Dismissing Decision Tasks : The Optimality of the M – Shaped Structure

We consider a sequential hypothesis-testing problem where the Decision Maker (DM) faces a random stream of decision tasks that accumulate over time, creating congestion. As in the classical set-up, the agent needs to dynamically choose when to terminate the information collection process and make a final decision. In our set-up, however, unattended tasks accumulate in a queue and incur additional delay-related costs. This gives the DM an incentive to dismiss tasks from the queue, in the sense that the DM makes her decision a priori without running any test. In this note, we examine when it is desirable to dismiss decision tasks such as these. To that end, we model the problem as a Partially Observed Markov Decision Process and fully characterize the optimal policy which maximizes the long-run average profit. Our analysis reveals the optimality of an M-shaped structure. This structure implies that dismissing tasks can mitigate inefficiencies in the decision process that have been reported in the literature.