Table 11 Results summery of sensitivity analysis w.r.t number of workers at \(\alpha = 0.1\)
No. of worker | Case | \(\lambda\) | \(\mu _{ij}\) | Objective values | Optimum allocations \(x_{ij}\) |
|---|---|---|---|---|---|
Workers-7 | 1 | 0.7480 | (0.8986, 0.9066, 0.8964) (0.9182, 0.9036, 0.8840) (0.8606, 0.8387, 0.7480) | (105, 132, 168.9) (68, 95, 131.9) (36.7, 61, 87.1) | \({x_{13}, x_{112}, x_{115}, x_{24}, x_{210},}\) \({x_{31}, x_{36}, x_{38}, x_{411}, x_{413},}\) \({x_{55}, x_{59}, x_{62}, x_{67}, x_{614}}\) |
2 | 0.8067 | (0.9198, 0.9280, 0.9414) (0.8768, 0.8616, 0.8491) (0.9052, 0.8875, 0.8067) | (100.9, 127, 156.7) (76.1, 104, 140) (29.6, 53, 79.1) | \({x_{11}, x_{14}, x_{111}, x_{23}, x_{210},}\) \({x_{215}, x_{38}, x_{312}, x_{45}, x_{52},}\) \({ x_{56}, x_{513}, x_{69}, x_{614}, x_{77}}\) | |
3 | 0.7303 | (0.7716, 0.7433, 0.7303) (0.8944, 0.8933, 0.8805) (0.9648, 0.9577, 0.9162) | (85.2, 114, 148.2) (84.9, 111, 148.8) (40.7, 65, 91.1) | \({x_{12}, x_{18}, x_{112}, x_{23}, x_{24},}\) \({x_{36}, x_{37}, x_{314}, x_{49}, x_{411},}\) \({x_{413}, x_{52}, x_{610}, x_{615}, x_{75}}\) | |
4 | 0.8131 | (0.8131, 0.8202, 0.8304) (0.8362, 0.8263, 0.8287) (0.9597, 0.9523, 0.9070) | (80.6, 104, 133.7) (98.3, 128, 163.1) (42.7, 67, 93.1) | \({x_{13}, x_{19}, x_{111}, x_{21}, x_{213},}\) \({x_{32}, x_{35}, x_{314}, x_{44}, x_{46},}\) \({x_{47}, x_{58}, x_{512}, x_{515}, x_{610}}\) | |
5 | 0.7539 | (0.8179, 0.8122, 0.8251) (0.9353, 0.9320, 0.9332) (0.8937, 0.8652, 0.7539) | (90, 117, 147.6) (113.4, 144, 180.9) (23.6, 47, 74) | \({x_{19}, x_{111}, x_{215}, x_{33}, x_{34},}\) \({x_{314}, x_{45}, x_{48}, x_{51}, x_{512},}\) \({x_{513}, x_{62}, x_{610}, x_{76}, x_{77}}\) | |
Workers-8 | 1 | 0.7932 | (0.9092, 0.9083, 0.9110) (0.8911, 0.8836, 0.8578) (0.8482, 0.8187, 0.7932) | (108.2, 137, 170.3) (71.8, 97, 134.8) (37.8, 63, 90) | \({x_{111}, x_{114}, x_{24}, x_{215}, x_{38},}\) \({x_{46}, x_{47}, x_{51}, x_{63}, x_{69},}\) \({x_{710}, x_{712}, x_{713}, x_{82}, x_{85}}\) |
2 | 0.7752 | (0.9492, 0.9511, 0.9385) (0.8113, 0.7849, 0.7752) (0.9389, 0.9266, 0.9225) | (97.9, 124, 161.8) (87.4, 118, 154) (21.4, 43, 69.1) | \({x_{11}, x_{13}, x_{112}, x_{210}, x_{34},}\) \({x_{314}, x_{46}, x_{47}, x_{411}, x_{58},}\) \({x_{513}, x_{62}, x_{615}, x_{85}, x_{89}}\) | |
