Section: Scientific Foundations

Stochastic programming

Numerous common application areas involve factors that are inherently random or uncertain (such as varying demands, machine failures, surgery duration times, and cost overruns). When such models also have discrete or binary decision variables, for any of the reasons already discussed, the combination of uncertainty and combinatorial nature makes these problems more difficult than if one were trying to address either the uncertain or the discrete aspects of these problems by themselves. Stochastic MIP models have been proposed for applications in resource acquisition planning [57] , internet server capacity expansion [47] , electric power management [149] , and inventory management [58] .

Despite their ubiquity, not much is yet known about how to solve practical MIPs in which uncertainty plays a major role, and in particular problems of the size often encountered in the real world. Our team is involved in research that is advancing our knowledge of how to solve large MIPs in which the data is random or uncertain, in application areas ranging from production planning [97] , [96] to health care logistics [17] .