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We study a pickup-and-delivery problem that arises when customers randomly submit requests over the course of a day from a choice of vendors on a collaborative e-commerce portal. Based on the attributes of a customer request, a dispatcher dynamically schedules the delivery service on either a dedicated vehicle or a crowdshipper, both of whom experience time dependent travel times. While dedicated vehicles are available throughout the day, the availability of crowdshippers is unknown a priori and they appear randomly for only portions of the day. With an objective of minimizing the sum of routing costs, piece-rate crowdshipper payments, and lateness charges, we model the uncertainty in request arrivals and crowdshipper appearances as a Markov decision process. To determine an action at each decision epoch, we employ a heuristic that partially destroys the existing routes and repairs them guided by a parameterized cost function approximation that accounts for the remaining temporal capacity of delivery vehicles. Through a set of computational experiments, we demonstrate the improvement of our approach over a myopic approach in several key performance metrics. In addition, we conduct computational experiments demonstrate the impact of inserting wait time in the route scheduling and the benefit of explicitly modeling time-dependent travel times. Through our computational testing, we also investigate the effect of demand management mechanisms that facilitate many-to-one request bundles or one-to-many request bundles on reducing the cost to service requests.
Stoia et al. (Wed,) studied this question.