Abdul Samad Shibghatullah
4
30052008
In practice, crew or bus rescheduling is manually managed based on supervisors’ capabilities and experiences in managing UE. They often employ commonsense and
past experiences that are blended in a messy, sometimes inconsistent, and not well- understood way Li et al., 2007. For example, the current practice in Taiwan as
mentioned by Cheng and Chang 1999, is that experienced dispatchers supervisors use their intuition and knowledge to manage abnormal conditions in an ad hoc manner.
This is more or less common practice in the rest of the world. We argue that manual crew rescheduling has many deficiencies that are hard to reschedule and result in slow
decisions when many UE happen at the same time, possibly breaking the EC driving hour rules, and that the decisions are not optimum in the use of crew resources. Thus in
this research we propose automated crew rescheduling to overcome these deficiencies. The following subsections discuss the limitations of current research approaches in
dealing with UE, then the limitations of manual crew rescheduling, and finally suggests our approach that may help to overcome those limitations.
1.2.1 Limitations of Current Research Approaches
Research into automated crew scheduling has attracted a large number of researchers since the 1960s Wren, 2004. Most the research was presented in a series of
international conference on Computer-Aided Scheduling of Public Transport since 1975 Preprints proceeding, 1975; Wren, 1981; Rousseau, 1985; Daduna and Wren, 1988;
Desrochers and Rousseau, 1992; Daduna et al., 1995; Wilson, 1999; Voss and Daduna, 2001; Hickman et al., 2004; Preprints proceeding, 2006.
The common objective of automated crew scheduling is to find the optimum schedule with the minimum number of dutiesshifts and minimum total duty costs. In fact,
minimisation of the total number of duties is regarded as more important since there are many costs that depend directly on the number of crews regardless of their wages Wren
and Rousseau, 1995. Crew expenses involve a large proportion of a bus’s operational costs and form at least 45 of total operational costs Yunes et al., 2000; Meilton,
2001. Duty costs depend on the combination of work that they contain, incorporating the hourly wage and penalty costs for undesirable features such as long or unsociable
hours.
Abdul Samad Shibghatullah
5
30052008
Current approaches used in bus crew scheduling can be grouped into three main groups: heuristics, mathematical programming, and others Li and Kwan, 2003; Fores et al.,
2002. These groups are not mutually exclusive as some mathematical programming approaches may involve heuristic techniques to some extent; other approaches such as
genetic algorithm or tabu search may involve mathematical programming, etc Fores et al., 2002; Li and Kwan, 2003; Wren, 2004; Li and Kwan, 2005. However, the most
common crew-scheduling package uses mathematical programming combined with heuristic approaches Wren, 2004.
Before the 1980s, heuristics were mainly used to solve crew scheduling problems because computers were not powerful enough to run mathematical
programming models, and the techniques in mathematical programming were also not advanced
Wren and Rousseau, 1995; Li and Kwan, 2003. Heuristic approaches rely on the knowledge of expert schedulers to build schedules or restrict the duty formation to those
duties that are likely to appear in good schedules. Many of the approaches are first to construct an initial schedule, and then improve the schedule by making limited
alterations Wren and Rousseau, 1995; Wren, 1998. In mathematical programming approaches, crew-scheduling problems are usually
formulated as set covering problems. A set-covering model is established to find a set of feasible duties that covers all pieces of work and minimises the total costs of the
operation Smith and Wren, 1988; Fores et al., 2002; Wren et al., 2003. If the objective is to cover each piece of work with exactly one duty then it is called a set-partitioning
model Banihashemi and Haghani, 2001. According to Banihashemi and Haghani 2001, there are three different approaches for solving this problem. These are first,
formulating the problem as an integer linear programming model then finding the best combination of the feasible duties. Second, a column generation approach is used to
find the best combination of the feasible duties. The third starts from a set of feasible pre-constructed duties but continues to produce other feasible duties if they could
improve the solution. Other approaches exist such as genetic algorithm Clement and Wren, 1995; Kwan et
al., 1999, tabu search Cavique et al., 1999; Shen and Kwan, 2001, ant system
Abdul Samad Shibghatullah
6
30052008
Forsyth and Wren, 1997, and constraint programming Layfield et al., 1999. In the genetic algorithm approach, the pieces of bus work are represented as chromosomes and
the value of each gene identifies the duties that cover it. It then discards or chooses duties from the complete set until the bus work is covered and no duty is redundant Li
and Kwan, 2001; Li and Kwan, 2003. Tabu search is a searching approach that searches from a large set of feasible duties by iteratively removing some inefficient
duties and then repairing the broken schedule Shen and Kwan, 2001. In the ant system, the virtual ants trace paths through a bus schedule with the paths representing
crew duties to create crew schedules. Good duties will be used more often by the ants and are more likely to be chosen for a crew schedule Forsyth and Wren, 1997.
Constraint programming provides a powerful and easy system for modelling restrictions and uses these restrictions to search for a solution. In bus crew scheduling, problem
variables represent pieces of work and the domain of each variable is the set of indices of the duties that covered the piece of work. The algorithm performs iterative process to
construct a feasible crew schedule that satisfies all the constraints Layfield et al., 1999.
Most of the current approaches described above are primarily focused on finding optimum or near-optimum crew schedules. These approaches assume a static
deterministic environment where complete knowledge of the problem is available without consideration of any kind of UE. This is rarely the case in the real world. Most
real-world scheduling systems operate in dynamic environments subject to various UE that can happen at any time. The probability of occurrence of such events is usually
higher when buses operate in high-frequency routes and in busy cities. UE usually disrupt bus operation and they are difficult or impossible to foresee. Consequently, the
resulting schedule may be neither feasible nor nearly optimum any more. To the best of our knowledge, there are two pieces of research Wren et al., 2003 and
Huisman and Wagelmans, 2006 that look at how to deal with UE that relate to crew. However, TRACS II Techniques for Running Automatic Crew Scheduling, Mark II -
by Wren et al., 2003 only deals with planned changes, that is those that can be predicted several days or weeks in advance, and not unpredictable events. Wren et al.
2003 argue that any automatic approach that deals with UE has to rely on the drivers
Abdul Samad Shibghatullah
7
30052008
acceptance of new workings which may extend the working day and interfere with leisure activities.
Huisman and Wagelmans 2006 have proposed a dynamic integrated bus and crew scheduling system that will reschedule the crew and bus simultaneously whenever an
UE occurs. However, in our opinion, and in realistic situations, it is not practical to reschedule the whole crew schedule whenever a crew becomes unavailable. This is
because the complexity associated with rescheduling can be understood from the constraints i.e. driving hour rules of the crew itself. When trying to conduct any
rescheduling activities, schedulers need to consider cost and time factors, such as the number of available members, driving hours left for each one, and their location of
every crew. With such added constraints it becomes very difficult for the system to find an optimum schedule.
There are a few assumptions in the research by Huisman and Wagelmans 2006 that are not feasible in a real world. First, the passengers have a higher priority than crews.
Thus, there is a possibility of violation of the crew rules whenever a bus late occurs before the break time. The crew has to shorten the break or not take a break just to make
sure the bus operate on time. Although this is appropriate to guarantee that the bus services run smoothly, the EC driving rules should not be broken. Furthermore, this is
not acceptable to crews. Second, a trip can only start late due to a delay of the vehicle and thus not due to the crew. This assumption is not real due to the fact that crews are
one of the causes of UE. Third, availability of unlimited crew members, however, this is hardly realistic.
1.2.2 Limitations of Manual Way of Crew Rescheduling
