Time window optimization for attended home service delivery under multiple sources of uncertainties

We consider a vehicle routing problem variant to optimize time window assignments together with vehicle routing and scheduling decisions, under the uncertainties of trip time, service time and possible customers’ cancellations. We minimize the expected cost of vehicles’ overtime, idleness, and customer waiting, when also allowing to add new customers to existing schedules. We formulate a two-stage stochastic mixed-integer programming model using finite samples of the uncertain parameters, where in the first stage, we optimize vehicle routes and assign service time windows to customers, and in the second stage, we construct a linear program to compute the resultant undesirable cost given routes and time windows. We also propose a re-optimization method and an insertion-based linear program for accommodating real-time requests in a rolling horizon way for dynamic operations. To speed up computation, we further decompose the problem into three phases and propose Assignment–Routing–Scheduling heuristics. We first design three clustering algorithms based on spatial similarities to assign customers to vehicles, and then combine the nearest-neighbor and smallest-variance rules to decide the route for each vehicle. Finally, we cast the scheduling part as a Newsvendor problem variant and apply inventory approximations to derive closed-form solutions for determining time windows. We conduct numerical studies on diverse instances generated using both well-established benchmark data sets and Ford’s mobile service data, to compare different approaches and demonstrate the benefits of allowing flexible time-window assignments.