Mark E. Lewis
Industrial and Operations Engineering Department
University of Michigan
1205 Beal Avenue
Ann Arbor, MI 48109-2117
David L. Kaufman
Industrial and Operations Engineering
Department
University of Michigan
1205 Beal Avenue
Ann Arbor, MI 48109-2117
davidlk 'at' umich 'dot' edu 734-615-7148
Hyun-soo Ahn
Operations and Management Science, Michigan Business School
University of Michigan
701 Tappan Street, Ann Arbor, Michigan 48109-1234
hsahn 'at' umich 'dot' edu, 734-764-6862
We consider a tandem queueing system where customers arrive according to a Poisson process and must receive service at both stations before leaving the system. Neither queue is equipped with dedicated servers. Instead, all servers are capable of performing both jobs as long as they remain in the system. We consider three different scenarios for the fluctuations of workforce level. In the first, a decision-maker can hire and fire workers as is deemed appropriate; the unrestricted case. In the other two cases, workers arrive randomly and can be hired to work at either station and fired when deemed appropriate in one case (the controlled firing case) and leave randomly (the uncontrolled firing case) in the other. In any case, workers that are hired can work at either station. We show for all cases, that all workers should be allocated to one queue or the other (never split between queues) and that they should serve exhaustively at one of the queues depending on the direction of an inequality. This extends previous studies on flexible systems to the case where the capacity varies over time. We then show in the unrestricted case that the optimal number of workers to hire is non-decreasing in the number of customers in either queue.