Proceeding of the First International Conference on Modeling, Simulation and Applied Optimization, Sharjah, U.A.E. February 1-3, 2005
SCHEDULING LABORATORY TECHNICIANS AT AN OIL REFINERY
Hesham K. Alfares
King Fahd University of Petroleum & Minerals
Systems Engineering Department
PO Box 5067, Dhahran 31261, Saudi Arabia
hesham@ccse.kfupm.edu.sa
ABSTRACT
In this paper, the methodology and recommendations of an employee
scheduling study at the industrial laboratory of a large oil refinery
are presented. The objectives were to determine labor requirements
for each shift on each day of the week, the optimum workforce,
and the most effective employee work schedules. The steps of the
methodology included: (1) calculating the average workload for
each shift and each day of the week, (2) developing a integer
programming model of the problem, and (3) determining the
optimum shift schedule and workforce size. Implementing the
recommendations of the study is expected to improve the
laboratory’s operational efficiency, reduce the number and the
cost of employees, and improve their morale.
1.
INTRODUCTION
This paper presents an employee scheduling study conducted at
the industrial Laboratory Unit of a large oil refinery, whose
identity will be kept confidential upon the client’s request. The
Laboratory Unit is composed of three sections: (1) General Lab,
(2) Gas Lab, and (3) Water Lab. These sections are not physically
separated, and do not employ different sets of employees, but
rather designate the different types of tests conducted in the Unit.
The laboratory technicians perform a variety of routine and nonroutine tests on samples of end and intermediate products and
byproducts. For routine tests, these samples are taken from
specific locations at specific times according to a predetermined
weekly schedule. These laboratory tests are designed to: (i) ensure
the smooth running of the refinery, (ii) assure the quality of the
different products, and (iii) deduct any occurring or potential
problems. Non-routine lab tests are needed in all cases of
abnormal situations such as scheduled maintenance, equipment
failure, construction or expansion of facilities, and irregularities in
the crude inflow.
The Laboratory Unit has been operating on the 7/2-7/2-7/3
schedule, with three 8-hour shifts per day, seven days a week.
Shift 1 (the morning shift) lasts from 6:00 a.m. to 2:00 p.m., while
shift 2 (the swing shift) lasts from 2:00 p.m. to 10:00 p.m., and
shift 3 (the night shift) lasts from 10:00 p.m. to 6:00 a.m. Over a
four-week cycle, the 7/2-7/2-7/3 schedule assigns employees to
four equally-sized teams (1, 2, 3, and 4), as shown in Figure 1.
On any given day, three teams are assigned to the three daily
shifts, while the fourth team is off. Currently, the Lab Unit has 28
technicians, who are equally distributed among four seven-man
teams.
According to the 7/2-7/2-7/3 schedule, the number of employees
assigned to work is constant in every day and every shift
throughout the week. However, sharp variations have been
observed in the workload among the three shifts and between
regular workdays and weekends. Thus, employees have
experienced excessive pressures during peak hours in the morning
shift, especially on regular workdays. This has negatively
impacted the employees’ morale and also the operational
efficiency of the laboratory. Moreover, management felt that
assigning the same number of employees to low-demand periods,
such as the night shift, is very wasteful of labor resources. The
purpose of this study was to determine the best schedule and
staffing level of the Laboratory Unit in order to reduce cost,
enhance operational efficiency, and improve employee morale.
Specifically, the aim was to achieve the three following
objectives:

Determining the varying labor requirements that match the
workload for each shift during each day of the week for the
Laboratory Unit.

Deciding the most efficient and cost effective work schedules
for the Lab Unit that satisfy labor requirements and help in
improving employee morale.

