgruen,et al.  Simple Power-of-Two Policies are Close to Optimal in a General Class of Production/Distribution Networks with General Joint Setup Costs , 1992 .

[20]  Yu-Sheng Zheng.  On properties of stochastic inventory systems , 1992 .

[21]  Maurice Queyranne,et al.  Lot Sizing Policies for Finite Production Rate Assembly Systems , 1992, Oper. Res..

[22]  Awi Federgruen,et al.  The Joint Replenishment Problem with General Joint Cost Structures , 1992, Oper. Res..

[23]  Awi Federgruen,et al.  The Joint Replenishment Problem with Time-Varying Costs and Demands: Efficient, Asymptotic and ε-Optimal Solutions , 1994, Oper. Res..

[24]  Derek R. Atkins,et al.  98%-Effective Lot Sizing for Series Inventory Systems with Backlogging , 1995, Oper. Res..