Models and Algorithms for Distribution Problems with Uncertain Demands

We consider the problem of distributing goods from one or more plants through a set of warehouses in anticipation of forecasted customer demands. Two results are provided in this paper. First, we present a methodology for approximating stochastic distribution problems that are computationally tractable for problems of realistic size. Comparisons are made to standard deterministic formulations and shown to give superior results. Then, we compare logistics networks with varying degrees of redundancy represented by the number of warehouses which serve each customer. Overlapping service regions for warehouses provides additional flexibility to handle real-time demands. We quantify the expected savings that might result from such strategies.

[1]  Yiannis Gabriel,et al.  Logistics of Production and Inventory , 1993, Handbooks in Operations Research and Management Science.

[2]  R. Wets.  Stochastic Programs with Fixed Recourse: The Equivalent Deterministic Program , 1974 .

[3]  U. Karmarkar,et al.  The one‐period, N‐location distribution problem , 1977 .

[4]  Darwin Klingman,et al.  A Multi-Period Production, Distribution, and Inventory Planning Model, , 1979 .

[5]  J. Aronson,et al.  A forward network simplex algorithm for solving multiperiod network flow problems , 1986 .

[6]  Jay E. Aronson,et al.  A survey of dynamic network flows , 1989 .

[7]  Stein W. Wallace,et al.  Solving stochastic programs with network recourse , 1986, Networks.

[8]  Warren B. Powell,et al.  An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management , 1996, Oper. Res..

[9]  Warren B. Powell,et al.  Stochastic programs over trees with random arc capacities , 1994, Networks.

[10]  Warren B. Powell,et al.  A network recourse decomposition method for dynamic networks with random arc capacities , 1994, Networks.

[11]  W. Zangwill.  A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[12]  U. Karmarkar.  Convex/stochastic programming and multilocation inventory problems , 1979 .

[13]  James F. Robeson,et al.  The Distribution Handbook , 1984 .

[14]  Uday S. Karmarkar.  The Multilocation Multiperiod Inventory Problem: Bounds and Approximations , 1987 .

[15]  Jeremy F. Shapiro,et al.  Mathematical programming models and methods for production planning and scheduling , 1988 .

[16]  R. Ballou.  Business Logistics Management , 1991 .

[17]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[18]  John M. Mulvey,et al.  Formulating Two-Stage Stochastic Programs for Interior Point Methods , 1991, Oper. Res..

[19]  Uday S. Karmarkar,et al.  The Multiperiod Multilocation Inventory Problem , 1981, Oper. Res..

[20]  Roger J.-B. Wets,et al.  The aggregation principle in scenario analysis stochastic optimization , 1989 .