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Table 1 The sensitivity analysis on parameters (Note that \(M^{j*}\) is in days, \(F^{j}\) is in percentage)

From: Two retailer–supplier supply chain models with default risk under trade credit policy

Parameters

Nash game

Decision without trade credit

Supplier-Stackelberg game

\(\frac{{\Pi_{r}^{3} }}{{\Pi_{r}^{0} }}\)

\(\frac{{\Pi_{s}^{3} }}{{\Pi_{s}^{0} }}\)

\(\frac{{\Pi_{sc}^{3} }}{{\Pi_{sc}^{0} }}\)

\(M^{2*}\)

\(F^{2}\)

\(D^{2}\)

\(\Pi_{r}^{2}\)

\(\Pi_{s}^{2}\)

\(\Pi_{sc}^{2}\)

\(\Pi_{r}^{0}\)

\(\Pi_{s}^{0}\)

\(\Pi_{sc}^{0}\)

\(\Pi_{sc}^{1}\)

\(M^{3*}\)

\(F^{3}\)

\(D^{3}\)

\(\Pi_{r}^{3}\)

\(\Pi_{s}^{3}\)

\(\Pi_{sc}^{3}\)

a

                   

1.4

266

19.7

10,001

135,670

50,654

186,324

40,517

37,153

77,670

77,918

266

19.7

10,001

135,670

50,654

186,324

3.349

1.363

2.400

1.2

228

17.1

7606

100,451

43,880

144,331

40,517

37,153

77,670

77,918

234

17.5

7780

103,210

43,889

147,099

2.547

1.181

1.894

1

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

0.8

13

1.1

3707

42,141

37,187

79,328

40,517

37,153

77,670

77,918

28

2.3

3827

43,961

37,199

81,160

1.085

1.001

1.045

0.6

0

0

3600

40,517

37,153

77,670

40,517

37,153

77,670

77,918

0

0

3600

40,517

37,153

77,670

1.000

1.000

1.000

0.4

0

0

3600

40,517

37,153

77,670

40,517

37,153

77,670

77,918

0

0

3600

40,517

37,153

77,670

1.000

1.000

1.000

A

                   

16,000

149

11.6

5421

67,885

39,588

107,473

40,517

37,316

77,833

78,148

162

12.4

5606

70,778

39,605

110,382

1.747

1.061

1.418

14,000

149

11.5

5408

67,674

39,514

107,188

40,517

37,277

77,794

78,092

160

12.3

5585

70,450

39,529

109,979

1.739

1.060

1.414

12,000

147

11.4

5390

67,395

39,416

106,811

40,517

37,225

77,742

78,019

158

12.2

5558

70,017

39,430

109,447

1.728

1.059

1.408

10,000

147

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

8000

143

11.1

5328

66,436

39,077

105,514

40,517

37,044

77,561

77,771

152

11.8

5463

68,543

39,087

107,629

1.692

1.055

1.388

6000

139

10.8

5268

65,503

38,747

104,250

40,517

36,863

77,380

77,535

146

11.3

5372

67,127

38,752

105,879

1.657

1.051

1.368

W

                   

29

372

26.3

9962

90,595

75,818

166,412

18,917

58,753

77,670

77,918

373

26.4

10,000

91,081

75,820

166,901

4.815

1.291

2.149

27

302

22

8235

83,902

61,923

145,825

26,117

51,553

77,670

77,918

308

22.4

8372

85,782

61,930

147,711

3.285

1.201

1.902

25

227

17

6706

75,911

49,779

125,690

33,317

44,353

77,670

77,918

235

17.6

6855

78,092

49,788

127,881

2.344

1.123

1.647

23

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

155

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

21

56

4.5

4202

57,570

30,316

87,886

47,717

29,953

77,670

77,918

70

5.6

4357

60,137

30,331

90,468

1.260

1.013

1.165

19

0

0

3600

54,917

22,753

77,670

54,917

22,753

77,670

77,918

0

0

3600

54,917

22,753

77,670

1.000

1.000

1.000

b

                   

