Operation Systems with Discretionary Task Completion

Most performance evaluation models in operations management literature have assumed that tasks possess standardized completion criteria. However, in many operation systems, particularly in service and professional work, judgment is frequently required to determine when a task is completed. In thin 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 a single worker system with discretionary task completion as a controlled queue. After characterizing the optimal control policy and identifying identifying some practical heuristics, we use this model to examine the differences between discretionary and non-discretionary work. We show that adding capacity may actually increase congestion in systems with discretionary task completion, and information about job types in queue is less useful in systems with discretionary task completion than in systems with non-discretionary task completion.