MISTA 2009 Conference Program Committee

Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2009)
10-12 August 2009, Dublin, Ireland
n
Minimise W1
∑c
j x j + W2
∑
Subject to
where
j=
1
n
∑
j=
1
x j
aij x j
n is the number of candidate shifts
m is the number of work pieces
x j is a shift variable,
c j is the cost of shift j
a ij
≥
1
n
j=
1
x
j
i = 1,
2,......,
m
= 0 or 1 j = 1,
2,.......,
n
x j
⎧1
if shift j is selected
= ⎨
⎩0
otherwise
⎧1
if work piece i is covered by shift j
= ⎨
⎩0
otherwise
W1 and W2 are weight constants
Fig.2 Set covering ILP for train crew scheduling
In this section, the problem is further illustrated through a discussion of the input and output of a solution
process in practice.
Train units are basic units of rolling stock that would not be broken down into any smaller sub-units during
the operational day, even though a train unit may consist of multiple (e.g. 2, 4, 8, etc.) carriages. However, it is
common for train units to be coupled together for parts or all of their journeys. Train units are usually scheduled
before crew schedules are compiled to cover them. The schedule of a train unit is known as a ‘unit diagram’, an
example of which is shown in Fig.3.
In Fig.3, the main body of a train unit diagram describes timetabled journeys that the unit serves, e.g. from
Ebne at 14.55 to Vic at 16.31, via E Croy, is identified by the train ID (also known as a ‘headcode’) 1F37. The
header of the unit diagram indicates that it is operated on a Sunday (“Su”). The other important information in a
unit diagram concerns coupling (indicated by “ATTACH” or “ATTTT”) and decoupling (indicated by
“DETACH” or “DETTT”), e.g. another unit numbered 117 is coupled with it at Ebne and departs at 09.55, which
is later decoupled after arriving at Ebne again at 13.19. In scheduling train drivers, when multiple units are
coupled, it is obvious that the crew scheduling system should only use one driver for the whole coupled train
formation. For other crew types, e.g. Train Manager, when units are coupled, each unit might require its own
crew because it might not be possible for the crew to get through the coupled units.
Whilst wheel turning work forms the bulk of a crew schedule, some non-wheel-turning work not shown in
a unit diagram may also have to be done by a train crew. Such work has a significant impact on scheduling
because often it could not be pre-determined, but is inserted as required dictated by the scheduling rules. For
example, when a train unit is stationary at a platform, its engine may be left running if the driver remains
onboard. However, the schedule may allow the driver to be relieved by a new driver. In that case, the relieved
driver has to immobilize the engine before leaving, and the new driver may arrive some time after the other
driver has left, and then he has to mobilize the engine again. Both immobilization and mobilization tasks have to
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