Resource allocation in service and logistics systems
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Resource allocation is a problem commonly encountered in strategic planning, where a typical objective is to minimize the associated cost or maximize the resulting profit. It is studied analytically and numerically for service and logistics systems in this dissertation, with the major resource being people, services or trucks. First, a staffing level problem is analyzed for large-scale single-station queueing systems. The system manager operates an Erlang-C queueing system with a quality-of-service (QoS) constraint on the probability that a customer is queued. However, in this model, the arrival rate is uncertain in the sense that even the arrival-rate distribution is not completely known to the manager. Rather, the manager has an estimate of the support of the arrival-rate distribution and the mean. The goal is to determine the number of servers needed to satisfy the quality of service constraint. Two models are explored. First, the constraint is enforced on an overall delay probability, given the probability that different feasible arrival-rate distributions are selected. In the second case, the constraint has to be satisfied by every possible distribution. For both problems, asymptotically optimal solutions are developed based on Halfin-Whitt type scalings. The work is followed by a discussion on solution uniqueness with a joint QoS constraint and a given arrival-rate distribution in multi-station systems. Second, an extension to Naor’s analysis on the joining or balking problem in observable M=M=1 queues and its variant in unobservable M=M=1 queues is presented to incorporate parameter uncertainty. The arrival-rate distribution is known to all, but the exact arrival rate is unknown in both cases. The optimal joining strategies are obtained and compared from the perspectives of individual customers, the social optimizer and the profit maximizer, where differences are recognized between the results for systems with deterministic and stochastic arrival rates. Finally, an integrated ordering and inbound shipping problem is formulated for an assembly plant with a large number of suppliers. The objective is to minimize the annual total cost with a static strategy. Potential transportation modes include full truckload shipping and less than truckload shipping, the former of which allows customized routing while the latter does not. A location-based model is applied in search of near-optimal solutions instead of an exact model with vehicle routing, and numerical experiments are conducted to investigate the insights of the problem.