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Table 6 The value of decision variables in both scenarios; italics shows the infeasible solutions for the main problem

From: A joint inventory–finance model for coordinating a capital-constrained supply chain with financing limitations

α

Dk

Coordinated supply chain

Non-coordinated supply chain

β

Debt

λk

dk

tk

Tk

Qk

Debt

λk

Tk

Qk

0.1

5000

0.334

0

1

0

0

62

854.01

 

1

40

547.65

5000

1

0

0

59

814.63

9,267,600

2

42

577.24

5000

1

0

0

100

1369.86

 

1

82

1117.72

5000

1

0

0

68

929.96

 

1

50

683

20,000

1

0

0

58

3204.29

 

2

36

1998.89

10,000

1

0

0

58

1597.61

 

2

46

1264.56

10,000

1

0

0

52

1431.49

 

1

39

1073.74

5000

1

0

0

60

817.72

 

1

44

608.21

5000

1

0

0

50

682.73

 

1

40

547.65

5000

1

0

0

49

627.57

 

2

42

577.24

0.2

10,000

0.334

0

1

0

0

44

1207.75

 

1

28

774.49

10,000

1

0

0

42

1152.06

18,513,000

2

30

816.35

10,000

1

0

0

72

1979.36

 

1

58

1580.70

10,000

1

0

0

48

1315.16

 

1

35

965.91

40,000

1

0

0

41

4531.55

 

2

26

2826.86

20,000

1

0

0

41

2259.37

 

2

33

1788.36

20,000

1

0

0

37

2024.43

 

1

28

1518.49

10,000

1

0

0

42

1156.43

 

1

31

860.14

10,000

1

0

0

35

965.53

 

1

26

704.68

10,000

1

0

0

35

951.15

 

2

25

675.71

0.3

15,000

0.333

0

1

0

0

36

1479.19

 

1

23

948.55

15,000

1

0

0

34

1410.98

27,756,000

2

24

999.82

15,000

1

0

0

59

2424.21

 

1

47

1935.95

15,000

1

0

0

39

1610.73

 

1

29

1183

60,000

1

0

0

34

5549.99

 

2

21

3462.18

30,000

1

0

0

34

2767.14

 

2

27

2190.28

30,000

1

0

0

30

2479.41

 

1

23

1859.76

15,000

1

0

0

34

1416.33

 

1

26

1053.45

15,000

1

0

0

29

1182.52

 

1

21

863.05

15,000

1

0

0

28

1164.92

 

2

20

827.57

0.4

20,000

0.333

0

1

0

0

31

1708.02

 

1

20

1095.29

20,000

1

0

0

30

1629.26

36,997,000

2

21

1154.49

20,000

1

0

0

51

2799.23

 

1

41

2235.45

20,000

1

0

0

34

1859.91

 

1

25

1366.01

80,000

1

0

0

29

6408.57

 

2

18

3997.78

40,000

1

0

0

29

3195.22

 

2

23

2529.12

40,000

1

0

0

26

2862.97

 

1

20

2147.47

20,000

1

0

0

30

1635.44

 

1

22

1216.42

20,000

1

0

0

25

1365.46

 

1

18

996.57

20,000

1

0

0

25

1345.13

 

2

17

955.60

0.5

25,000

0.333

0

1

0

0

28

1909.62

 

1

18

1224.58

25,000

1

0

0

27

1821.57

46,238,000

2

19

1290.76

25,000

1

0

0

46

3129.64

 

1

36

2499.31

25,000

1

0

0

30

2079.44

 

1

22

1527.24

100,000

1

0

0

26

7165

 

2

16

4469.65

50,000

1

0

0

26

3572.37

 

2

21

2827.64

50,000

1

0

0

23

3200.90

 

1

18

2400.94

25,000

1

0

0

27

1828.47

 

1

20

1360

25,000

1

0

0

22

1526.63

 

1

16

1114.20

25,000

1

0

0

22

1503.90

 

2

16

1068.39

0.6

30,000

0.333

0

1

0

0

25

2091.89

 

1

16

1342.45

30,000

1

0

0

24

1995.43

55,479,000

2

17

1413.95

30,000

1

0

0

42

3428.35

 

1

33

2737.85

30,000

1

0

0

28

2277.92

 

1

20

1673.01

120,000

1

0

0

24

7848.87

 

2

15

4896.26

60,000

1

0

0

24

3913.33

 

2

19

3097.53

60,000

1

0

0

21

3506.41

 

1

16

2630.10

30,000

1

0

0

24

2002.99

 

1

18

1489.0

30,000

1

0

0

20

1672.34

 

1

15

1220.54

30,000

1

0

0

20

1647.44

 

2

14

1170.36

0.7

35,000

0.333

0

1

0

0

24

2259.50

 

1

15

1448.94

35,000

1

0

0

22

2155.31

64,719,000

2

16

1527.24

35,000

1

0

0

39

3703.04

 

1

31

2957.22

35,000

1

0

0

26

2460.43

 

1

19

1807.06

140,000

1

0

0

22

8477.75

 

2

14

5288.57

70,000

1

0

0

22

4226.88

 

2

17

3345.71

70,000

1

0

0

20

3787.36

 

1

15

2840.83

35,000

1

0

0

23

2163.48

 

1

17

1609.17

35,000

1

0

0

19

1806.33

 

1

14

1318.34

35,000

1

0

0

19

1779.44

 

2

13

1264.14

0.8

40,000

0.333

0

1

0

0

22

2415.51

 

1

14

1548.98

40,000

1

0

0

21

2304.12

73,958,000

2

15

1632.69

40,000

1

0

0

36

3958.72

 

1

29

3161.40

40,000

1

0

0

24

2630.31

 

1

18

1931.83

160,000

1

0

0

21

9063.09

 

2

13

5653.72

80,000

1

0

0

21

4518.73

 

2

16

3576.72

80,000

1

0

0

18

4048.85

 

1

14

3036.98

40,000

1

0

0

21

2312.86

 

1

16

1720.27

40,000

1

0

0

18

1931.05

 

1

13

1409.36

40,000

1

0

0

17

1902.30

 

2

12

1351.42

0.9

45,000

0.333

0

1

40

40

21

2562.22

 

1

13

1642.94

45,000

1

70

70

20

2444.37

83,197,000

2

14

1731.73

45,000

1

60

60

34

4199.48

 

1

27

3353.7

45,000

1

50

50

23

2790.15

 

1

17

2049.01

180,000

1

40

40

19

9615.73

 

2

12

5996.67

90,000

1

60

60

19

4793.97

 

2

15

3793.68

90,000

1

60

60

17

4294.89

 

1

13

3221.20

45,000

1

60

60

20

2453.30

 

1

15

1824.63

45,000

1

90

90

17

2048.29

 

1

12

1494.85

45,000

1

40

40

16

2017.80

 

2

12

1433.39

1

50,000

0.333

0

1

40

40

20

2700.82

 

1

13

1731.81

50,000

1

70

70

19

2576.59

92,436,000

2

13

1825.40

50,000

1

60

60

32

4426.64

 

1

26

3534.55

50,000

1

50

50

21

2941.07

 

1

16

2159.85

200,000

1

40

40

18

10,135.87

 

2

12

6321.05

100,000

1

60

60

18

5053.29

 

2

15

3998.89

100,000

1

60

60

17

4527.21

 

1

12

3395.45

50,000

1

60

60

19

2586.01

 

1

14

1923.33

50,000

1

90

90

16

2159.09

 

1

12

1575.71

50,000

1

40

40

16

2126.95

 

2

11

1510.93