Table 5 Compromised solutions with respect to improvement desired in various objective at confidence level \(\alpha =0.1\) 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 | \(15.8 \le z_{11} \le 32,\) | 0.8025 | (26.9, 35, 48.5), | \(x_{11}, x_{23}, x_{36}, x_{44}, x_{55}\),\(x_{62}\) |
\(23 \le z_{12} \le 41,\) | (31.3, 43, 58.3), | ||||
\(32 \le z_{13}\le 56.3\) | (12.1, 22, 32.8) | ||||
2 | Quality | \(3.9\le z_{31}\le 7,\) | 0.8611 | (32, 41, 56.3), | \(x_{13}, x_{14}, x_{31}, x_{46}, x_{55}\),\(x_{62}\) |
\(12 \le z_{32} \le 16,\) | (33.1, 43, 57.4), | ||||
\(22.8 \le z_{33} \le 26.8\) | (3.9, 12, 22) | ||||
Aspiration level: (0.9, 0.7, 0.8) | |||||
1 | Cost | \(15.8 \le z_{11}\le 28.9,\) | 0.7104 | (22.8, 30, 40.8), | \(x_{11}, x_{23}, x_{35}, x_{44}, x_{46}\),\(x_{62}\) |
\(23 \le z_{12} \le 41,\) | (43.4, 56, 72.2), | ||||
\(37 \le z_{13} \le 51.4\) | (10.1, 20, 30.8) | ||||
Aspiration level: (0.7, 0.8, 0.9) | |||||
1 | Cost | \(15.8 \le z_{11} \le 32.9\) | 0.8143 | (25.9, 34, 47.5), | \(x_{11}, x_{13}, x_{44}, x_{46}, x_{55}\),\(x_{62}\) |
\(23 \le z_{12}\le 41,\) | (35.3, 47, 62.3), | ||||
\(32 \le z_{13} \le 56.3\) | (7, 26, 26.8) | ||||
Shape parameter: (−2, −5, −1) | |||||
Aspiration level: (0.8, 0.85, 0.7) | |||||
1 | Time | \(20 \le z_{21} \le 47.3,\) | 0.8159 | (24.9, 33, 46.5), | \(x_{13}, x_{14}, x_{46}, x_{51}, x_{55}, x_{62}\) |
\(29 \le z_{22} \le 59,\) | (33.3, 45, 59.4), | ||||
\(40.7 \le z_{23} \le 75.2\) | (11, 20, 30.8) | ||||
Shape parameter: (−1, −2, −5) | |||||
Aspiration level: (0.8, 0.7, 0.75) | |||||
1 | Quality | \(3.9 \le z_{31}\le 13.1\), | 0.7784 | (23.7, 30, 41.7), | \(x_{12}, x_{15}, x_{23}, x_{34}, x_{46}, x_{61}\) |
\(12 \le z_{32} \le 22\), | (46.3, 58, 75.1), | ||||
\(22.8\le z_{33} \le 32.8\) | (8.1, 18, 28.8) | ||||