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 |