Shipment Path Planning for Rail Networks Considering Elastic Capacity

Abstract

The rail shipment path (RSP) optimization problem is part of the operating plan. Unlike other transportation modes, the physical path of traffic flow in a rail system has its own unique characteristics, among which the most particular is that shipments gradually converge into one single traffic flow and then travel together through a tree-shaped path. More specifically, when two or more shipments arrive at a rail yard, those intended for the same destination are treated as one single freight flow and are shipped through the same path during the remainder of the trip, regardless of their origins. The RSP plan is intended for an intermediate planning horizon (one to two years), not for controlling day-to-day operations. Thus, storage capacities are required for links, resulting in available link capacities having an elastic feature. Based on this background, this article introduces the forming mechanism of the tree-shaped path from the perspective of rail yard operations and develops a nonlinear fuzzy 0-1 programming model for the RSP problem. Since the fuzzy capacity constraints and a notably large number of high-order terms are generated from the tree recursive expression, the model is hard to solve even for small-sized instances by typical methods of operational research. In this article, to solve RSP problems with the tree-shaped and the elastic capacity constraints in the rail network, we employ a simulated annealing algorithm. The numerical experiments based on the southwest rail network of China show that the solution efficiency of this approach is significant.