Stochastic Capacity and Facility Location Planning with Ambiguous Probabilities
Motivated by the pharmaceutical industry, we consider two strategic models - a capacity planning model and a facility location planning model - where demand in each period of the problem horizon will be determined by the outcome of series of random events with two possible outcomes. These strategic planning problems are complicated by the fact that the probability of each of the alternative outcomes of these events is uncertain. Given this setting, we develop approaches for solving these models that are robust to ambiguities in outcome probabilities.
In the first model, we consider a capacity planning model under this setting. We develop approaches to solving capacity expansion models in this setting that are robust to ambiguities in probability of success, and we consider a variety of different objective functions, including minimizing expected cost, minimizing value at risk and minimizing conditional value at risk. We formulate these models as multistage (stochastic) robust integer programs. For cases where these integer programs are challenging to solve to optimality, we propose two heuristic approaches, a straightforward rolling horizon approach and the more sophisticated event spike approach. The idea of event spike is adapted from Beltran-Royo et al. (2014), and in our version, we relax the stage-wise independence restriction which is the assumption in the original approach. These approaches are further developed to be applicable in the robust setting with different objectives. The effectiveness of these heuristics is shown through computational experiments. We also explore how alternative objectives and parameters affect solutions, and when explicitly modeling ambiguous probabilities adds value.
In the second model, we extend the capacity planning model by considering the additional decisions of facility location and demand allocation. In addition to ambiguous probabilities of binary event outcomes, we assume that the uncertainty of demand has not completely resolved after the binary event occurs. We formulate models that are robust to ambigui- ties in both probabilities and demands by using (stochastic) robust integer programs. We propose variants of Nested Decomposition and Stochastic Dual Dynamic Programming to solve these models more efficiently. We extend these approaches by incorporating ambigu- ities in probabilities and demand. We also propose approaches that involve decomposing our large problem into a smaller number of sub-problems with longer horizons, and then applying Nested Decomposition and Stochastic Dual Dynamic Programming in this revised setting. In the computational study, we explore the effectiveness of the robust approach in this setting, and demonstrate the performance of the proposed heuristic approaches.