Table 6 Compromised solutions with respect to improvement desired in various objective at confidence level \(\alpha =0.5\) with different shape parameter
Case | Obj. function | Bounds | \(\lambda\) | Objective values | Solution variables |
|---|---|---|---|---|---|
(\(Z_{1}, Z_{2}, Z_{3}\)) | \(x_{ij}\) | ||||
Shape parameter: (−5, −1, −2) | |||||
Aspiration level: (0.8, 0.85, 0.7) | |||||
1 | Cost | \(19 \le z_{11} \le 36.5\), | 0.8255 | (30.5, 35, 42.5), | \(x_{11}, x_{23}, x_{36}, x_{44}, x_{55}, x_{62}\) |
\(23 \le z_{12} \le 42\), | (36.5, 43, 51.5), | ||||
\(28 \le z_{13} \le 50.5\) | (16.5, 22, 28) | ||||
2 | Quality | \(7.5 \le z_{31} \le 11\), | 0.7311 | (32.5, 37, 45) | \(x_{11}, x_{14}, x_{23}, x_{46}, x_{55}, x_{62}\) |
\(12 \le z_{32} \le 16\), | (37, 43, 51.5), | ||||
\(18 \le z_{33} \le 22\) | (9, 14, 20) | ||||
3 | Quality | \(7.5 \le z_{31} \le 9\), | 0.8644 | (36, 41, 49.5) | \(x_{13}, x_{14}, x_{31}, x_{46}, x_{55}, x_{62}\) |
\(12 \le z_{32} \le 14\), | (37.5, 43, 51), | ||||
\(18 \le z_{33} \le 20\) | (7.5, 12, 18) | ||||
Aspiration level: (0.9, 0.7, 0.8) | |||||
1 | Cost | \(19 \le z_{11} \le 32.5\), | 0.7550 | (26, 30, 36), | \(x_{11}, x_{23}, x_{35}, x_{36}, x_{44}, x_{62}\) |
\(23 \le z_{12} \le 37\), | (46, 53, 61.5), | ||||
\(28 \le z_{13} \le 45\) | (18.5, 24, 30) | ||||
2 | Quality | \(7.5 \le z_{31} \le 9\), | 0.8644 | (36, 41, 49.5) | \(x_{13}, x_{14}, x_{31}, x_{46}, x_{55}, x_{62}\) |
\(12 \le z_{32} \le 14\), | (37.5, 43, 51), | ||||
\(18 \le z_{33} \le 20\) | (7.5, 12, 18) | ||||
Aspiration level: (0.7, 0.8, 0.9) | |||||
1 | Cost | \(19 \le z_{11} \le 36\), | 0.8142 | (29.5, 34, 41.5), | \(x_{11}, x_{23}, x_{24}, x_{46}, x_{55}, x_{62}\) |
\(23 \le z_{12} \le 41,\) | (40.5, 47, 56), | ||||
\(28 \le z_{13} \le 49.5\) | (12.5, 18, 24) | ||||
Shape parameter: (−2, −5, −1) | |||||
Aspiration level: (0.8, 0.85, 0.7) | |||||
1 | Cost | \(19 \le z_{11} \le 25.5\), | 0.8187 | (21.5, 25, 30.5), | \(x_{13}, x_{24}, x_{35}, x_{46}, x_{61}, x_{62}\) |
\(23 \le z_{12} \le 29\), | (63.5, 71, 81), | ||||
\(28 \le z_{13} \le 35.5\) | (14.5, 20, 26) | ||||
2 | Time | \(24 \le z_{21} \le 51.5\), | 0.8048 | (32.5, 37, 45), | \(x_{11}, x_{14}, x_{23}, x_{46}, x_{55}, x_{62}\) |
\(29 \le z_{22} \le 58\), | (37, 43, 51.5), | ||||
\(35.5 \le z_{23} \le 67.5\) | (9, 14, 20) | ||||
Shape parameter: (−1, −2, −5) | |||||
Aspiration level: (0.7, 0.8, 0.85) | |||||
1 | Quality | \(7.5 \le z_{31} \le 15\), | 0.8124 | (28.5, 33, 40.5), | \(x_{11}, x_{13}, x_{24}, x_{46}, x_{55}, x_{62}\) |
\(12 \le z_{32} \le 20\), | (41.5, 48, 56.6), | ||||
\(18 \le z_{33} \le 26\) | (9, 14, 20) | ||||
2 | Quality | \(7.5 \le z_{31} \le 11\), | 0.7199 | (31, 36, 44.5), | \(x_{11}, x_{13}, x_{34}, x_{46}, x_{55}, x_{62}\) |
\(12 \le z_{32} \le 16\), | (41.5, 48, 56.6), | ||||
\(18 \le z_{33} \le 22\) | (9, 14, 20) | ||||
Aspiration level: (0.8, 0.85, 0.7) | |||||
1 | Quality | \(7.5 \le z_{31} \le 17\), | 0.7848 | (26.5, 30, 36.5), | \(x_{14}, x_{23}, x_{35}, x_{46}, x_{51}, x_{62}\) |
\(12 \le z_{32} \le 22\), | (51.5, 58, 67.5), | ||||
\(18 \le z_{33} \le 28\) | (12.5, 18, 24) | ||||