Three Essays on Resource Allocation: Load Balancing on Highly Variable Service Time Networks, Managing Default Risk via Subsidies and Supplier Diversification, and Optimal Hotel Room Assignment.

Abstract

The first essay considers a service center with two stations in accordance with independent Poisson processes. Service times at either station follow the same general distribution, are independent of each other and are independent of the arrival process. The system is charged station-dependent holding costs at each station per customer per unit time. At any point in time, a decision-maker may decide to move, at a cost, some number of jobs from one queue to the other. We study the problem with the purpose of providing insights into this decision-making scenario. We do so, in the important case that the service time distribution is highly variable or simply has a heavy tail. We propose that the savvy use of Markov decision processes can lead to easily implementable heuristics when features of the service time distribution can be captured by introducing multiple customer classes. The second essay studies the problem solved by a manufacturer who faces supplier disruptions. In order to understand the interactions between three strategies (subsidizing the supplier, supplier diversification, and the creation of back-up inventory), the problem is analyzed using a simple model with inventory storage costs and shortage penalties. The model allows us to derive conditions when these strategies are appropriate, either in isolation or in combination. A sensitivity analysis shows that the optimal decisions may not change monotonically when the parameters change. The third essay studies a hotel room assignment problem. The assignment is generally performed by the front desk staff on the arrival day using a lexicographic approach, but this may create empty room-nights between bookings that are hard to fill. This problem shares some features with the job shop problem and with the classroom assignment problem, both of which have been studied in the literature, but the problem itself has not been widely studied. We suggest a heuristic method to solve it, which can be run in a short time with the nightly batch operations that hotels routinely perform. The algorithm considerably improves the results from the lexicographic approach.