Chance-Constrained Programming with Decision-Dependent Uncertainty

We study a class of joint chance-constrained stochastic problems CC-DD with decision-dependent and exogenous uncertainty. A coupling function models the relationship between decision and decision-dependent random variables. We propose reformulations equivalent to the general chance-constrained problem with decision-dependent uncertainty and applicable to any coupling function. We define the properties of coupling functions and explain the importance of properly modeling decision-dependent uncertainty. We then provide the explicit formulation of problem CC-DD in the decision-dependent service uncertainty context and show its versatility and suitability for a wide range of business problems. We design a data-driven algorithmic framework which includes the derivation of convex integer relaxation problems, the use of new multiterm convexification methods, the derivation of tight bounding schemes, and the design of a nonlinear branch-and-bound algorithm featuring a conification method and a new branching rule. Experiments based on real-life data validate the scalability and computational efficiency of the method. To conduct the data-driven analysis, we develop a new medical evacuation chance-constrained model with exogenous and decision-dependent uncertainty which endogenizes the calculation of individual busy probabilities.