Scheduling customer arrivals to a stochastic service system

An efficient algorithm for determining the optimal arrival schedule for customers in a stochastic service system is developed. All customers arrive exactly when scheduled, and service times are modeled as independent identically distributed Erlang random variables. Costs are incurred at a fixed rate per unit of time each customer waits for service, and an additional cost is incurred for every unit of time the server operates beyond a scheduled closing time. The objective is to minimize total operating cost. This type of problem arises in many operational contexts including transportation, manufacturing, and appointment-based services.