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Because customers must usually arrange their schedules to be present for home services, they desire an accurate estimate of when the service will take place. However, even when firms quote large service time windows, they are often missed, leading to customer dissatisfaction. Wide time windows and frequent failures occur because time windows must be communicated to customers in the face of several uncertainties: future customer requests are unknown, final service plans are not yet determined, and when fulfillment is outsourced to a third party, the firm has limited control over routing procedures. Even when routing is performed in-house, time windows typically do not receive explicit consideration. In this paper, we show how companies can communicate reliable and narrow time windows to customers in the face of arrival time uncertainty. Under mild assumptions, our main result characterizes the optimal policy, identifying structure that reduces a high-dimensional stochastic non-linear optimization problem to a root-finding problem in one dimension. The result inspires 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, providing results that nearly achieve the lower bound on the optimal solution. Our results show that (i) time windows should be tailored to individual customers, (ii) time window sizes should be proportional to the service level, (iii) larger time windows should be assigned to earlier requests and smaller time windows to later requests, (iv) larger time windows should be assigned to customers further from the depot of operation and smaller time windows to closer customers, and (v) two time windows for one customer are helpful in some cases.
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