M. Laguna
Operations Research Proceedings 1994, U. Derigs, A. Bachem, and A. Drexl (Eds.),
Springer-Verlag, Berlin Heidelberg, pp. 103-108 (1995)
Robust Optimization (RO) was recently proposed to provide a practical approach for handling noisy data and uncertainty. Almost all decision problems in practice contain some degree of uncertainty, e.g., rates of return for different investment opportunities, demands for products and services, the time to complete a job, the amount of resources needed to complete an activity in a large project, etc. So far, the RO approach has only been used in problems where the decision variables range in the domain of the real numbers. This paper proposes to expand the robust optimization methodology to deal with decision problems where some of the relevant variables are discrete. This is an important enhancement of the RO approach because a large number of business problems can be modeled using discrete optimization formulations (e.g., investment decisions, production and staff scheduling, air line crew scheduling, research and development project funding, etc.). Since the large size of discrete RO formulations makes the use of classical optimization techniques impractical, we propose a heuristic procedure based on a probabilistic sampling approach. The mechanics of the proposed procedure are illustrated in the context of a project funding problem.
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