In the previous paragraph, I have described some of the necessary inputs for the equipment assignment problem. In this section, I will describe in more detail what the output of the equipment duty planning task is.
The output of the equipment duty planning is a specification of a set of ``duties'' that are connected into ``rotations'' (a set of consecutive duties between two maintenances). A duty is a daily plan for one engine of a particular type. The equipment duty planning never deals with the actual physical engines. Rather, it must be viewed as a planning at a logical level. A duty thus corresponds to a logical engine. In principle, a logical engine will be associated with a physical one.
There are two important reasons why the equipment duty planning never deals with the actual physical engines. On the one hand, a large part of the equipment duty planning is concerned with the actual driving of trains. These trains must be ensured even if the physical engine that drives a train cannot resume its normal operation. On the other hand, a planning at a logical level increases maintenance flexibility. A physical engine that suddenly requires maintenance may be easily replaced by another physical engine of the same type without interrupting the logical plan that the first engine was executing.
Logical engines (duties) are denoted by a four letter code (e.g. ``A713''). The first two letters refer to the type of engine (``A7'' in this case). The last two digits refer to a ``duty number''. The duty itself describes all the actions that one engine of the indicated type will perform in one period of 24 hours. A ``diagram'' contains the set of duties performed by all engines of the same type.
Duties are graphically represented on the X-t diagrams. Figure 2 shows an example. It describes the duties that need to be performed on Sunday by engines of type HLE-11 (electrical engines). The engines receive maintenance in station FMBZ (Brussels South Station). Consider for example the duty ``A903'' (which starts in station FN). The small squared symbol which is before the symbol ``A903'' indicates a local operation that belongs to that duty. The details of this operation can be found in the window. Here we can see that the operation is called PERQUAI (which means that the engine will drive from the parking place to the platform). We also see that the operation is only executed on Sundays, that it starts at 06:25 and ends at 06:32.
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