Abdul Samad Shibghatullah
29
30052008
Constraint programming provides a powerful and easy system for modelling restrictions and using these restrictions to search for a solution Tsang, 1993. Layfield et al. 1999
used constraint programming to remove relief points that are unlikely to be used in good schedules, thus reducing the problem size. The program first produces the morning part
of the schedule simulating the manual scheduling process. It puts a limit on the number of spells to prevent too short duties being produced. A morning schedule is constructed
by using randomised heuristics to build the partial schedule one duty at a time. Several morning schedules are constructed, and the relief points not used in these schedules are
removed. Then the algorithm performs iterative process to construct a feasible crew schedule that satisfies all the constraints. This program can also be used to produce the
evening part of a schedule. The process has speeded up TRACS II in several cases, but its solution cost is mostly slightly higher Layfield et al., 1999.
2.3.4 Critiques of the Current Approaches
In this section we will provide a brief critique of the approaches described in the previous subsections. The aim is to assess whether or not they are able to deal with the
UE problem. If there is any approach which can, then we will investigate details of that approach and identify its advantages and disadvantages.
Heuristic approaches rely upon the knowledge of expert schedulers and they are useful in some applications, since they were customised for individual companies and thus
could be fully tailored to meet the specific requirements for individual companies. However, these approaches were not easily adaptable to other companies and had to be
substantially modified to fit new conditions. Furthermore they were not suitable for general optimisation Wren and Rouseau, 1995; Wren, 1998. Regarding the ability to
deal with UE in real time, we find that heuristic approaches do not have a feature to deal with them. To the best of our knowledge, none of the heuristic approaches touch the
issues of UE. We believed that as most of the approaches were employed in the early stage of automated-scheduling before the 1980s, the prime goal is to automate the
scheduling process and obtain an optimum schedule or at least the same results as produced through the manual way of scheduling. This is due to the fact that automating
and finding an optimum schedule is really hard task and proven to be NP-Hard Wren and Rousseau, 1995; Fores et al., 1998; Kwan et al., 2000; Wren, 2004.
Abdul Samad Shibghatullah
30
30052008
Mathematical approaches were the most appealing in terms of commercial prevalence. According to Wren 2004, integer programming combined with heuristics is the best
near-optimum solution currently available. This is supported by the fact that most of the prominent scheduling packages use this approach such as IMPACS Parker and Smith,
1981; Smith and Wren, 1988, HASTUS Lessard et al., 1981; Rousseau and Blais, 1985, EXPRESS Falkner and Ryan, 1992, and TRACS II Willers et al., 1995; Fores
et al., 1999, 2001, Wren et al., 2003. However, to the best of our knowledge, most of the mathematical approaches do not have mechanisms for dealing with the UE problem,
except in TRACS II and the research by Huisman and Wagelmans 2006. In our opinion, the reason why most of them do not have mechanisms for dealing with UE is
because obtaining optimum schedules is the main issue. The issue of UE has become important only recently because of privatisation and the subsequent demand for quality
service Huisman and Wagelman, 2006. That is supported by the fact that research looking at UE only started to emerge in 2003. Although TRACS II was developed in
1994, its flexibility utilities were only reported in 2003 Wren et al., 2003; Kwan et al., 2004.
There is a limitation in TRACS II when it comes to dealing with UE. According to Wren et al. 2003, TRACS II only deals with planned changes, that is, those which can
be predicted several days or weeks in advance, and with not day-to-day unpredictable events. Wren et al. 2003 argue that any automatic approach that changes crew
schedules in real-time has to rely on the crews acceptance of new workings, which may extend the working day and interfere with leisure activities. However, Wren et al.
2003 suggest that it is possible any real-time system can rely on the data produced by TRACS II, and when UE take place the real-time system will generate a number of
possible quick responses, which may be discussed with the crews involved. This suggestion by Wren et al. 2003 supported the fact that UE are an important issue and
TRACS II is still not fully capable in dealing with UE and the urgent need for automatic real-time systems.
Huisman and Wagelmans 2006 have proposed a dynamic integrated bus and crew scheduling system that will reschedule the crew and bus simultaneously whenever
lateness takes place. Several reschedulings may be required in a single day. The method
Abdul Samad Shibghatullah
31
30052008
produced good results but there are a few assumptions in the research that are not feasible in the real world. First, “passengers have a higher priority than crews”. Thus,
there is a possibility of violation of crew rules whenever a bus is late. That means crews may have to shorten their break or not take a break just to make sure the bus is running
on time. Although this is appropriate to guarantee that bus service run smoothly, EU driving rules should not be broken which is the case here. Furthermore, this is not
acceptable to the crew. Second, “a trip can only start late due to a delay of the vehicle and not due to the crew”. This assumption is not realistic due to the fact that the crew is
one of the causes of UE. Third, “the number of vehicles and crews is unlimited”. This is not possible as bus companies usually have a limited number of buses and crews.
Mathematical programming approaches have had more success in obtaining optimum schedules. However the nature of the mathematical approach is such that each computer
run may take a long time and larger problems have to be sub-divided, and there is no guarantee that an integer solution can be found within practical computational limits
Kwan et al., 1999. Other approaches genetic algorithm, tabu search, ant system, and constraint programming aim to tackle these shortcomings. Some of the approaches
were reported producing good results when compared to heuristics such as genetic algorithm Li and Kwan, 2001; 2003. However, the capability of these approaches for
dealing with UE there is still not present. In our opinion, the reason for is because this is not part of their aim, thus their attention and direction is only directed towards obtaining
optimum schedules. In summary, although the current approaches have been successful in finding optimum
or near-optimum schedules, more research is needed to develop approaches that would effectively cope with the UE problem. When considering scheduling of public transport,
the management of UE, such as lateness, delay and crew unavailability, are of paramount importance. To cope with these conditions the scheduling system needs to
have some mechanism for dynamically rescheduling previously agreed schedules in real-time. To tackle this issue this research proposes a MAS approach to bus crew
rescheduling that is able to reschedule in real-time without disrupting the whole schedule. The definition and descriptions of MAS is provided in the Section 2.5. Prior
to that, the following section presents interviews with bus companies that tell us
Abdul Samad Shibghatullah
32
30052008
practical experiences of bus companies in day-to-day operation especially in dealing with the UE problem.
2.4 Interviews with Bus Companies
