One-block train formation in large-scale railway networks: An exact model and a tree-based decomposition algorithm

Abstract

We investigate the one-block train formation problem (TFP) in the railway freight transportation industry given a car route for each shipment. The TFP considers both the block design and the car-to-block assignment in the tactical level. Moving beyond current researches on service network design, the unitary rule and the intree rule are taken into account in this study based on the Chinese railway background. We develop a linear binary programming formulation to minimize the sum of train cost and classification delay subject to limitations on the classification capacity and the number of sort tracks at each station. Furthermore, we propose a novel solution methodology that applies a tree-based decomposition algorithm. Here, we first decompose the whole network into a series of rooted trees for each destination separately. Then, we divide the trees into sufficiently small subtrees, whose size is regulated by a node size parameter. Finally, we construct a restricted linear binary model for each subtree and solve these models sequentially to find their optimal solutions. Our computational results on a realistic network from the Chinese railway system with 83 stations, 158 links and 5700 randomly generated demands show that the proposed algorithm can derive high-quality solutions within 3 hours. These solutions are on average 43.89% better than those obtained after solving the linear binary program for 1 day.

A mathematical formulation and an LP‐based neighborhood search matheuristic solution method for the integrated train blocking and shipment path problem

“…Chen et al [4] addressed the one-block train formation problem in the railway freight transportation industry based on the Chinese railway. For solving the problem, a two-stage tree-based decomposition approach was used which integrates exact and heuristic principles based on slope scaling.…”

“…The scope of this article will focus on designing optimal railway scheduling plans for the integrated train blocking and shipment path (TBSP) problem according to the tonnage-based operating strategy. The TBSP problem aims to determine a minimum-cost shipment plan that answers the following questions: (1) which pairs of yards should have a block (train service) in between?, (2) how frequent should the train services be?, (3) what should be the physical paths of these trains?, and (4) what should be the shipment-block sequence?…”

The Systematic Optimization of Train Formation in Loading Stations

“…Chen et al [15] investigated the one-block train formation problem, and a linear programming model was established aimed at minimizing the total accumulation cost and reclassification delay, limited by the reclassification capacity and the number of sorting tracks. A linear and clear equation for counting the number of cars contained in blocks was proposed, which can be regarded as an excellent reference for formulating the traffic flows of shipments in the rail network.…”

“…The optimization results of TFP are actually the preliminary works of TFLS, which also prevents the mathematical model of TFP from being employed in the TFLS problem. Due to the abovementioned reasons, the linear mathematical model proposed by Chen et al [15] cannot serve for the train formation problem arising from loading stations.…”

Optimizing Train Formation Problem With Car Flow Routing and Train Routing by Benders-and-Price Approach

“…A solution method integrating exact and heuristic principles based on slope scaling was used to address the comprehensive model. Chen et al [18] developed a binary linear model to minimize the total sum of accumulation costs and classification costs, and a novel tree-based decomposition algorithm was proposed. Zhao and Lin [19] formulated the multi-shipment train formation problem as a nonlinear binary model, which was linearized and then solved by LINGO.…”