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The required time for surgical interventions in operating rooms (OR) may vary significantly from the predicted values depending on the type of operations being performed, the surgical team, and the patient. These deviations diminish the efficient utilization of OR resources and result in the disruption of projected surgery start times. This paper proposes a two-stage chance-constrained model to solve the OR scheduling problem under uncertainty. The goal is to minimize the costs associated with OR opening and overtime as well as reduce patient waiting times. The risk of OR overtime is controlled using chance constraints. Numerical experiments show that the proposed model provides a better trade-off between minimizing costs and reducing solution variability when compared to two existing models in the literature. It is also shown that the three models converge as the overtime probability threshold approaches one. Moreover, it is observed that the individual chance constraints result in the opening of fewer rooms, lower waiting times, and shorter solution times when compared to that of joint chance constraints. A decomposition algorithm is applied that solves large test instances of the OR scheduling problem, that of which is known to be NP-hard. Strong valid inequalities are derived in order to accelerate the convergence speed. The proposed approach outperformed both a commercial solver and a basic decomposition algorithm after solving all test instances with up to 89 surgeries and 20 ORs in less than 48 minutes.

This paper proposes a new method to extend the flight capability of drones in real time. The new method combines two wireless charging methods (stationary wireless charging systems and dynamic wireless charging systems) into a hybrid mode. The drones must frequently return to a ground control center to replace or recharge its battery due to the limited performance of batteries mounted in the drones. To reduce the need of returning to the center, stationary wireless charging systems and dynamic wireless charging systems have been proposed. However, a few drawbacks of the two systems include the needs of landing/stopping on the stationary charging systems and the uncertainty of charging efficiency over the dynamic charging systems. Hence, to resolve the current limitations, we propose the hybrid approach for extending drone flight duration in real time. A mathematical formulation model is proposed to decide an optimal installation location and operating time of the hybrid mode. A case study is conducted to illustrate feasibility and effectiveness of the proposed method. Results from the case study show that we can lengthen the flight duration per charge from the initial launching point (30 min → 32⁻59 min), and if the value of charging efficiency of the dynamic charging systems is maintained above a certain level, the time spent on the stationary charging systems is significantly reduced (58 min → 22 min).