Optimal interventions in robust optimization with time-dependent uncertainties

Abstract

Uncertainties can be time-dependent, particularly in areas such as maintenance scheduling and cancer radiotherapy planning, where the condition of the system (or patient) can change over the course of the operation (or treatment). When solving problems in such areas, it is crucial to intervene and observe the condition of the system prior to adapting the decisions. However, observations can be costly, and the timing of observations is directly impacted by time-dependent uncertainties. We address these challenges by developing optimal intervention policies for robust optimization models that employ time-dependent uncertainty sets where (i) making an observation fully resets the uncertainty yet incurs a cost, and (ii) the solution of the static robust optimization problem without making observation continuously becomes more conservative. Further, we provide heuristic procedures to compute adaptive robust solutions from the models, efficiently. We evaluate the practicality of the developed procedures by applying them to problems in maintenance planning of devices, where our results provide an efficient procedure to obtain an optimal maintenance policy. Moreover, in cancer radiotherapy, we develop optimally-intervened robust treatment plans that reduce dose to healthy organs without affecting tumor dose when compared to naively-intervened robust models and other deterministic approaches.