Train Platforming Problem - Geoinformatics for Intelligent Transportation - page 146

the problem of train routing as a weighted node packing problem, using bivalent
programming, while the solution algorithm applies the branch-and-cut method.
A disadvantage of the above presented models is that the calculations connected
with them are computationally too complex and time consuming. Another, prac-
tically oriented approach has given up on applying the integer programming
methods, and replaced them by the heuristics, solving the scheduling and routing
problems at a time [ 4 ]. The algorithm incorporates, or considers, the operational
rules, costs, preferences and trade-offs, which are applied by experts creating plans
manually. The shortcoming of this approach is obvious: since it is a heuristics, the
optimality of the resulting plan is not guaranteed.
Other way of research, e.g. Ba ka [ 5 ], Chakroborty and Vikram

[ 6 ], has been directed at operational train management. In real time it is necessary to
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ect the requirements of the operation burdened with irregularities, i.e. to re-
schedule the arrival and departure times, and/or re-route trains.
In this paper we propose a mixed integer programming (MIP), bi-criteria model
of the train platforming problem. The problem can be solved by a lexicographic
approach, where particular criteria are ranked according to their importance.

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2 Problem Formulation

The train platforming problem consists of the following partial issues. For each
train,

a platform track must be speci ed at which the train should arrive; the platform

track assignment determines the route, on which the train approaches,

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arrival time at the platform and departure time from the platform need to be
determined.

￿

The solution should minimise deviations from the planned arrival and departure
times and maximise the total preferences for platforms and routes.
The inputs to the mathematical programming model are as follow:

1. track layout of the station, which is necessary for determining feasible platform

tracks for a train and con fl icting routes,

2. list of trains, where the data required for each train include:

(a) planned time of its arrival at the platform,
(b) planned time of its departure from the platform,
(c) line on which the train arrives (in-line) and departs (out-line),
(d) list of feasible platform tracks with their desirability for the train,
(e) category of the train.
All time data are given in minutes.
Further on we present the formulation of the MIP model. First we need to
explain the symbols used: