Soal
Penjadwalan Tenaga kerja
Developing a Workforce Schedule
• There are many block scheduling heuristics.
– Manual
– Not efficient and most non-optimizing
– Difficult to test sensitivity
• Linear programming easily applied and much more
powerful.
• Example: suppose we wish to schedule our
employees so that each works five days and has two
consecutive days off each week. Requirement for
employees is:
M
T
W
TH
F
S
SU
6
4
8
9
10
3
2
Workforce Scheduling (cont)
M
6
•
T
4
W
8
TH
9
F
10
S
3
SU
2
Decision variables:
– X1= employees working M,T,W,Th,F
– X7= employees working
Su,M,T,W,Th
Min Z  X 1  X 2  X 3  X 4  X 5  X 6  X 7
St : X 1 
X4  X5  X6  X7  6
X1  X 2 
X5  X6  X7  4
X1  X 2  X 3 
X6  X7  8
X1  X 2  X 3  X 4 
X1  X 2  X 3  X 4  X 5
X2  X3  X4  X5  X6
X7  9
 10
3
X3  X4  X5  X6  X7  2
The manager of a supermarket is trying to calculate the number of
cashiers and grocery baggers she needs to meet fluctuating demand
during the day. The store is open from 6:00 am to midnight every day
of the week. Cashiers work a 6 hour shift, whereas the grocery
baggers work a 9 hour shift. Cashiers can begin working at 6:00 am,
9:00 am, noon, 3:00 pm or 6:00 pm. Baggers can begin working at 6:00
am, 9:00 am, noon, or 3:00 pm. The following table shows the number
of cashiers and baggers required in order to meet the demand.
Cashiers
Time
6:00
9:00
Noon
3:00
6:00
9:00
Period
am to 9:00 am
am to Noon
to 3:00 pm
pm to 6:00 pm
pm to 9:00 pm
pm to Midnight
6
8
10
10
12
6
Baggers
7
9
11
11
13
7
Formulate and solve a linear programming model that minimizes the
number of cashiers and baggers while covering the demand requirements
for a day. Assume that employees can work as baggers or cashiers
exclusively and cannot do both jobs.