3. Specifying and Validating Probabilistic Inputs for Prescriptive Models of Decision Making over Time

Optimization models for making decisions over time in uncertain environments rely on probabilistic inputs, such as scenario trees for stochastic mathematical programs. The quality of model outputs, i.e., the solutions obtained, depends on the quality of these inputs. However, solution quality is rarely assessed in a rigorous way. The connection between validation of model inputs and quality of the resulting solution is not immediate. This chapter discusses some efforts to formulate realistic probabilistic inputs and subsequently validate them in terms of the quality of solutions they produce. These include formulating probabilistic models based on statistical descriptions understandable to decision makers; conducting statistical tests to assess the validity of stochastic process models and their discretization; and conducting re-enactments to assess the quality of the formulation in terms of solution performance against observational data. Studies of long-term capacity expansion in service industries, including electric power, and short-term scheduling of thermal electricity generating units provide motivation and illustrations. The chapter concludes with directions for future research.