Operations systems with discretionary task completion

Most performance evaluation models in the operations management literature implicitly assume that tasks possess standardized completion criteria. However, in many systems, particularly service and professional work, judgment is frequently required to determine how much time to allocate to a task. In this paper, we show that introducing discretion in task completion adds a fourth variability buffer, quality, to the well-known buffers of capacity, inventory and time. To gain insight into the managerial implications of this difference, we model the work of one- and two-worker systems with discretionary task completion as controlled queues. After characterizing the optimal control policy and identifying some practical heuristics, we use this model to examine the differences between discretionary and nondiscretionary work. We show that in systems with discretionary task completion, (i) adding capacity may actually increase congestion, and (ii) task variability in service time can improve system performance. This implies that it may be suboptimal to expect shorter delays as a result of a capacity increase, and that task variability reduction may not be an appropriate goal in systems with discretionary task completion. We also find that the benefit of queue pooling is smaller in systems with discretionary task completion than in systems with nondiscretionary task completion.