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921 shift scheduling applied.
Table 1: Cut of the shift scheduling applied Staff
Date 1
2 3
4 5
6 A
N N
E ME
M O
B E
ME M
O N
N C
M O
N N
E ME
The first column in Table 1 shows the staff name and the second until sixth column show the shift assigned to
each staff for each day shown in date. The alphabet in each cell show the shift assigned to each staff each day. “M”
refers to morning shift, “E” for evening shift, “N” for night shift, and “O” for one-day-off. The shift pattern in 1 cycle
period will be applied overlapping among 3 staffs, so that when 1 staff has one-day-off then 2 other staffs will be on
duty, i.e. 1 staff assigned for 1 shift and the other staff assigned for 2 others consecutive shifts. Staff A in Table 1
starts on 1
st
date with the 1
st
day of the cycle shift N, but staff B starts with the 3
rd
day of the cycle and staff C with the 5
th
day of the cycle. This overlapping condition is applied in order to ensure that there will be no staff
shortage when 1 staff has one-day-off. Staff C has one-day- off on date 3, so that in the same day staff A is assigned in
shift N and staff B is assigned in shift M continued in shift E. The shift E assigned to staff B is considered as overtime.
This cyclic shift pattern results in short between-days break-time, 8 hours between days, i.e. from shift N to shift
E next day and form shift E to shift M next day. Table 1 shows that staff A is assigned in shift N on date 2 which
will finish at 7 a.m. next day, i.e. date 3. Staff A on date 3 is assigned in shift E start at 3 a.m., consequently staff A just
has 8 hours for break, i.e. from 7 a.m. until 3 p.m. This condition is repeated for date 3 to date 4 and also for date 4
to date5 from shift E to M. As a result, staff will be late to come in shift M at 7 a.m. because in the previous day he
has been assigned in shift E finished at 11 p.m. Moreover, managements view that this cyclic shift pattern will give
indirectly influence to staff performance because for 3 consecutive days staff just has 8 hours leisure time for rest,
family, and social activities.
For the problem addressed in this article, the major concern is to determine cyclic shift pattern that give
adequate between-days break-time for Front Office staffs to have leisure time for rest, family, and social activities.
Minimum between-days break-time is considered based on remaining time of 1 day 24 hours after a staff is on duty
for 1 shift. The management will regulate new shift time arrangement, i.e. morning shift M from 8 a.m. to 4 a.m.,
evening shift E from 4 a.m. to 11 a.m., and night shift N from 11 a.m. to 8 a.m. The longest shift duration is the shift
N, i.e. for 9 hours, so minimum between-days break-time that could be given to a staff is 15 hours. The number of
staff is remain constant 3 staffs during a month and staffs are not allowed to select a certain day for one-day-off. The
shift pattern is arranged in cyclic period that evenly distribute each shift type among all staffs, and should be
easy to remember for staffs.
The remainder of this paper is organized as follows. Section 2 describes the relevant literatures on shift
scheduling and cyclic scheduling. In section 3, we describe the solution method in detail and the result. Finally, section
4 presents conclusions and some suggestions for future research.
2. LITERATURE REVIEW
Workforce scheduling problem classified into 3 categories, i.e. 1 day-off scheduling, 2 shift scheduling,
and 3 tour scheduling, which combine simultaneously day-off and shift scheduling. Scheduling problem addressed
in this article focus on tour scheduling, that is develop cyclic shift pattern for staff rostering in which also
considering day-off assignment in the pattern and between- days break-time constraint. The major concern is to
determine the work stretch length, one-day-off assignment, and shift assignment in work days. The developed work
stretch length, day-off assignment, and shift pattern should be in cyclic manner and prevent workforce shortage.
Elshafei and Alfares 2008 has conducted research in day- off assignment to minimize labor cost using dynamic
programming algorithm. Elshafei and Alfares 2008 has considered work-stretch-length, maximum number of
word-day and off-day in a week, and work-sequence- dependent cost structure as a constraint, but has not
considered multi-shift application yet.
