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A Quantitative Analysis About Optimization of Number of Employees and Rebalancing Workload

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Economic and Financial Challenges for Eastern Europe

Abstract

In an organization, the workload of the employees is very important in terms of efficiency and motivation toward work. Workloads must be at the same level as employees can achieve.

In the study, a large faculty of one of Turkey’s leading universities was selected as a pilot. There are 25 different business units and 92 employees in the faculty. AHP and LP are preferred as models. With AHP, utility values ​​of employees in each job type are calculated separately for 25 job types. The obtained utility values ​​are assigned as the objective function coefficients of the decision variables of the LP model. Three different LP models were obtained and solved to obtain optimal workload values. According to the results of three different models, the manager will be able to complete the missing workloads of the employees from different units.

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Authors and Affiliations

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Corresponding author

Correspondence to Yılmaz Gökşen .

Editor information

Editors and Affiliations

Appendices

Appendix 1: Comparison Matrix of Alternatives for X1, C1

x1

x2

x3

x4

x5

x6

x7

x8

x9

x10

x11

x12

x13

x14

x15

x16

x17

x18

x19

x20

x21

x22

x23

x24

x25

x2

1.0

1.5

2.5

1.5

2.0

2.5

2.0

3.0

2.0

1.0

3.0

1.5

2.5

1.5

2.0

2.0

1.5

1.0

2.5

1.0

1.0

2.0

3.0

2.0

x3

0.7

1.0

2.5

2.5

2.5

3.0

1.5

1.5

2.5

2.0

2.0

2.5

2.5

2.0

2.5

1.5

1.5

1.5

2.5

1.5

2.0

1.0

1.0

2.0

x4

0.4

0.4

1.0

1.5

1.0

2.0

3.0

3.0

2.5

1.5

1.0

1.5

1.0

2.5

2.5

2.0

2.5

1.0

3.0

1.0

1.5

1.5

3.0

2.0

x5

0.7

0.4

0.7

1.0

2.5

2.5

2.0

1.0

1.5

2.5

1.0

2.0

3.0

2.0

1.5

2.5

2.5

3.0

2.5

2.0

1.0

2.5

2.0

2.0

x6

0.5

0.4

1.0

0.4

1.0

2.0

1.5

2.5

2.0

2.0

1.0

1.5

2.5

1.0

1.0

2.5

1.0

1.0

3.0

1.5

2.0

2.0

2.5

2.5

x7

0.4

0.3

0.5

0.4

0.5

1.0

1.5

1.0

2.0

2.5

1.5

2.5

2.0

2.5

2.0

2.0

2.0

1.0

2.0

1.5

1.5

1.5

2.0

1.5

x8

0.5

