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Table 2 Crisp and fuzzy values for Gumbel deterioration

From: Periodic review inventory model for Gumbel deteriorating items when demand follows Pareto distribution

β

λ d

Q m

n d

n 1

N

E(TC)

E(TC)/Qm

 0.1

8.4

443.4

3.88

4.81

4.9

14170.9

31.96

 0.2

28.1

733.14

3.52

3.1

3.13

7656.05

10.443

 0.3

14.6

617.22

3.7

3.93

5.06

5713.74

9.26

0.4

17.3

708.91

3.71

3.97

17.39

5353.43

7.552

 0.5

24.7

1057.93

3.69

3.85

30.36

8962.51

8.472

 0.6

37.45

3646.41

3.66

3.72

43.2

43586.39

11.953

 0.7

53.2

5342.03

3.648

3.67

55.92

103839.8

19.44

 0.8

70.4

117.9

3.65

3.665

67.82

4176.02

35.429

 0.9

86.63

4.913

3.66

3.7

78.41

586.243

119.324

\( \overset{\sim }{\beta } \)

\( {\overset{\sim }{\lambda}}_d \)

\( \kern0.50em {\overset{\sim }{Q}}_m \)

\( {\overset{\sim }{n}}_d \)

\( {\overset{\sim }{n}}_1 \)

\( \overset{\sim }{N} \)

\( E\left(\overset{\sim }{TC}\right) \)

\( E\left(\overset{\sim }{TC}\right)/{\overset{\sim }{Q}}_m \)

 0.1

8.5

445.8

3.89

4.841

5.13

13097.2

29.382

 0.2

28.2

733.83

3.52

3.1

3.15

7636.5

10.41

 0.3

17.8

666.5

3.65

3.78

3.72

6307.9

9.465

 0.4

22.2

793.81

3.645

3.675

15

5835.1

7.351

 0.5

29.13

1178.221

3.644

3.7

28.784

9707.942

8.2395

 0.6

36.3

3359.6

3.66

3.7462

43.39

39928.98

11.885

 0.7

44.7

14491.579

3.7

3.867

57.16

282737.4

19.511

 0.8

70.5

122.64

3.645

3.7

67.73

4292.7

35.004

 0.9

86.7

5.24

3.65

3.686

78.33

600.1

114.62