Some of researches in shift scheduling have been done by Bard and Wan 2005, Burke et al. 2006, Bhulai et al.
2008, and Rekik et al. 2010. Bard and Wan 2005 has proposed algorithm for weekly scheduling in service
industry which has full-time and part-time employees. The developed algorithm overcomes workforce shortage due to
high workforce requirement by applying overtime, increasing number of part-time hours, and calling in casual
workers. The resulting shift scheduling provides daily assignments for each worker only for 1 week based on
weekly demand requirement. Burke et al. 2006 also provides daily assignment in shift scheduling. It is for nurse
rostering to handle personnel requirement in term of time interval, that is the representation of the personnel
requirements per day in terms of the start and end times of personnel attendance. Shift type combinations that fulfill
the personnel requirements is developed by split or combine the shifts. Bhulai et al. 2008 have also proposed
Yuniartha
922 daily assignment in shift scheduling which considering
multi-skill workers. The proposed method consists of 2 steps, staffing level and shift scheduling. Staffing level
translate the amount of workload into number of required workers. Shift scheduling then uses such that staffing level
to assign worker in pairing of shift into a rosters.
For considering shift flexibility, Rekik et al. 2010 have developed a model of shift scheduling problem that
includes different forms of flexibility in terms of shift starting times, break lengths, and break placement in order
to determine total workforce size. Other researches in shift flexibility have been done by Rekik et al. 2004, Addou
and Soumis 2007, Brunner et al. 2009, and Brunner et al
. 2011. In contrast to Rekik et al. 2010, these researches have considered the day-off scheduling. Rekik et
al . 2004 and Addou and Soumis 2007 focus on
minimizing total labor cost of all shifts to determine total workforce size. Brunner et al. 2009 and Brunner et al.
2011 also focus on minimizing labor cost but not in rostering problem, that is personnel assignment under the
restrictions by regulation or individual preferences.
Litchfield et al. 2003 and Kaluzny and Hill 2011 have provided rostering regarding shift scheduling and day-
off assignment. Day-off assignment in Litchfield et al. 2003 considers constraints of staffing requirement,
employees avaibility, maximum and minimum number of shift per week, and employee experience requirement per
period. While Kaluzny 2011 assigns security personnel in cyclic six days work pattern base on required number of
personnel each day. The shift in cyclic six day pattern is previously determined. The resulting roster in Litchfield et
al
. 2003 and Kaluzny and Hill 2011 is only for 1 planning period and it may vary for other period by the
personnel requirement. Whereas the same work pattern may repeat each n periods, called cyclic scheduling. Cyclic
scheduling may apply in day-off scheduling, shift scheduling, or tour scheduling. Alfares 2001 have
proposed a method in cyclic day-off scheduling. The objective of the proposed model in Alfares 2001 is
minimizing number of worker in 7 work days with 2 consecutive day-off. While for cyclic shift scheduling,
Maenhout and Vanhoucke 2009 have proposed algorithm in rostering problem considering specific characteristics of
personnel. The considered employee characteristics are cyclical roster type, degree of employment, skill categories,
and general preferences. Cyclical roster type is previously predetermined shift and day-off assignment in a week. And
there are 2 types of cyclical roster type.
Cyclic tour scheduling problem has been investigated in Carter and Lapierre 2001, Felici and Gentile 2004,
Laporte and Pesant 2004, Bard and Purnomo 2007, and Lezaun et al. 2010. These researches have proposed
algorithm to assign work day and off-day in evenly distribution among personnel. The number of consecutive
work day or cycle length of these researches, except in Felici and Gentile 2004, is considered as parameter or
constraint, not as solution. Carter and Lapierre 2001 and Bard and Purnomo 2007 explicitly use certain amount
hours of break time as constraint for consecutive shifts. Felici and Gentile 2004, Laporte and Pesant 2004, and
Lezaun et al. 2010 use shift change pattern as break constraint.
3. SOLUTION METHOD
