STOCHASTIC MODELS FOR RESOURCE ALLOCATION, SERIES PATIENTS SCHEDULING, AND INVESTMENT DECISIONS

Abstract

We develop stochastic models to devise optimal or near-optimal policies in three different areas: resource allocation in virtual compute labs (VCL), appointment scheduling in healthcare facilities with series patients, and capacity management for competitive investment. A VCL consists of a large number of computers (servers), users arrive and are given access to severs with user-specified applications loaded onto them. The main challenge is to decide how many servers to keep “on”, how many of them to preload with specific applications (so users needing these applications get immediate access), and how many to be left flexible so that they can be loaded with any application on demand, thus providing delayed access. We propose dynamic policies that minimize costs subject to service performance constraints and validate them using simulations with real data from the VCL at NC State. In the second application, we focus on healthcare facilities such as physical therapy (PT) clinics, where patients are scheduled for a series of appointments. We use Markov Decision Processes to develop the optimal policies that minimize staffing, overtime, overbooking and delay costs, and develop heuristic secluding policies using the policy improvement algorithm. We use the data from a local PT center to test the effectiveness of our proposed policies and compare their performance with other benchmark policies. In the third application, we study a strategic capacity investment problem in a duopoly model with an unknown market size. A leader chooses its capacity to enter a new market. In a continuous-time Bayesian setting, a competitive follower dynamically learns about the favorableness of the new market by observing the performance of the leader, and chooses its capacity and timing of investment. We show that an increase in the probability of a favorable market can strictly decrease the leaders expected discounted profit due to non-trivial interplay between leaders investment capacity and timing of the dynamically-learning follower.Doctor of Philosoph