Task release control for decision making queues

We consider the optimal duration allocation in a decision making queue. Decision making tasks arrive at a given rate to a human operator. The correctness of the decision made by the human evolves as a sigmoid function of the duration allocated to the task. Each task in the queue loses its value continuously. We elucidate on this trade-off and determine optimal policies for the human operator. We show the optimal policy requires the human to drop some tasks. We present a receding horizon optimization strategy, and compare it with the greedy policy.