Multi-modal, multi-period, multi-commodity transportation : models and algorithms

Abstract

In this paper we present a mixed integer optimization framework for modeling the shipment of goods between origin destination (O-D) pairs by vehicles of different types over a time-space network. The output of the model is an optimal schedule and routing of vehicle movements and assignment of goods to vehicles. Specifically, this framework allows for: multiple vehicles of differing characteristics (including speed, cost of travel, and capacity), transshipment locations where goods can be transferred between vehicles; and availability times for goods at their origins and delivery time windows for goods at their destinations. The model is composed of three stages: In the first, vehicle quantities, by type, and goods are allocated to routes in order to minimize late deliveries and vehicle movement costs. In the second stage, individual vehicles, specified by vehicle identification numbers, are assigned routes, and goods are assigned to those vehicles based on the results of the first stage and a minimization of costs involved with the transfer of goods between vehicles. In the third stage we reallocate the idle time of vehicles in order to satisfy crew rest constraints. Computational results show that provably optimal or near optimal solutions are possible for realistic instance sizes.