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Optimal Interventions in Robust Optimization with Application in Radiotherapy

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Document pages: 22 pages

Abstract: Uncertainties can be time-dependent, particularly in areas such as machine repair, maintenance scheduling, and cancer radiotherapy, where the condition of the system (or patient) can change during the course of the operation (or treatment). When solving such problems, 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 are directly impacted by time-dependent uncertainties. We address these challenges by developing an optimally-intervened robust optimization model that employs a time-dependent uncertainty set. We formulate counterparts of robust linear programs and propose an algorithm to compute adaptive robust solutions. Then, optimal intervention policies are derived that recommend the optimal number and timing of observations as functions of the observation cost and parameters of the uncertainty set. The proposed methodology is demonstrated using an application in cancer radiotherapy, where the optimally-intervened robust model improves tumor dose by up to 3 subject to nominal, best-case, and worst-case conditions, compared to a naive robust model that employs a single intervention. Furthermore, the optimally-intervened model improves tumor dose by up to 20 compared to three deterministic approaches used in the clinic; this method also reduces dose to healthy organs by up to 18 . Improvements in tumor and organ dose criteria can lead to a better quality of life for the patient. The proposed methodology is generic and can be applied to other time-dependent processes, such as machine repair or maintenance scheduling.

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