Rail freight transportation: A review of recent optimization models for train routing and empty car distribution

Abstract

This paper describes two types of rail transportation problems in detail. These are train routing and makeup, and empty car distribution problems. Some of the recent optimization models which address these problems are reviewed and the areas for potential improvements in rail transportation literature are identified. The type of interactions which exist between routing, makeup, and empty car distribution decisions are highlighted and potential areas for future research are identified.

Timetabling optimization of a mixed double- and single-tracked railway network

“…Constraint DT2 means that if trains i 1 and i 2 use track t of segment j, at least one of the variables x i 1 ;i 2 ;j or y i 1 ;i 2 ;j must be 1. Note that given a double track segment two trains i 1 and i 2 running in the same direction can use the two tracks in parallel in the same segment j, because this is possible for x i 1 ;i 2 ;j ¼ 0 and y i 1 ;i 2 ;j ¼ 0 (see constraints (9)-(12)), because this solution satisfies (19) and (18) because q i 1 ;j;t þ q i 2 ;j;t 6 1.…”

“…Since we need cases in which x i 1 ;i 2 ;j ¼ y i 1 ;i 2 ;j ¼ 0, constraint (19) cannot be written = 1 instead of < = 1, because we do not know ''a priori" which train uses which track. It is the program who assigns only one track (constraint DT1 forces each train to use one and only one track) to each train by means of the binary variable q i 1 ;j;t (the variable q i 1 ;j;t ¼ 1 if train i 1 uses track t in segment j) depending on the other trains.…”

A hybrid solution method for fuzzy train formation planning

“…An implicit enumeration algorithm with -optimality to solve the TFP model is proposed by Lin [11]. Haghani pointed out there exist intense interactions between the routing of trains, their makeup and frequency, and the empty car distribution process [12]. However, the models that consider all these aspects often become extremely complex, if not simply intractable.…”

Single European Sky and Single European Railway Area: A system level analysis of air and rail transportation

“…The methods proposed are summarized in several surveys (Assad, 1980;Caprara et al, 2007;Cordeau et al, 1998;Haghani, 1987;Hansen, 2006;Huisman et al, 2005;Liebchen et al, 2008;Lusby et al, 2011;Törnquist, 2006). Typically, these methods seek for the optimal timetable at a macroscopic level, i.e., considering only lines and neglecting detailed constraints at stations and junctions.…”