0.7

0.3

0.5

0.7

0.7

1.0

2.0

1.5

2.5

2.0

1.5

2.0

1.5

2.0

2.5

1.5

1.5

1.0

2.5

2.0

2.0

1.5

2.5

x9

0.3

0.7

0.3

1.0

0.4

1.0

0.5

1.0

2.0

2.5

2.0

1.5

3.0

1.0

2.5

2.0

2.5

1.5

2.0

1.0

2.0

1.5

3.0

1.5

x10

0.5

0.4

0.4

0.7

0.5

0.5

0.7

0.5

1.0

2.0

2.5

1.5

1.0

2.0

2.0

2.0

2.0

1.5

2.0

2.0

2.5

1.5

2.0

1.5

x11

1.0

0.5

0.7

0.4

0.5

0.4

0.4

0.4

0.5

1.0

2.5

1.5

2.0

3.0

3.0

2.0

2.5

1.5

2.0

2.0

2.5

2.5

3.0

1.5

x12

0.3

0.5

1.0

1.0

1.0

0.7

0.5

0.5

0.4

0.4

1.0

1.0

2.5

2.5

1.5

2.5

1.5

2.0

2.0

2.0

1.0

2.5

2.0

2.0

x13

0.7

0.4

0.7

0.5

0.7

0.4

0.7

0.7

0.7

0.7

1.0

1.0

2.5

2.0

2.5

2.0

1.5

3.0

2.0

3.0

2.5

2.5

3.0

2.0

x14

0.4

0.4

1.0

0.3

0.4

0.5

0.5

0.3

1.0

0.5

0.4

0.4

1.0

2.5

1.5

1.5

1.0

2.5

2.0

2.5

2.0

2.0

1.0

2.0

x15

0.7

0.5

0.4

0.5

1.0

0.4

0.7

1.0

0.5

0.3

0.4

0.5

0.4

1.0

2.0

2.0

2.5

1.5

2.5

2.0

1.5

2.5

2.0

2.0

x16

0.5

0.4

0.4

0.7

1.0

0.5

0.5

0.4

0.5

0.3

0.7

0.4

0.7

0.5

1.0

2.0

2.0

2.0

3.0

3.0

2.0

1.5

3.0

1.5

x17

0.5

0.7

0.5

0.4

0.4

0.5

0.4

0.5

0.5

0.5

0.4

0.5

0.7

0.5

0.5

1.0

1.5

2.0

2.5

1.5

2.5

2.0

1.5

2.0

x18

0.7

0.7

0.4

0.4

1.0

0.5

0.7

0.4

0.5

0.4

0.7

0.7

1.0

0.4

0.5

0.7

1.0

2.0

1.5

1.5

2.0

2.0

1.0

2.5

x19

1.0

0.7

1.0

0.3

1.0

1.0

0.7

0.7

0.7

0.7

0.5

0.3

0.4

0.7

0.5

0.5

0.5

1.0

2.5

2.0

2.0

2.0

2.0

1.5

x20

0.4

0.4

0.3

0.4

0.3

0.5

1.0

0.5

0.5

0.5

0.5

0.5

0.5

0.4

0.3

0.4

0.7

0.4

1.0

2.0

3.0

2.0

2.0

2.5

x21

1.0

0.7

1.0

0.5

0.7

0.7

0.4

1.0

0.5

0.5

0.5

0.3

0.4

0.5

0.3

0.7

0.7

0.5

0.5

1.0

3.0

2.0

2.0

2.0

x22

1.0

0.5

0.7

1.0

0.5

0.7

0.5

0.5

0.4

0.4

1.0

0.4

0.5

0.7

0.5

0.4

0.5

0.5

0.3

0.3

1.0

1.0

2.0

2.0

x23

0.5

1.0

0.7

0.4

0.5

0.7

0.5

0.7

0.7

0.4

0.4

0.4

0.5

0.4

0.7

0.5

0.5

0.5

0.5

0.5

1.0

1.0

2.5

2.0

x24

0.3

1.0

0.3

0.5

0.4

0.5

0.7

0.3

0.5

0.3

0.5

0.3

1.0

0.5

0.3

0.7

1.0

0.5

0.5

0.5

0.5

0.4

1.0

3.0

x25

0.5

0.5

0.5

0.5

0.4

0.7

0.4

0.7

0.7

0.7

0.5

0.5

0.5

0.5

0.7

0.5

0.4

0.7

0.4

0.5

0.5

0.5

0.3

1.0

Appendix 2: Utility Matrix for Job Types

 

