A comparison of optimal control and stochastic programming from a formulation and computation perspective

Operating in a changing and uncertain environment, firms must make strategic and operational decisions while trying to satisfy many conflicting goals. For example, in order to maximize expected profit and minimize risk, they must periodically decide when and by how much to expand capacity and even more often how much to produce, all in the face of unknown future demands, available technology, and so on. We refer to this class of problem as multi-objective decision processes under uncertainty. We investigate two major methodologies from different research streams that formulate and solve this class of problem: optimal control and stochastic programming. We introduce an example problem of coordinated capacity planning and production-inventory control to illustrate the issues on formulations and solutions of these two methodological approaches. We show that two methodologies are equivalent in that the decision prescribed by the optimal policy found by optimal control is the same as the corresponding optimal decision found by stochastic programming. Both solution approaches suffer from the "curse of dimensionality" but in different ways: the former approach has an immense state space while the latter a large sample space. They possess distinctive advantages and disadvantages for specific problems, which determine that one approach may be preferably used. We discuss and compare two methods on the example problem in terms of their model formulations, computation efficiency, and handling of multiple objectives. We propose an approximation architecture that combines different approaches to solve large-scale problems. We finally present the numerical results obtained from the example problem to demonstrate that one should tailor solution strategies to specific problems. (C) 2004 Elsevier Ltd. All rights reserved.