Network planning with random demand

We study a planning problem associated with networks for private line services. In these networks, demands are known to exhibit considerable variability, and as such, they should be treated as random variables. The proposed planning model is a two-stage stochastic linear program (SLP) with recourse. Due to the enormous size of the deterministic equivalent, we choose a sampling based algorithm calledstochastic decomposition (SD). For very large-scale SLPs, such as the ones solved in this application, SD provides an effective methodology. The model presented in this paper is validated by using a detailed simulation of the network. We report results with a network that has 86 demand pairs, 89 links and 706 potential routes.

[1]  R. Wets,et al.  L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING. , 1969 .

[2]  R. H. Cardwell,et al.  Design and optimization of networks with dynamic routing , 1981, The Bell System Technical Journal.

[3]  A. Soyster,et al.  Electric Utility Capacity Expansion Planning with Uncertain Load Forecasts , 1982 .

[4]  Roger J.-B. Wets,et al.  Stochastic Programming: Solution Techniques and Approximation Schemes , 1982, ISMP.

[5]  A. Ionescu-Graff.  A sequential projection algorithm for special-services demand , 1982, The Bell System Technical Journal.

[6]  D. R. Smith.  A model for special-service circuit activity , 1983, The Bell System Technical Journal.

[7]  K. Kiwiel.  Methods of Descent for Nondifferentiable Optimization , 1985 .

[8]  K. Krishnan,et al.  State-dependent routing for telephone traffic: Theory and results , 1986, 1986 25th IEEE Conference on Decision and Control.

[9]  Yuri Ermoliev,et al.  Numerical techniques for stochastic optimization , 1988 .

[10]  Yuri Ermoliev,et al.  Stochastic quasigradient methods. Numerical techniques for stochastic optimization , 1988 .

[11]  Linus Schrage,et al.  OR Practice - A Scenario Approach to Capacity Planning , 1989, Oper. Res..

[12]  George B. Dantzig,et al.  Parallel processors for planning under uncertainty , 1990 .

[13]  Julia L. Higle,et al.  Statistical verification of optimality conditions for stochastic programs with recourse , 1991, Ann. Oper. Res..

[14]  Julia L. Higle,et al.  Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse , 1991, Math. Oper. Res..

[15]  Gerd Infanger,et al.  Monte Carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs , 1991, Ann. Oper. Res..

[16]  Robert Doverspike,et al.  Comparison of Routing Methods for DCS-Switched Networks , 1993 .

[17]  Julia L. Higle,et al.  Solution of Large Scale Stochastic Programs with Stochastic Decomposition Algorithms , 1994 .