Determining the optimum workforce size required to
efficiently operate the laboratory by qualified employees.
2.
LITERATURE REVIEW
The main aim of employee scheduling is to assign employees to
work times within a given planning horizon. Employee scheduling
problems are generally classified into three types: shift (time-ofday) scheduling, days-off (day-of-week) scheduling, and tour
scheduling, which combines the first two types. The scheduling of
the Laboratory Unit’s technicians is classified as a tour scheduling
problem, because it involves the determination of both work hours
ICMSAO/05-1
Proceeding of the First International Conference on Modeling, Simulation and Applied Optimization, Sharjah, U.A.E. February 1-3, 2005
Day
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Shift 1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
Shift 2
3
3
4
4
4
4
4
4
4
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
Shift 3
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
1
1
1
1
1
1
1
2
2
2
Figure 1. The 3-shift 7/2–7/2–7/3 schedule.
(working shift) of the day and workdays of the week for each
employee. A large number of optimal and heuristic methods have
been proposed for modeling and solving the tour scheduling
problem. Alfares (2004) provides a comprehensive review and
classification of recent tour approaches.
While the literature on general employee scheduling is very huge,
previous work on employee scheduling in laboratories is very
scarce. Franses and Post (2003) offer the only model that
specifically addresses this problem. They model the assignment of
tasks to lab employees as a maximal matching problem in a set of
interrelated bipartite graphs. They also describe an algorithm that
utilizes user-supplied profiles to assure the continuity of tasks
over the week.
Other authors have considered laboratory scheduling as a small
component of a larger production planning system or decision
support system (DSS). Chase and Rajagopalatan (1993) describe a
production planning and scheduling system at a chemical testing
laboratory, but their main focus is not employee scheduling, but
sample scheduling. Van Merode et al. (1995) describe a
laboratory DSS, which helps in assigning staff and samples to
workstations. Van Merode et al. (1996) also describe a simulation
model for testing the performance of various planning rules, given
the lab’s workload and capacity (i.e., equipment and staffing).
3.
Extensive observations of technicians in all lab sections were
performed, and thorough time measurements of their activities
were recorded. These observations focused on measuring the
duration and frequency non-routine activities during the morning
shift, since it constitutes the period of the heaviest workload. No
observations and time measurements were needed for routine
activities, since detailed routine test schedules and accurate time
estimates were supplied by the Laboratory Unit. The Unit’s
supervisor input was also obtained to verify and update the list of
observed and scheduled activities. Based on the observations and
the supervisor’s input, an extra 40% was added to the routine
workload to account for non-routine samples.
Data was collected on applicable employee work schedules and
their costs. Labor regulations allow only two work schedules to be
used by the laboratory technicians. The first schedule is the usual
5/2 morning-shift work schedule, with five workdays and two
consecutive off-days per week. The second schedule is the 7/27/2-7/3 work schedule, in which each employee works 21 days on
three different shifts during each 28-day cycle. Since the 7/2-7/27/3 schedule involves overtime payments and shift premium, its
costs is higher than the cost of the 5/2 schedule. The average
annual cost per employee is $21,900 for the 5/2 schedule, and
$27,100 for the 7/2-7/2-7/3 schedule.
DATA COLLECTION
4.
General information on the processes and policies of the
Laboratory Unit was obtained by interviewing the concerned
personnel, including the Unit’s supervisor, group leaders, and all
available lab technicians. Data was collected on the lab test
schedules, technicians work schedules, and current workforce
size. Information was also gathered on the company’s employee
scheduling regulations, and the lab’s varying daily workload.
Other relevant statistics were also collected. Sources of data
included:
1.
Daily, weekly, and monthly routine sample test schedules.
Data includes the duration and frequency of each routine
(scheduled) sample test in each lab section.
2.
Monthly employee shift schedules.
3.
Company manuals and regulations on employee work
schedules.
DATA ANALYSIS
Using the data obtained, the number of lab technicians required to
satisfy the current workload in each shift was calculated. Data
analysis proceeded in two steps as follows:
1.
Total man-hours of routine work (i.e., scheduled lab tests)
were calculated for the whole lab, classified by shift and day
type (weekdays and weekends). These man-hours represent
the best estimate of the routine workload for each shift
during weekdays and weekends. These values, displayed in
Table 1, show that the morning shift accounts for 75% of the
lab’s routine workload. On average, non-routine activities
constitute 40% additional workload. Therefore, the values of
Table 1 need to be multiplied by a factor of 1.4 in order to
obtain total man-hours of workload.
2.
In order to determine the number of full time equivalent
employees, it was assumed that each employee works an
average of 21 days (3 weeks) per month and 7.5 hours per
ICMSAO/05-2
Proceeding of the First International Conference on Modeling, Simulation and Applied Optimization, Sharjah, U.A.E. February 1-3, 2005
day. Thus, monthly work time per employee is 157.5 =
112.5 hours on weekdays, and 67.5 = 45 hours on
weekends. Consequently, the following equations were used
to obtain the labor demands shown in Table 2 for each shift
and each day of the week:
ri,s = 1.4Ds / 112.5, i = 1, …, 5, s = 1, …, 3
(1)
ri,s = 1.4Es / 45,
i = 6, 7,
s = 1, …, 3
(2)
where
ri,s = minimum number of technicians required for shift
s on day i
Ds= man-hours required shift s on weekdays (Table 1)
Es = man-hours required for shift s on weekends (Table
1)
a = minimum integer  a
Table 1. Total man-hours per month for the Laboratory Unit
Shift
No.
Work
days
Weekends
Shift
Shift
s
Ds
Es
Total
Morning
Swing
Night
1
2
3
936.6
139.1
176.1
288.6
33.4
70.5
1225.2
172.6
246.6
%
Work
load
74.5%
10.5%
15%
Table 2. Number of technicians required per shift and day type
Shift No.
Workdays
Weekends
Shift
s
ri,s (i = 1,…, 5)
ri,s (i = 6, 7)
Morning
1
12
9
Swing
2
2
2
Night
3
3
3
5.
aisj =  1 if shift s on day i is a work day for tour j
 0 otherwise

