Service Quality versus Efficiency in Tandem Systems

We study the tradeoff between efficiency and service quality in tandem systems. We reward efficiency by assuming that a revenue is earned each time a job is completed, and we penalize poor service quality by incorporating positive holding costs. We study the dynamic assignment of servers to tasks with the objective of maximizing the long-run average profit. For systems of arbitrary size, generalist servers, and linear or nonlinear holding costs, we determine the server assignment policy that maximizes the profit. For systems with two stations, two specialist servers, and linear holding costs, we show that the optimal server assignment policy is of threshold type and determine the value of this threshold as a function of the revenue and holding cost. We also provide numerical results that suggest that the optimal policy has a threshold structure for nonlinear holding costs. Finally, for larger systems with specialist servers, we propose effective server assignment heuristics.