0.4

0

0

3600

40,517

37,153

77,670

40,517

37,153

77,670

77,918

0

0

3600

40,517

37,153

77,670

1.000

1.000

1.000

0.35

64

6

4294

50,689

37,652

88,341

40,517

37,153

77,670

77,918

76

7

4431

52,732

37,665

90,397

1.302

1.014

1.164

0.3

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

0.25

246

15.5

7061

94,095

42,779

136,873

40,517

37,153

77,670

77,918

254

16

7230

96,865

42,788

139,653

2.391

1.152

1.798

0.2

373

18.5

10,000

143,730

49,868

193,598

40,517

37,153

77,670

77,918

373

18.5

10,000

143,730

49,868

193,598

3.547

1.342

2.493

C

                   

16

0

0

3600

40,517

22,753

63,270

40,517

22,753

63,270

63,518

0

0

3600

40,517

22,753

63,270

1.000

1.000

1.000

14

1

0.1

3612

40,691

29,956

70,647

40,517

29,953

70,470

70,718

14

1.2

3743

42,579

29,970

72,549

1.051

1.001

1.030

12

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

10

316

22.9

8562

119,074

54,116

173,191

40,517

44,353

84,870

85,118

323

23.3

8722

121,782

54,123

175,905

3.006

1.220

2.073

8

373

26.4

10,000

143,730

75,745

219,475

40,517

51,553

92,070

92,318

373

26.4

10,000

143,730

75,745

219,475

3.547

1.469

2.384

S s

                   

400

135

10.5

5212

64,632

38,436

103,069

40,517

36,482

76,999

77,452

151

11.7

5443

68,231

38,464

106,695

1.684

1.054

1.386

350

140

10.9

5288

65,817

38,858

104,675

40,517

36,817

77,334

77,680

153

11.8

5481

68,825

38,877

107,702

1.699

1.056

1.393

300

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

250

150

11.7

5442

68,207

39,701

107,908

40,517

37,488

78,005

78,169

158

12.2

5558

70,017

39,707

109,724

1.728

1.059

1.407

200

156

12

5519

69,412

40,122

109,534

40,517

37,824

78,340

78,434

161

12.4

5596

70,615

40,125

110,740

1.743

1.061

1.414

150

161

12.4

5596

70,624

40,543

111,167

40,517

38,159

78,676

78,716

163

12.6

5634

71,216

40,544

111,759

1.758

1.063

1.421

h s

                   

5.5

143

11.1

5332

66,499

39,100

105,599

40,517

37,056

77,573

77,787

153

11.8

5469

68,639

39,109

107,748

1.694

1.055

1.389

5

144

11.2

5348

66,753

39,189

105,942

40,517

37,105

77,621

77,852

154

11.9

5494

69,027

39,200

108,227

1.704

1.057

1.394

4.5

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

4

147

11.4

5381

67,266

39,370

106,636

40,517

37,201

77,718

77,985

158

12.2

5545

69,817

39,383

109,200

1.723

1.059

1.405

3.5

148

11.4

5398

67,525

39,461

106,987

40,517

37,249

77,766

78,053

159

12.3

5570

70,218

39,476

109,694

1.733

1.060

1.411

3

149

11.5

5415

67,786

39,553

107,340

40,517

37,298

77,814

78,122

161

12.4

5596

70,624

39,569

110,194

1.743

1.061

1.416

I s

                   

0.14

104

8.2

4785

58,091

38,356

96,447

40,517

37,153

77,670

77,918

114

9

4923

60,196

38,368

98,565

1.486

1.033

1.269

0.12

124

9.7

5053

62,183

38,769

100,952

40,517

37,153

77,670

77,918

134

10.4

5199

64,433

38,781

103,214

1.590

1.044

1.329

0.1

146

11.3

5365

67,010

39,279

106,289

40,517

37,153

77,670

77,918

156

12

5519

69,420

39,291

108,711

1.713

1.058

1.400

0.08

170

13

5733

72,778

39,910

112,688

40,517

37,153

77,670

77,918

180

13.8

5898

75,370

39,921

115,291

1.860

1.075

1.484

0.06

197

14.9

6176

79,790

40,688

120,478

40,517

37,153

77,670

77,918

207

15.7

6350

82,581

40,700

123,280

2.038

1.096

1.587

0.04

228

17.1

6715

88,476

41,655

130,131

40,517

37,153

77,670

77,918

237

17.7

6901

91,484

41,667

133,151

2.258

1.122

1.714

  1. Underline is means the optimal trade credit period is \(M_{\rm max}\)