The stochastic transportation problem with single sourcing

We propose a branch-and-price algorithm for solving a class of stochastic transportation problems with single-sourcing constraints. Our approach allows for general demand distributions, nonlinear cost structures, and capacity expansion opportunities. The pricing problem is a knapsack problem with variable item sizes and concave costs that is interesting in its own right. We perform an extensive set of computational experiments illustrating the efficacy of our approach. In addition, we study the cost of the single-sourcing constraints.

[1]  J. F. Benders,et al.  A property of assignment type mixed integer linear programming problems , 1982 .

[2]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[3]  E. Balas,et al.  Set Partitioning: A survey , 1976 .

[4]  H. Romeijn,et al.  The continuous‐time single‐sourcing problem with capacity expansion opportunities , 2005 .

[5]  Kaj Holmberg,et al.  Efficient decomposition and linearization methods for the stochastic transportation problem , 1995, Comput. Optim. Appl..

[6]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[7]  G. Ribiere,et al.  Experiments in mixed-integer linear programming , 1971, Math. Program..

[8]  A. Williams.  A Stochastic Transportation Problem , 1963 .

[9]  Zuo-Jun Max Shen,et al.  A Joint Location - Inventory Model , 2003, Transp. Sci..

[10]  Chung-Piaw Teo,et al.  Warehouse-Retailer Network Design Problem , 2004, Oper. Res..

[11]  Lap Mui Ann Chan,et al.  On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures , 2002, Oper. Res..

[12]  Martin W. P. Savelsbergh,et al.  A Branch-and-Price Algorithm for the Generalized Assignment Problem , 1997, Oper. Res..

[13]  Jean-Baptiste Hiriart-Urruty,et al.  On optimality conditions in nondifferentiable programming , 1978, Math. Program..

[14]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[15]  H. Edwin Romeijn,et al.  Designing two-echelon supply networks , 2007, Eur. J. Oper. Res..

[16]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[17]  Bala Shetty,et al.  The nonlinear knapsack problem - algorithms and applications , 2002, Eur. J. Oper. Res..

[18]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[19]  A. Lau,et al.  The newsstand problem: A capacitated multiple-product single-period inventory problem , 1996 .

[20]  Albert P. M. Wagelmans,et al.  A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem , 1999, Oper. Res..