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 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.

Optimal Stochastic Delivery Planning in Full-Truckload and Less-Than-Truckload Delivery

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.