Optimal Stochastic Package Delivery Planning with Deadline: A Cardinality Minimization in Routing

Vehicle Routing Problem with Private fleet and common Carrier (VRPPC) has been proposed to help a supplier manage package delivery services from a single depot to multiple customers. Most of the existing VRPPC works consider deter- ministic parameters which may not be practical and uncertainty has to be taken into account. In this paper, we propose the Optimal Stochastic Delivery Planning with Deadline (ODPD) to help a supplier plan and optimize the package delivery. The aim of ODPD is to service all customers within a given deadline while considering the randomness in customer demands and traveling time. We formulate the ODPD as a stochastic integer programming, and use the cardinality minimization approach for calculating the deadline violation probability. To accelerate computation, the L-shaped decomposition method is adopted. We conduct extensive performance evaluation based on real customer locations and traveling time from Google Map.