Automatica, Vol.44, No.6, 1569-1584, 2008
Step decision rules for multistage stochastic programming: A heuristic approach
Stochastic programming with step decision rules (SPSDR) aims to produce efficient solutions to multistage stochastic optimization problems. SPSDR, like plain multistage Stochastic Programming (SP), operates on a Monte Carlo "computing sample" of moderate size that approximates the stochastic process. Unlike SP, SPSDR does not strive to build a balanced event tree out of that sample. Rather, it defines a solution as a special type of decision rule, with the property that the decisions at each stage are piecewise constant functions on the sample of scenarios. Those pieces define a partition of the set of scenarios at each stage t, but the partition at t + 1 need not be refinement of the partition at t. However, the rule is constructed so that the non-anticipativity condition is met, a necessary condition to make the rules operational. To validate the method we show how to extend a non-anticipatory decision rule to arbitrary scenarios within a very large validation sample of scenarios. We apply three methods, SPSDR, SP and Robust Optimization, to the same 12-stage problem in supply chain management, and compare them relatively to different objectives and performance criteria. It appears that SPSDR performs better than SP in that it produces a more accurate estimate (prediction) of the value achieved by its solution on the validation sample, and also that the achieved value is better. (c) 2008 Elsevier Ltd. All rights reserved.
Keywords:multistage stochastic programming