An efficient column-and-constraint generation algorithm for solving the adaptive robust elective surgery problem under uncertainties in surgery duration, length of stay, and emergency arrivals
Résumé
This paper addresses the robust elective surgery problem in the context of Operating Room (OR) planning, incorporating downstream resource constraints related to the Intensive Care Unit (ICU) and uncertainties in surgery duration, length of stay in the ICU, and emergency arrivals. We propose a novel two-stage robust optimization approach, using the “here-and-now” and “wait-and-see” decision-making principles. In the first stage, decisions on the master surgical schedule and surgical case assignment problem are made, allocating patients, surgeons, and specialties to OR sessions under the block scheduling strategy, using symmetry breaking inequalities. The second stage addresses multiple uncertainties and aims to minimize the costs in the worst-case scenarios, considering session overtime, emergency costs, and the costs of denied ICU beds. Polyhedral uncertainty sets and structural properties enable the use of the Column-and-Constraint Generation algorithm for efficient problem resolution. Computational experiments using real data from a medium-sized French hospital demonstrate the approach’s superior resource utilization and computational efficiency over the cutting-plane method. Value at Risk, Conditional Value at Risk, and Monte Carlo simulation are used to assess robustness, aiding in parameter adjustments for risk prevention and cancellations. This research contributes to enhancing decision-making in elective surgery planning under multiple uncertainties, offering practical insights for improving hospital productivity.
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