Optimal Time Window Sizing

From the perspective of a firm providing on-location services, we address the problem of determining service time windows that must be communicated to customers at the time of request. We set service time windows under incomplete information on arrival times to customers. We show how to minimize expected time window width subject to a constraint on service level. We use analytical results of the problem to inspire a practice-ready heuristic for the more general case. Relative to the industry standard of communicating uniform time windows to all customers, and to other policies applied in practice, our method of quoting customer-specific time windows yields a substantial increase in customer convenience without sacrificing reliability of service.