  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
deterministic 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.
