Case 2.3 Staffing A Call Center - Book

Case 2.
3 Staffing a Call Center
Avg No. of Calls Total Calls per No. of calls

Work Shift No. of calls from No. of Operators
(per hr) shift from
English Spanish
English Speaking
Speakers Speakers
7 am to 9 am 40 80 64 16 5.333333 6
9 am to 11 am 85 170 136 34 11.33333 12
11 am to 1 pm 70 140 112 28 9.333333 10
1 pm to 3 pm 95 190 152 38 12.66667 13
3 pm to 5 pm 80 160 128 32 10.66667 11
5 pm to 7 pm 35 70 56 14 4.666667 5
7 pm to 9 pm 10 20 16 4 1.333333 2
Decision Variables - English Speaking Operators
7 am to 9 am 9 am to 11 am 11 am to 1 pm 1 pm to 3 pm 3 pm to 5 pm 5 pm to 7 pm
Full Time 6 12 5 1 2 0
Part Time 0 0 0 0 4 0
Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00
Constraints - English Speaking Operators
7 am to 9 am 1 0 0 0 0 0
9 am to 11 am 0 1 0 0 0 0
11 am to 1 pm 1 0 1 0 0 0
1 pm to 3 pm 0 1 0 1 0 0
3 pm to 5 pm 0 0 1 0 1 0
5 pm to 7 pm 0 0 0 1 1 1
7 pm to 9 pm 0 0 0 0 1 1
Objective Function - Minimise Cost English Speaking Operators

MINIMISE COST Z $ 1,228.00
Decision Variables - Spanish Speaking Operators
Full Time 2 3 2 2 1 0
Part Time
Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00
Constraints - Spanish Speaking Operators
7 am to 9 am 1 0 0 0 0 0
9 am to 11 am 0 1 0 0 0 0
11 am to 1 pm 1 0 1 0 0 0
1 pm to 3 pm 0 1 0 1 0 0
3 pm to 5 pm 0 0 1 0 1 0
5 pm to 7 pm 0 0 0 1 0 0
7 pm to 9 pm 0 0 0 0 1 0
Objective Function - Minimise Cost Spanish Speaking Operators
MINIMISE COST Z $ 412.00
Solution
7 am to 9 am 9 am to 11 am 11 am to 1 pm
Full Time English Speaking Operator 6 12 5
Full Time Spanish Speaking Operator 2 3 2

Part Time English Speaking Operator 0 0 0
Minimum Cost $ 1,640.00

1640
No. of Operators
Spanish Speaking
1.333333 2
2.833333 3
2.333333 3
3.166667 4
2.666667 3
1.166667 2
0.333333 1
6 6 >=
12 12 >=
11 10 >=
13 13 >=
11 11 >=
5 5 >=
2 2 >=
2 2 >=
3 3 >=
4 3 >=
5 4 >=
3 3 >=
2 2 >=
1 1 >=
1 pm to 3 pm 3 pm to 5 pm 5 pm to 7 pm
1 2 0
2 1 0
0 4 0
Case 2.3 Staffing a Call Center
Avg No. of Calls Total Calls per No. of calls

Work Shift No. of calls from No. of Operators
(per hr) shift from
English Spanish
English Speaking
Speakers Speakers
7 am to 9 am 40 80 64 16 5.333333 6
9 am to 11 am 85 170 136 34 11.33333 12
11 am to 1 pm 70 140 112 28 9.333333 10
1 pm to 3 pm 95 190 152 38 12.66667 13
3 pm to 5 pm 80 160 128 32 10.66667 11
5 pm to 7 pm 35 70 56 14 4.666667 5
7 pm to 9 pm 10 20 16 4 1.333333 2
Decision Variables - English Speaking Operators
Full Time 6 12 7 1 1 0
Part Time 0 0 0 0 3 1
Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00
Constraints - English Speaking Operators
7 am to 9 am 1 0 0 0 0 0
9 am to 11 am 0 1 0 0 0 0
11 am to 1 pm 1 0 1 0 0 0
1 pm to 3 pm 0 1 0 1 0 0
3 pm to 5 pm 0 0 1 0 1 0
5 pm to 7 pm 0 0 0 1 1 1
7 pm to 9 pm 0 0 0 0 1 1
Objective Function - Minimise Cost English Speaking Operators

