Seminar by Tuğçe Işık Georgia Institute of Technology
Server flexibility can be used to improve various performance measures of manufacturing and service systems. One advantage of server flexibility is the possibility of collaboration since each server can perform multiple tasks. However, collaboration may not always be possible due to the physical limitations in the system or the nature of the tasks. In this talk, we focus on non-collaborative systems with flexible servers and examine how server allocation decisions should be made. In the first part, we consider a tandem line with finite buffers and equal number of tasks and servers, where the servers can be reallocated instantaneously at no cost. We prove that a threshold-type server allocation policy is optimal for systems of two stations and develop near-optimal server allocation heuristics for larger systems. We also provide a numerical comparison of collaborative, non-collaborative and non- flexible systems, and show that server flexibility can indefinitely improve the long- run average throughput in the absence of collaboration. In the second part, we assume that each server reallocation results in a setup cost. For a two-station system with homogeneous tasks and constant setup costs, we characterize the optimal policy, and investigate how the optimal policy depends on the magnitude of the setup cost and the buffer size. For systems with non-constant setup costs and/or non-homogeneous tasks, near-optimal heuristics are provided. Finally, we consider larger queueing networks with infinite buffers, and propose a linear program that yields an upper bound on the achievable long-run average throughput. Furthermore, we introduce a class of round- robin policies that asymptotically achieve this upper bound for systems with two stations, and are near-optimal for longer lines even when the buffers are finite.