This thesis investigates two issues arise from operations research.

In the first part, we consider the surgery sequencing and scheduling problem with uncertain durations in an operating theater. Based on a widely implemented practice, we propose a mathematical framework to balance the delay risk and the idle risk with a Punctuality Index, which accounts for both the probability and intensity of delay and idle time. We develop a computationally efficient solution procedure based on Benders Decomposition, offering exact solutions for the problem. The framework can also accommodate a robust setting when the underlying probability distribution is not fully available. For practical use, we propose two effective heuristics for sequencing decisions by approximating the model. One sort...[ Read more ]

This thesis investigates two issues arise from operations research.

In the first part, we consider the surgery sequencing and scheduling problem with uncertain durations in an operating theater. Based on a widely implemented practice, we propose a mathematical framework to balance the delay risk and the idle risk with a Punctuality Index, which accounts for both the probability and intensity of delay and idle time. We develop a computationally efficient solution procedure based on Benders Decomposition, offering exact solutions for the problem. The framework can also accommodate a robust setting when the underlying probability distribution is not fully available. For practical use, we propose two effective heuristics for sequencing decisions by approximating the model. One sorts surgeries in ascending order of the variance of the durations. The second one is based on the forward and backward deviations, which capture the right and left tail of the uncertain surgical durations, respectively. Finally, we carry out numerical studies to demonstrate the benefits of the model and the heuristics.

In the second part, we study a robust auction design problem for multi-object auctions allowing for ambiguity. We relax the critical assumptions that the underlying valuation distribution is exactly known in the optimal auction literature. To handle the ambiguity, we assume that bidders' valuation follows a probability distribution which is not known but restrictive to lie in an ambiguity set of probability distributions. By extending Armstrong (2000)'s framework, we show that even a slight deviation of the belief about the distribution may lead to an infeasible solution, and the seller tends to withhold the objects as the ambiguity level increases. Furthermore, our results imply that selling the objects separately cannot always be optimal no matter how uncertain the belief is, which contrasts with the separation results in literature.