3 | 0.7408 | (0.7504, 0.7408, 0.7626) (0.8687, 0.8702, 0.8712) (0.9754, 0.9685, 0.9638) | (91, 118, 146.8) (90.8, 116, 149.3) (34.7, 59, 85.1) | \({x_{111}, x_{112}, x_{21}, x_{23}, x_{215},}\) \({x_{314}, x_{45}, x_{48}, x_{49}, x_{52},}\) \({x_{59}, x_{610}, x_{84}, x_{87}, x_{813}}\) | |
4 | 0.8069 | (0.8112, 0.8181, 0.8096) (0.8719, 0.8666, 0.8621) (0.9698, 0.9604, 0.9537) | (83.6, 107, 139.4) (90, 117, 152.1) (37.8, 63, 89.1) | \({x_{14}, x_{111}, x_{115}, x_{29}, x_{38},}\) \({x_{314}, x_{46}, x_{412}, x_{55}, x_{513},}\) \({x_{62}, x_{610}, x_{77}, x_{83}}\) | |
5 | 0.8168 | (0.8434, 0.8352, 0.8423) (0.9572, 0.9560, 0.9540) (0.8645, 0.8347, 0.8168) | (90, 117, 147.6) (104.2, 132, 168.9) (25.6, 49, 76) | \({x_{14}, x_{111}, x_{215}, x_{314}, x_{46},}\) \({x_{48}, x_{53}, x_{55}, x_{59}, x_{61},}\) \({x_{610}, x_{612}, x_{77}, x_{82}, x_{813}}\) | |
Workers-9 | 1 | 0.7975 | (0.9192, 0.8991, 0.8994) (0.9197, 0.9064, 0.8898) (0.8401, 0.8158, 0.7975) | (108.8, 143, 177.2) (65.7, 90, 125.1) (37.6, 61, 87.1) | \({x_{16}, x_{111}, x_{113}, x_{28}, x_{29},}\) \({x_{215}, x_{31}, x_{37}, x_{44}, x_{52},}\) \({x_{73}, x_{85}, x_{812}, x_{910}, x_{914}}\) |
2 | 0.8208 | (0.9371, 0.9380, 0.9279) (0.8636, 0.8265, 0.8208) (0.9149, 0.8936, 0.8810) | (104.1, 132, 168.9) (77.4, 108, 142.2) (23.6, 47, 74) | \({x_{113}, x_{21}, x_{210}, x_{312}, x_{44},}\) \({x_{48}, x_{411}, x_{55}, x_{62}, x_{67},}\) \({x_{714}, x_{89}, x_{93}, x_{96}, x_{915}}\) | |
3 | 0.7298 | (0.7346, 0.7429, 0.7298) (0.9093, 0.8960, 0.8809) (0.9524, 0.9381, 0.9258) | (94.8, 120, 154.2) (80, 107, 144.8) (43.8, 69, 95.1) | \({x_{14}, x_{112}, x_{115}, x_{23}, x_{29},}\) \({x_{211}, x_{38}, x_{314}, x_{46}, x_{51},}\) \({x_{62}, x_{75}, x_{713}, x_{97}, x_{910}}\) | |
4 | 0.7653 | (0.8351, 0.8271, 0.8083) (0.8056, 0.7922, 0.7653) (0.9626, 0.9497, 0.9435) | (81.8, 107, 141.2) (105.2, 134, 176.3) (39.8, 65, 90.2) | \({x_{17}, x_{18}, x_{111}, x_{23}, x_{26},}\) \({x_{34}, x_{314}, x_{45}, x_{49}, x_{413},}\) \({x_{52}, x_{512}, x_{61}, x_{910}, x_{915}}\) | |
5 | 0.7615 | (0.8495, 0.8517, 0.8607) (0.9718, 0.9657, 0.9585) (0.8275, 0.7847, 0.7615) | (90.8, 111.6, 145.7) (94.3, 124, 164.5) (28.7, 53, 80) | \({x_{111}, x_{38}, x_{314}, x_{44}, x_{46},}\) \({x_{413}, x_{55}, x_{61}, x_{610}, x_{77},}\) \({x_{89}, x_{812}, x_{815}, x_{92}, x_{93}}\) |