x1

x2

x3

x4

x5

x6

x7

x8

x9

x10

x11

x12

x13

x14

x15

x16

x17

x18

x19

x20

x21

x22

x23

x24

x25

x1

1.00

0.07

0.07

0.07

0.06

0.06

0.06

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

0.03

0.02

0.02

0.02

0.02

x2

0.07

1.00

0.07

0.07

0.07

0.06

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.02

0.02

0.02

x3

0.07

0.06

1.00

0.06

0.06

0.06

0.06

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

0.03

0.02

0.02

0.02

0.02

x4

0.07

0.07

0.06

1.00

0.06

0.06

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.02

0.02

x5

0.07

0.07

0.06

0.06

1.00

0.06

0.05

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.02

0.02

0.02

0.02

x6

0.07

0.07

0.06

0.06

0.06

1.00

0.05

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.02

0.02

0.02

x7

0.07

0.07

0.07

0.06

0.06

0.06

1.00

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.02

0.02

0.02

0.02

x8

0.03

0.03

0.02

0.02

0.02

0.02

0.07

1.00

0.06

0.07

0.06

0.06

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

x9

0.03

0.03

0.02

0.02

0.02

0.02

0.08

0.06

1.00

0.06

0.06

0.06

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x10

0.03

0.02

0.02

0.02

0.02

0.02

0.08

0.07

0.07

1.00

0.06

0.06

0.06

0.06

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

x11

0.03

0.03

0.02

0.02

0.02

0.02

0.07

0.07

0.06

0.06

1.00

0.06

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x12

0.03

0.03

0.03

0.02

0.02

0.02

0.07

0.06

0.07

0.06

0.06

1.00

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x13

0.03

0.03

0.03

0.02

0.02

0.02

0.07

0.06

0.07

0.06

0.06

0.06

1.00

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x14

0.03

0.03

0.02

0.02

0.02

0.02

0.08

0.07

0.06

0.06

0.06

0.06

0.05

1.00

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x15

0.03

0.03

0.02

0.02

0.02

0.02

0.08

0.07

0.07

0.06

0.06

0.05

0.05

0.05

1.00

0.05

0.04

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x16

0.03

0.02

0.02

0.03

0.02

0.02

0.07

0.07

0.06

0.07

0.06

0.06

0.05

0.05

0.05

1.00

0.05

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03

x17

0.03

0.03

0.02

0.02

0.02

0.02

0.07

0.07

0.06

0.06

0.06

0.05

0.05

0.05

0.05

0.04

1.00

0.04

0.04

0.04

0.03

0.03

0.03

0.03

0.03

x18

0.03

0.03

0.02

0.02

0.02

0.02

0.07

0.07

0.06

0.06

0.06

0.05

0.06

0.05

0.05

0.04

0.04

1.00

0.04

0.04

0.03

0.03

0.03

0.03

0.03

x19

0.03

0.03

0.02

0.03

0.02

0.02

0.07

0.07

0.07

0.06

0.06

0.06

0.06

0.05

0.05

0.04

0.04

0.04

1.00

0.04

0.03

0.03

0.03

0.03

0.03

x20

0.03

0.02

0.02

0.02

0.02

0.02

0.07

0.07

0.07

0.06

0.06

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

1.00

0.04

0.03

0.03

0.03

0.03

x21

0.03

0.03

0.02

0.02

0.02

0.02

0.07

0.06

0.07

0.07

0.06

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.04

1.00

0.04

0.03

0.03

0.03

x22

0.03

0.03

0.02

0.02

0.02

0.02

0.07

0.07

0.07

0.06

0.06

0.05

0.05

0.05

0.05

0.04

0.04

0.04

0.04

0.04

0.03

1.00

0.03

0.03

0.03

x23

0.02

0.02

0.02

0.02

0.03

0.03

0.03

0.03

0.03

0.03

0.04

0.04

0.04

0.04

0.05

0.05

0.05

0.06

0.06

0.06

0.06

0.06

1.00

0.07

0.07

x24

0.02

0.02

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.04

0.04

0.04

0.04

0.05

0.05

0.05

0.05

0.06

0.06

0.06

0.06

0.06

1.00

0.07

x25

0.02

0.02

0.02

0.02

0.03

0.03

0.03

0.03

0.03

0.03

0.04

0.04

0.04

0.04

0.04

0.05

0.05

0.05

0.06

0.06

0.06

0.07

0.07

0.07

1.00

Appendix 3: Matlab Code for Model 3

Appendix 4: Results of Model 1 and Model 2

Job type i

Staff j

Workload

Job type i

Staff j

Workload

Job type i

Staff j

Workload

Job type i

Staff j

Workload

1

1

0.778

21

19

0.0198

22

40

1

22

74

0.0476

23

1

0.222

23

19

0.53

22

41

1

25

74

0.9524

2

2

0.685

12

20

0.698

22

42

1

22

75

0.0476

22

2

0.315

23

20

0.302

22

43

1

25

75

0.9524

3

3

0.553

13

21

0.2285

22

44

1

22

76

0.0476

22

3

0.447

16

21

0.1185

22

45

1

25

76

0.9524

4

4

0.841

23

21

0.653

22

46

1

22

77

0.0476

23

4

0.159

13

22

0.2285

22

47

1

25

77

0.9524

5

5

0.538

16

22

0.1185

22

48

1

22

78

0.0476

23

5

0.462

23

22

0.653

22

49

1

25

78

0.9524

6

6

0.3545

14

23

0.655

22

50

1

22

79

0.0476

22

6

0.6455

23

23

0.345

23

51

1

25

79

0.9524

6

7