Decision Variables - Spanish Speaking Operators
Full Time 2 3 2 2 1 0
Part Time
Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00
Constraints - Spanish Speaking Operators
7 am to 9 am 1 0 0 0 0 0
9 am to 11 am 0 1 0 0 0 0
11 am to 1 pm 1 0 1 0 0 0
1 pm to 3 pm 0 1 0 1 0 0
3 pm to 5 pm 0 0 1 0 1 0
5 pm to 7 pm 0 0 0 1 0 0
7 pm to 9 pm 0 0 0 0 1 0
Objective Function - Minimise Cost Spanish Speaking Operators
MINIMISE COST Z $ 412.00
Solution
7 am to 9 am 9 am to 11 am 11 am to 1 pm
Full Time English Speaking Operator 6 12 7
Full Time Spanish Speaking Operator 2 3 2

Part Time English Speaking Operator 0 0 0
Minimum Cost $ 1,680.00

No. of Operators
Spanish Speaking
1.333333 2
2.833333 3
2.333333 3
3.166667 4
2.666667 3
1.166667 2
0.333333 1
6 6 >=
12 12 >=
13 10 >=
13 13 >=
11 11 >=
5 5 >=
2 2 >=
2 2 >=
3 3 >=
4 3 >=
5 4 >=
3 3 >=
2 2 >=
1 1 >=
1 pm to 3 pm 3 pm to 5 pm 5 pm to 7 pm
1 1 0
2 1 0
0 3 1
Avg No. of Calls Total Calls per

Work Shift No. of Operators
(per hr) shift
Required
7 am to 9 am 40 80 6.666667 7
9 am to 11 am 85 170 14.16667 15
11 am to 1 pm 70 140 11.66667 12
1 pm to 3 pm 95 190 15.83333 16
3 pm to 5 pm 80 160 13.33333 14
5 pm to 7 pm 35 70 5.833333 6
7 pm to 9 pm 10 20 1.666667 2
Avg No. of Calls Total Calls per

Work Shift No. of Operators
(per hr) shift
Required
7 am to 9 am 40 80 6.666667 7
9 am to 11 am 85 170 14.16667 15
11 am to 1 pm 70 140 11.66667 12
1 pm to 3 pm 95 190 15.83333 16
3 pm to 5 pm 80 160 13.33333 14
5 pm to 7 pm 35 70 5.833333 6
7 pm to 9 pm 10 20 1.666667 2
Decision Variables - Bilingual Call Operators
Full Time 7 15 7 1 2 0
Part Time 0 0 0 0 5 0
Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00
Constraints - Bilingual Call Operators
7 am to 9 am 1 0 0 0 0 0
9 am to 11 am 0 1 0 0 0 0
11 am to 1 pm 1 0 1 0 0 0
1 pm to 3 pm 0 1 0 1 0 0
3 pm to 5 pm 0 0 1 0 1 0
5 pm to 7 pm 0 0 0 1 1 1
7 pm to 9 pm 0 0 0 0 1 1
Objective Function - Minimise Cost Bilingual Call Operators

1512
$ 128.00
8.47%
7 7 >=
15 15 >=
14 12 >=
16 16 >=
14 14 >=
6 6 >=
2 2 >=
Cost with monolingual operators $ 1,640.00
Cost with bilingual operators $ 1,512.00
Difference $ 128.00
Maximum percentage increase

8.466% 128/1512
in the hourly wage rate

Case 2.3 Staffing A Call Center - Book

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Case 2.

3 Staffing a Call Center

Avg No. of Calls Total Calls per No. of calls

Decision Variables - English Speaking Operators

Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00

Constraints - English Speaking Operators

Objective Function - Minimise Cost English Speaking Operators

Decision Variables - Spanish Speaking Operators

Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00

Constraints - Spanish Speaking Operators

Objective Function - Minimise Cost Spanish Speaking Operators

MINIMISE COST Z $ 412.00

Full Time English Speaking Operator 6 12 5

Full Time Spanish Speaking Operator 2 3 2

Minimum Cost $ 1,640.00

Avg No. of Calls Total Calls per No. of calls

Decision Variables - English Speaking Operators

Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00

Constraints - English Speaking Operators

Objective Function - Minimise Cost English Speaking Operators

Decision Variables - Spanish Speaking Operators

Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00

Constraints - Spanish Speaking Operators

Objective Function - Minimise Cost Spanish Speaking Operators

MINIMISE COST Z $ 412.00

Full Time English Speaking Operator 6 12 7

Full Time Spanish Speaking Operator 2 3 2

Minimum Cost $ 1,680.00

Avg No. of Calls Total Calls per

Avg No. of Calls Total Calls per

Decision Variables - Bilingual Call Operators

Unit Cost $ 40.00 $ 40.00 $ 40.00 $ 44.00 $ 44.00 $ 48.00

Constraints - Bilingual Call Operators

Objective Function - Minimise Cost Bilingual Call Operators

Maximum percentage increase

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