For the Laboratory Unit, the difference in the workload between
the morning shift and either the swing or the night shift is very
high. Therefore, it is very inefficient to use only the current 7/27/2-7/3 work schedule, which assigns an equal number of
employees to all work periods. The integer programming model
deals with the variation in labor demands by reassigning some lab
technicians to the 5/2 schedule (morning shift only). By solving
the model, we aim to find the optimum combination of the current
three-shift 7/2-7/2-7/3 schedule with the morning-shift 5/2
schedule that best fits the workload profile.
Inputting all the relevant parameters, the optimum solution of the
above integer programming model is obtained by Excel Solver.
The optimum tour schedule of the Laboratory Unit has 12
technicians (4 teams, each of size 3) assigned to the 7/2-7/2-7/3
schedule to cover all three shifts. Moreover, 12 other technicians
are assigned to the 5/2 schedule to provide additional coverage for
the morning shift with different days off (not necessarily the
weekend) as follows:
Off on days 1-2 = 1
Off on days 4-5 = 1
Off on days 6-7 = 4
Off on days 3-4 = 2
Off on days 5-6 = 2
Off on days 7-1 = 2
The required workforce size and annual labor cost of the proposed
employee schedule can be calculated as:
Proposed workforce size
Proposed annual labor cost
= 12 + 12 = 24 employees
= 12(21,900) + 12(27,100)
= $588,000
Currently, all 28 technicians of the Lab Unit are assigned to the
7/2-7/2-7/3 schedule (4 teams, each of size 7). The annual cost of
the current schedule is equal to 2827,100 = $758,800. Therefore,
the expected reduction in workforce size is 4 employees (14.3%),
while the expected saving in labor cost is $170,800 per year
(22.5%).
MODEL FORMULATION AND SOLUTION
6.
The mathematical programming model of the lab technicians’ tour
scheduling problem can be formulated as follows.
Minimize Z =

J
j 1
cjxj
(3)
Subject to

J
a xj
j 1 is j
 ri,s, i = 1, …, 7, s = 1, …, 3
xj  0 and integer,
j = 1, …, J
(4)
(5)
where
cj = annual cost of assigning one technician to tour j,
($21,900 for 5/2 schedule tours, and $27,100 for
7/2-7/2-7/3 schedule tours),
xj = number of technicians assigned to tour j,
CONCLUSIONS
An employee scheduling problem at an industrial laboratory has
been presented. Originally, the use of a single type of employee
schedules has lead to a mismatch between the varying labor
demands and the constant number of employees assigned to all
time periods. This mismatch created excessive workloads during
peak periods which negatively impacted employees’ productivity
and morale. Several steps were taken in order to solve these
problems. First, the varying staffing requirements were estimated
during each shift on each day of the week. Second, the scheduling
of laboratory technicians to satisfy these staffing requirements at
minimum cost was formulated as an integer programming model.
By allowing different types of employee schedules, the model
provides greater flexibility in matching the varying labor
demands. The optimal solution of this model succeeds in meeting
the staffing demands with a fewer number of lab technicians and a
significantly lower labor cost.
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Proceeding of the First International Conference on Modeling, Simulation and Applied Optimization, Sharjah, U.A.E. February 1-3, 2005
7.
REFERENCES
[1]. Alfares, H., "Survey, categorization,, and comparison of
recent tour scheduling literature," Annals of Operations
Research, Vol. 127, 2004, p 145-175.
[2]. Chase, R.B. and Rajagopalatan, S., "A production planning
and scheduling system at a chemical testing laboratory,"
International Journal of Production Economics, Vol. 29,
1993, p 125-138.
[3]. Franses, P. and Post, G., "Personnel scheduling in
laboratories," in Practice and Theory of Automated
Timetabling IV: Lecture Notes in Computer Science, Vol.
2740, 2003, p 113-119.
[4]. Van Merode, G.G., Hasman, A., Derks, J., Golschmidt,
H.M.J., Schoenmaker, B., Oosten, M., "Decision support for
clinical laboratory capacity planning," International Journal
of Bio-Medical Computing, Vol. 38, 1995, p 75-87.
[5]. Van Merode, G.G., Hasman, A., Derks, J., Schoenmaker, B.,
Golschmidt, H.M.J., "Advanced management facilities for
clinical laboratories," Computer Methods and Programs in
Biomedicine, Vol. 50, 1996, p 195-205.
Acknowledgment
The author is grateful to King Fahd University of Petroleum and
Minerals for supporting this research project.
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