Lookahead scenario relaxation for dynamic time window assignment in service routing

We consider a problem where customers dynamically request next-day home service, e.g., repair or installments. Unlike attended home delivery, customers cannot select a time window (TW), the service provider assigns a next-day TW to each new customer if the customer can feasibly be inserted in the service route of the next day without violating the TWs of the existing customers. Otherwise, customer service will be postponed to another day (which is outside the scope of this work). The provider aims to serve many customers the next day for fast service and efficient operations. Thus, TWs have to be assigned to keep the flexibility of the fleet for future requests. For such anticipatory assignments, we propose a stochastic lookahead method that samples a set of future request scenarios, solves the corresponding team-orienteering problems with TWs, and uses the solutions to evaluate current TW assignment decisions. For real-time solutions to the team orienteering problem, we propose to approximate its optimal solution value with an upper bound. The bound is obtained by solving the linear relaxation of a set packing reformulation via column generation. We test our algorithm on Iowa City data and compare it to several benchmark policies. The results show that our method significantly increases customer service, and our relaxation is essential for effective decisions. We further show that our policy does not lead to observable discrimination against inconveniently located customers.