Taxonomic classification of planning decisions in health care: a review of the state of the art in OR/MS

We provide a structured overview of the typical decisions to be made in resource capacity planning and control in health care, and a review of relevant OR/MS articles for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making

Learning Algorithms for Minimizing Queue Length Regret

We consider a system consisting of a single transmitter/receiver pair and $N$ channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may attempt a frame transmission on one channel at a time, where each frame includes a packet if one is in the queue. For each channel, an attempted transmission is successful with an unknown probability. The transmitter's objective is to quickly identify the best channel to minimize the number of packets in the queue over $T$ time slots. To analyze system performance, we introduce queue length regret, which is the expected difference between the total queue length of a learning policy and a controller that knows the rates, a priori. One approach to designing a transmission policy would be to apply algorithms from the literature that solve the closely-related stochastic multi-armed bandit problem. These policies would focus on maximizing the number of successful frame transmissions over time. However, we show that these methods have $\Omega(\log{T})$ queue length regret. On the other hand, we show that there exists a set of queue-length based policies that can obtain order optimal $O(1)$ queue length regret. We use our theoretical analysis to devise heuristic methods that are shown to perform well in simulation.Comment: 28 Pages, 11 figure

Distributionally robust views on queues and related stochastic models

This dissertation explores distribution-free methods for stochastic models. Traditional approaches operate on the premise of complete knowledge about the probability distributions of the underlying random variables that govern these models. In contrast, this work adopts a distribution-free perspective, assuming only partial knowledge of these distributions, often limited to generalized moment information. Distributionally robust analysis seeks to determine the worst-case model performance. It involves optimization over a set of probability distributions that comply with this partial information, a task tantamount to solving a semiinfinite linear program. To address such an optimization problem, a solution approach based on the concept of weak duality is used. Through the proposed weak-duality argument, distribution-free bounds are derived for a wide range of stochastic models. Further, these bounds are applied to various distributionally robust stochastic programs and used to analyze extremal queueing models—central themes in applied probability and mathematical optimization

Distributionally robust views on queues and related stochastic models

This dissertation explores distribution-free methods for stochastic models. Traditional approaches operate on the premise of complete knowledge about the probability distributions of the underlying random variables that govern these models. In contrast, this work adopts a distribution-free perspective, assuming only partial knowledge of these distributions, often limited to generalized moment information. Distributionally robust analysis seeks to determine the worst-case model performance. It involves optimization over a set of probability distributions that comply with this partial information, a task tantamount to solving a semiinfinite linear program. To address such an optimization problem, a solution approach based on the concept of weak duality is used. Through the proposed weak-duality argument, distribution-free bounds are derived for a wide range of stochastic models. Further, these bounds are applied to various distributionally robust stochastic programs and used to analyze extremal queueing models—central themes in applied probability and mathematical optimization