  With an increasing demand from emerging logistics businesses, Vehicle Routing
Problem with Private fleet and common Carrier (VRPPC) has been introduced to
manage package delivery services from a supplier to customers. However, almost
all of existing studies focus on the deterministic problem that assumes all
parameters are known perfectly at the time when the planning and routing
decisions are made. In reality, some parameters are random and unknown.
Therefore, in this paper, we consider VRPPC with hard time windows and random
demand, called Optimal Delivery Planning (ODP). The proposed ODP aims to
minimize the total package delivery cost while meeting the customer time window
constraints. We use stochastic integer programming to formulate the
optimization problem incorporating the customer demand uncertainty. Moreover,
we evaluate the performance of the ODP using test data from benchmark dataset
and from actual Singapore road map.
