Stochastic Modeling for Optimal Batch Scheduling of Prophylactic Dispensing Centers

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Title: Stochastic Modeling for Optimal Batch Scheduling of Prophylactic Dispensing Centers
Author: Moomaw, Lindsay M.
Advisors: Dr. Brian T. Denton, Committee Chair
Dr. Julie S. Ivy, Committee Member
Dr. Yahya Fathi, Committee Member
Abstract: We study stochastic optimization models for scheduling batch arrivals to a Point of Dispensing (POD) in response to a biological emergency in which mass vaccination or dispensing of antiviral medication is implemented. The objective of our model is to minimize the total expected waiting time for customers and idle time of servers while considering the stochasticity of service times and customer flow through the POD. We begin with a simplified design of a POD which includes three function-defined servers and the basic queuing elements that would be utilized in a realistic POD, including splitting and merging queues. We create two-stage stochastic programming formulations to model two cases. In the first case of splitting queues, numerical results suggest an optimal constant batch interarrival time can produce total expected waiting and idle time costs near those of the optimal solution to the stochastic program. Stochastic programming formulations for the second case of split and merged queues prove to be more difficult. We study information and integer relaxations which provide approximations that are easier to solve. However, our results indicate relatively wide gaps on the optimal solution value. We expand the POD design to include eight stations to better represent a realistic facility. Using discrete event simulation, we test two batch interarrival time heuristics and report the similarity in their best solutions with respect to lowest expected costs of waiting and total operating time.
Date: 2010-04-09
Degree: MS
Discipline: Industrial Engineering

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