An Integer Programming Model for the Deterministic Wave-Based Same-Day Pickup and Delivery Problem

This paper focuses on the development an Integer Programming (IP) model for the Deterministic Wave-based Same-day Pickup and Delivery Problem (D-WSDPD), where a vehicle is allowed to leave the depot at specific time periods, called waves. Moreover, each customer request comprises of a pair of services - namely pickup and delivery - not necessarily be completed in the same wave. If the request had been picked, it must be also be delivered by the end of the day. We explored how numbers of daily dispatch waves affect major service performance metrics, including total rewards from serving customer orders and the overall service level on 20 randomly generated instances. We found that, by increasing the numbers of daily dispatch waves, all service performance metrics could be potentially improved as expected, with greater numbers of dispatched waves. However, having too frequent daily dispatch waves would not significantly improve such metrics due to limited operational interval, i.e. planning horizon. In contrast, the computational times required grow exponentially; and, thence, cautious trade-offs between the desired service performance and operational costs must be made. While our mathematical formulation is only preliminary for the practical WSDPD, with high level of uncertainty, it could be regarded as a prelude to the development of efficient heuristics and policies that will be explored in the next steps.