0.3545

14

24

0.655

23

52

1

22

80

0.0476

22

7

0.6455

23

24

0.345

23

53

1

25

80

0.9524

7

8

0.881

14

25

0.655

23

54

1

22

81

0.0476

23

8

0.119

23

25

0.345

23

55

1

25

81

0.9524

8

9

0.7885

14

26

0.655

23

56

1

22

82

0.0476

10

9

0.0595

23

26

0.345

23

57

1

25

82

0.9524

22

9

0.152

15

27

0.139

23

58

1

22

83

0.0476

8

10

0.7885

23

27

0.861

23

59

1

25

83

0.9524

10

10

0.0595

15

28

0.139

23

60

1

22

84

0.0476

22

10

0.152

23

28

0.861

23

61

1

25

84

0.9524

8

11

0.7885

15

29

0.139

23

62

1

22

85

0.0476

10

11

0.0595

23

29

0.861

23

63

1

25

85

0.9524

22

11

0.152

15

30

0.139

23

64

1

22

86

0.0476

8

12

0.7885

23

30

0.861

23

65

1

25

86

0.9524

10

12

0.0595

16

31

1

23

66

1

22

87

0.0476

22

12

0.152

17

32

0.415

23

67

0.092

25

87

0.9524

9

13

1

23

32

0.585

24

67

0.908

22

88

0.0476

9

14

1

18

33

0.375

23

68

0.092

25

88

0.9524

10

15

1

23

33

0.625

24

68

0.908

22

89

0.0476

11

16

0.4502

9

34

0.357

22

69

0.0476

25

89

0.9524

21

16

0.0198

19

34

0.357

25

69

0.9524

22

90

0.0476

23

16

0.53

23

34

0.286

22

70

0.0476

25

90

0.9524

11

17

0.4502

20

35

0.714

25

70

0.9524

22

91

0.0476

21

17

0.0198

21

35

0.247

22

71

0.0476

25

91

0.9524

23

17

0.53

22

35

0.039

25

71

0.9524

22

92

0.0476

11

18

0.4502

21

36

1

22

72

0.0476

25

92

0.9524

21

18

0.0198

22

37

1

25

72

0.9524

23

93

4.331

23

18

0.53

22

38

1

22

73

0.0476

   

11

19

0.4502

22

39

1

25

73

0.9524

   

Appendix 5: Results of Model 3

Job type i

Staff j

Workload

Job type i

Staff j

Workload

Job type i

Staff j

Workload

Job type i

Staff j

Workload

1

1

0.778

12

20

0.698

22

41

1

22

74

0.0476

21

1

0.196

23

20

0.302

22

42

1

25

74

0.9524

22

1

0.026

13

21

0.2285

22

43

1

22

75

0.0476

2

2

0.685

16

21

0.1185

22

44

1

25

75

0.9524

22

2

0.315

23

21

0.653

22

45

1

22

76

0.0476

3

3

0.553

13

22

0.2285

22

46

1

25

76

0.9524

22

3

0.447

16

22

0.1185

22

47

1

22

77

0.0476

4

4

0.841

23

22

0.653

22

48

1

25

77

0.9524

22

4

0.159

14

23

0.655

22

49

1

22

78

0.0476

5

5

0.538

23

23

0.345

22

50

1

25

78

0.9524

22

5

0.462

14

24

0.655

23

51

1

22

79

0.0476

6

6

0.3545

23

24

0.345

23

52

1

25

79

0.9524

22

6

0.6455

14

25

0.655

23

53

1

22

80

0.0476

6

7

0.3545

23

25

0.345

23

54

1

25

80

0.9524

22

7

0.6455

14

26

0.655

23

55

1

22

81

0.0476

7

8

0.881

23

26

0.345

23

56

1

25

81

0.9524

21

8

0.119

15

27

0.139

23

57

1

22

82

0.0476

8

9

0.7885

23

27

0.861

23

58

1

25

82

0.9524

10

9

0.0595

15

28

0.139

23

59

1

22

83

0.0476

23

9

0.152

23

28

0.861

23

60

1

25

83

0.9524

8

10

0.7885

15

29

0.139

23

61

1

22

84

0.0476

10

10

0.0595

23

29

0.861

23

62

1

25

84

0.9524

23

10

0.152

15

30

0.139

23

63

1

22

85

0.0476

8

11

0.7885

23

30

0.861

23

64

1

25

85

0.9524

10

11

0.0595

16

31

1

23

65

1

22

86

0.0476

23

11

0.152

17

32

0.415

23

66

1

25

86

0.9524

8

12

0.7885

23

32

0.585

23

67

0.092

22

87

0.0476

10

12

0.0595

18

33

0.375

24

67

0.908

25

87

0.9524

23

12

0.152

23

33

0.625

23

68

0.092

22

88

0.0476

9

13

1

9

34

0.357

24

68

0.908

25

88

0.9524

9

14

1

19

34

0.357

22

69

0.0476

22

89

0.0476

10

15

1

23

34

0.286

25

69

0.9524

25

89

0.9524

11

16

0.4503

20

35

0.714

22

70

0.0476

22

90

0.0476

23

16

0.5497

21

35

0.011

25

70

0.9524

25

90

0.9524

11

17

0.4502

23

35

0.275

22

71

0.0476

22

91

0.0476

23

17

0.5498

21

36

1

25

71

0.9524

25

91

0.9524

11

18

0.4503

22

37

1

22

72

0.0476

22

92

0.0476

23

18

0.5497

22

38

1

25

72

0.9524

25

92

0.9524

11

19

0.4502

22

39

1

22

73

0.0476

23

93

4.331

23

19

0.5498

22

40

1

25

73

0.9524

   

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Gökşen, Y., Pala, O., Ünlü, M. (2019). A Quantitative Analysis About Optimization of Number of Employees and Rebalancing Workload. In: Sykianakis, N., Polychronidou, P., Karasavvoglou, A. (eds) Economic and Financial Challenges for Eastern Europe. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-12169-3_35

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