Abstract
This paper presents two contributions: A set of routines that manipulate instances of stochastic programming problems in order to make them more amenable for different solution approaches; and a development environment where these routines can be accessed and in which the modeler can examine aspects of the problem structure. The goal of the research is to reduce the amount of work, time, and cost involved in experimenting with different solution methods.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Benders, J.F. (1962). “Partitioning Procedures for Solving Mixed Variables Programming Problems.” Numerische Mathematik 4, 238–252.
Birge, J., M. Dempster, H. Gassmann, E. Gunn, A. King, and S. Wallace. (1987). “A Standard Input Format for Multiperiod Stochastic Linear Programs.” COAL Newsletter 17, 1–19.
Birge, J.R. (1985). “Decomposition and Partitioning Methods for Multi-Stage Stochastic Linear Programming.” Operations Research 33, 989–1007.
Birge, J.R. and F. Louveaux. (1997) Introduction to Stochastic Programming. Springer-Verlag.
Carøe, C. and R. Schulz. (1999). “Dual Decomposition in Stochastic Integer Programming.” Operations Research Letters 24, 37–45.
Condevaux-Lanloy, C. and E. Fragniere. (1998). Setstoch: A Tool for Multistage Stochastic Programming with Recourse. Technical Report, Logilab Department of Management Studies, University of Geneva, Switzerland.
Czyzyk, J., M.P. Mesnier, and J.J. Moré. (1998.) “The NEOS Server.” IEEE Computational Science and Engineering 5(3), 68–75, July.
Dempster, M., J. Scott, and G. Thompson. (2002). Stochastic Modelling and Optimization using Stochastics. Technical Report, Judge Institute of Management Studies.
Dempster, M.A.H. and R.T. Thompson. (1998). “Parallelization and Aggregation of Nested Benders Decomposition.” Annals of Operations Research 81, 163–187.
Fisher, M.L. (1981). “The lagrangian Relaxation Method for Solving Integer Programming Problems.” Managment Science 27, 1–18.
Fisher, M.L. (1985). “An Applications Oriented Guide to Lagrangian Relaxation.” Interfaces 15(2), 10–21.
Gassmann, H. (1990). MSLiP: A Computer Code for the Multistage Stochastic Linear Programming Problem. Mathematical Programming 47, 407–423.
Gassmann, H. and E. Schweitzer. (1996). “A Comprehensive Input Format for Stochastic Linear Programs.” Working Paper, School of Business Administration, Dalhousie Uinversity, Halifax, Canada.
Goux, J.-P., S. Kulkarni, J. Linderoth, and M. Yoder. (2000). An Enabling Framework for Master-Worker Applications on the Computational Grid. “Technical report, Argonne National Laboratories.”
Gupta, A. and N. Nishimura. (1998). “Finding Largest Subtrees and Smallest Supertrees.” Algorithmica 21(2), 183–210.
Kall, P. and J. Mayer. (1996). Slp-ior: An Interactive Model Management System for Stochastic Linear Programs. Mathematical Programming 75, 221–240.
King, A. (1994). SP/OSL V1.0, Stochastic Programming Interface Library, User's Guide.
Klaassen, P. (1998). “Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/liability Management: A Synthesis.” Management Science 44, 31–48.
Linderoth, J. and S. Wright. (2001). “Decomposition Algorithms for Stochastic Programming on a Computational Grid.” Technical Report ANL/MCS-P875-0401, Argonne National Laboratories, Apr.
Mulvey, J.M. and H. Vladimirou. (1992). “Stochastic network programming for Financial Planning Problems.” Management Science 38(11), 1642–1664.
Nowak, M.P. and W. Römisch. (2000). “Stochastic Lagrangian Relaxation applied to Power Scheduling in a Hydro-Thermal System under Uncertainty.” Annals of Operations Research 100, 251–272.
Rockafellar, R. and R.J.-B. Wets. (1991). “Scenarios and Policy Aggregation in Optimization Under Uncertainty.” Mathematics of Operations Research 16, 119–147.
Slyke, R.V. and R.J.-B. Wets. (1969). “L-shaped Linear Programs with Application to Optimal Control and Stochastic Programming.” SIAM Journal on Applied Mathematics 17, 638–663.
Takriti, S. and J. Birge. (2000). “Lagrangian Solution Tehniques and Bounds for Loosely Coupled Mixed-Integer Stochastic Programs.” Operations Research 48(1), 91–98.
Valente, P., G. Mitra, C. Poojari, and T. Kyriakis. (2001). “Software Tools for Stochastic Programming: A Stochastic Programming Integrated Environment (SPInE).” Technical report, Brunel University, Uxbridge, UK UB8 3PH.
Van Slyke, R. and R.J.-B. Wets. (1967). “L-shaped Linear Programs with Application to Optimal Control and Sotchastic Programming.” SIAM Journal on Applied Mathematics 17(4), 638–663.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fourer, R., Lopes, L. A management system for decompositions in stochastic programming. Ann Oper Res 142, 99–118 (2006). https://doi.org/10.1007/s10479-006-6163-1
Issue Date:
DOI: https://doi.org/10.1007/s10479-006-6163-1