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common sense and past experiences. The decisions are sometimes inconsistent and not well understood Li et al., 2007. There are not many articles in the literature on how
bus operators manage UE in a real world scenario. In order to obtain more information we conducted interviews with three bus companies in London and the outcomes are
presented in Section 2.5.
2.3 The Current Bus Crew Scheduling Approaches
In this section, we discuss the current approaches and their ability in tackling the UE problem. The current approaches used in bus crew scheduling can be grouped into three
main groups: heuristics, mathematical programming, and others Wren and Rousseau, 1995; Fores et al., 2002; Li and Kwan, 2003. The reviews are based on previous
research published in books; journals; conferences proceedings; theses; reports and websites. Before presenting the findings, Subsection 2.3.1 gives an overview of the
crew scheduling process, its definition, constraints and shift types. Thereafter, the following subsections present the three groups of current approaches. Subsection 2.3.5
presents evaluations and critiques to the current approaches in regard to tackling the UE problem.
2.3.1 Crew Scheduling Problem
This subsection explains the crew scheduling process, terminology used in this thesis, constraints and types of shifts that are referred to from Wren and Rousseau, 1995; Fores
et al., 1998; Fores et al., 2002; Li and Kwan, 2003; Li and Kwan, 2005. Crew scheduling is a process to find an optimum schedule with a minimum number of duties
and minimum total duty costs. From the vehicle schedules, we can get a list of a bus’s itinerary in a day. Figure 2.1 shows an itinerary for Bus 1. It shows the journey of Bus 1
in a day from depot A back to the same depot. A depot is a place where buses that are not in use park for some time. The bus starts from depot A at 7:15 and finishes at 19:45
in the same depot. Between these, the bus passes the relief points B and C. A relief point is a location and time where and when a change of crew may occur. Between a
relief point or a depot is a piece of work. The work of a single crew in a day is called a dutyshift, which consists of several spells of work. A spell contains a number of
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consecutive pieces of work on the same vehicle, and a crew schedule is a set of duties that covers all the required driving tasks.
Figure 2.2: Representation of a Bus Journey in a Day adapted from Li and Kwan, 2005
The main constraints that affects the bus crew scheduling problem is the labour agreement rules that exist between 1 the Transport and Workers’ Union and bus
operators and 2 European driving hours rules and the UK directive governing the working condition. The main purpose of these rules is to ensure that crews do not work
unacceptable duty; hence the rules provide rigid guidelines relating to the construction of duties. The following is a list of some global rules typically used by bus operators:
maximum total working time; minimum time allowance for signing on and off at the depot; paid allowance for signing on and off at the depot; minimum length of a meal
break and the shift pattern. Having these rules makes it is a challenge to find optimum schedules especially when involving large resources of crews and buses to serve the
high frequency route in an urban area. There are three types of shift: straight shift, split shift and overtime shift. The straight
shift is a shift consisting of two stretches separated by a meal break of thirty to sixty minutes. A split shift is spread over maybe about twelve hours containing two stretches
separated by a long break of several hours. A straight shift can be further divided into the following three types: an early shift that takes an early bus out of depot and covers
part of the morning peak, a late shift that takes a late bus into the depot and covers part of the afternoon peak, and middle shift. The main purpose of the split shift is to provide
drivers to cover the peak periods when more buses are in operation. They also assist in maintaining the service whilst drivers from other duties take their meal breaks.
715 805 855 945
1035 1125
1305 1215
1355 1445 1535 1625 1715 1805 1855 1945
Bus 1 Piece of work
A B
C A
B C
B C
B C
B C
B C
B C
Depot Depot
Relief Point
Relief Time
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Overtime shifts consist of one-part shift of around two to four hours. These are in addition to normal shifts for relatively high payment and may be useful in covering
peaks in demand.
2.3.2 Heuristics
