Decomposition and (importance) sampling techniques for multi-stage stochastic linear programs

Technical Report · Mon Nov 01 04:00:00 EST 1993

DOI:https://doi.org/10.2172/10128562· OSTI ID:10128562

Infanger, G

The difficulty of solving large-scale multi-stage stochastic linear programs arises from the sheer number of scenarios associated with numerous stochastic parameters. The number of scenarios grows exponentially with the number of stages and problems get easily out of hand even for very moderate numbers of stochastic parameters per stage. Our method combines dual (Benders) decomposition with Monte Carlo sampling techniques. We employ importance sampling to efficiently obtain accurate estimates of both expected future costs and gradients and right-hand sides of cuts. The method enables us to solve practical large-scale problems with many stages and numerous stochastic parameters per stage. We discuss the theory of sharing and adjusting cuts between different scenarios in a stage. We derive probabilistic lower and upper bounds, where we use importance path sampling for the upper bound estimation. Initial numerical results turned out to be promising.

• Research Organization: Stanford Univ., CA (United States). Systems Optimization Lab.
• Sponsoring Organization: USDOE, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: FG03-92ER25117
• OSTI ID: 10128562
• Report Number(s): SOL--93-7; ON: DE94007384; BR: KC0701010; CNN: Contract N00014-89-J-1659 Grant ECS-8906260 Grant DMS-89130; 89 Contract RP 8010-09 Grant CSA-4005335 Grant J0323-Phy
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200
ALGORITHMS
ITERATIVE METHODS
LINEAR PROGRAMMING
MATHEMATICS AND COMPUTERS
MONTE CARLO METHOD
SAMPLING
STOCHASTIC PROCESSES