UCL School of Management is delighted to welcome Dr Mehmet Begen, Ivey Business School, to host a research seminar.
We study scheduling of jobs (e.g., surgeries, physician appointments) on a highly utilized resource (e.g., operating room, physician) when the processing durations are stochastic and there are significant underage (resource idle-time) and overage (job waiting and/or resource overtime) costs. Random processing durations are integers and given by a discrete probability distribution. The objective is to determine an optimal appointment schedule (planned start times) for a given sequence of jobs minimizing the expected total underage and overage costs. We consider several extensions and applications. We show that an optimum solution is integer and can be found in polynomial time. In the case of unknown duration distributions, we determine bounds on the number of independent samples required to obtain a provably near-optimal solution with high probability. The objective can also be to minimize a percentile of the total. Last but not least, random arrivals of multiple type and priority of jobs can be considered to combine advance and appointment scheduling. Besides healthcare, there are other applications such as project scheduling, gate and runway scheduling of aircrafts in an airport, and inventory management.