Table 9 Results summery of sensitivity analysis w.r.t number of jobs at \(\alpha = 0.1\)
No. of jobs | Case | W | Membership values \(\left( \mu _{Z_{1j}}, \mu _{Z_{2j}}, \mu _{Z_{3j}} \right)\) | Objective values \(\left( Z_{1}, Z_{2}, Z_{3} \right)\) | Optimum allocations | |||||
|---|---|---|---|---|---|---|---|---|---|---|
\(x_{1j}\) | \(x_{2j}\) | \(x_{3j}\) | \(x_{4j}\) | \(x_{5j}\) | \(x_{6j}\) | |||||
Jobs-9 | 1 | 0.8235 | (0.9574, 0.9567, 0.9287) (0.8549, 0.8367, 0.8235) (0.9184, 0.9124, 0.9152) | (49.8, 66, 90.3) (47.9, 65, 85.7) (14.4, 27, 42.3) | \({x_{11}}\) \({x_{13}}\) \({x_{14}}\) | \(x_{37}\) | \({x_{48}}\) \({x_{49}}\) | \({x_{52}}\) \({x_{55}}\) \({x_{56}}\) | ||
2 | 0.8716 | (0.9148, 0.9170, 0.8824) (0.8899, 0.8757, 0.8716) (0.9270, 0.9124, 0.9066) | (55.9, 73, 96.4) (43.8, 60, 78.9) (13.5, 27, 43.2) | \({x_{11}}\) \({x_{14}}\) \({x_{19}}\) | \(x_{38}\) | \({x_{55}}\) \({x_{56}}\) | \({x_{62}}\) \({x_{63}}\) \({x_{67}}\) | |||
3 | 0.8436 | (0.9626, 0.9644, 0.9431) (0.8713, 0.8447, 0.8436) (0.8882, 0.8936, 0.8957) | (48.7, 64, 87.4) (46, 64, 82.9) (17.3, 29, 44.3) | \({x_{11}}\) \({x_{13}}\) \({x_{14}}\) | \(x_{36}\) | \({x_{48}}\) \({x_{49}}\) | \({x_{52}}\) \({x_{55}}\) | \(x_{67}\) | ||
4 | 0.8036 | (0.8671, 0.8829, 0.8684) (0.8233, 0.8243, 0.8036) (0.9515, 0.9442, 0.9423) | (40.4, 53, 71) (60.8, 77, 100.4) (24.6, 39, 54.3) | \({x_{11}}\) \({x_{14}}\) \({x_{17}}\) | \(x_{23}\) | \({x_{32}}\) \({x_{35}}\) \({x_{38}}\) | \({x_{46}}\) \({x_{49}}\) | |||
5 | 0.7452 | (0.7856, 0.7832, 0.7452) (0.9174, 0.8998, 0.8813) (0.9740, 0.9709, 0.9709) | (45.7, 61, 81.7) (47, 65, 87.5) (19.5, 33, 48.3) | \({x_{11}}\) \({x_{13}}\) | \(x_{38}\) | \({x_{44}}\) \({x_{46}}\) \({x_{49}}\) | \({x_{52}}\) \({x_{55}}\) | \(x_{67}\) | ||
6 | 0.8434 | (0.8763, 0.8807, 0.8434) (0.9665, 0.9623, 0.9527) (0.8902, 0.8552, 0.8466) | (44.6, 59, 80.6) (59, 77, 101.3) (12.6, 27, 43.2) | \(x_{13}\) | \({x_{21}}\) \({x_{24}}\) | \(x_{37}\) | \({x_{46}}\) \({x_{48}}\) \({x_{49}}\) | \(x_{55}\) | \(x_{62}\) | |
Jobs-11 | 1 | 0.8528 | (0.9490, 0.9456, 0.9283) (0.8735, 0.8685, 0.8528) (0.9241, 0.9203, 0.9201) | (63.3, 84, 111) (57.2, 77, 102.2) (17.7, 33, 51.9) | \({x_{11}}\) \({x_{13}}\) \({x_{14}}\) | \(x_{38}\) | \({x_{46}}\) \({x_{411}}\) | \({x_{52}}\) \({x_{55}}\) \({x_{59}}\) | \({x_{67}}\) \({x_{610}}\) | |
2 | 0.8516 | (0.9503, 0.9567, 0.9406) (0.8655, 0.8552, 0.8516) (0.9241, 0.9203, 0.9201) | (63, 81, 108) (58.3, 79, 102.4) (17.7, 33, 51.9) | \({x_{13}}\) \({x_{14}}\) \({x_{111}}\) | \(x_{210}\) | \(x_{31}\) | \({x_{46}}\) \({x_{48}}\) \({x_{49}}\) | \({x_{52}}\) \({x_{55}}\) | \(x_{67}\) | |
3 | 0.8706 | (0.9296, 0.9456, 0.9359) (0.8885, 0.8881, 0.8706) (0.8995, 0.8908, 0.8883) | (66.9, 84, 109.2) (55.1, 74, 99.2) (20.8, 37, 55.9) | \({x_{13}}\) \({x_{14}}\) \({x_{111}}\) | \(x_{210}\) | \(x_{31}\) | \({x_{46}}\) \({x_{47}}\) | \({x_{55}}\) \({x_{58}}\) | \({x_{62}}\) \({x_{69}}\) | |
4 | 0.8304 | (0.8498, 0.8519, 0.8304) (0.8409, 0.8402, 0.8461) (0.9651, 0.9609, 0.9587) | (50.9, 68, 90.5) (72.3, 93, 116.4) (27.9, 45, 63.9) | \({x_{13}}\) \({x_{111}}\) | \(x_{21}\) | \({x_{36}}\) \({x_{37}}\) \({x_{38}}\) | \({x_{44}}\) \({x_{45}}\) \({x_{49}}\) | \({x_{62}}\) \({x_{610}}\) | ||
5 | 0.8105 | (0.9074, 0.9081, 0.8874) (0.8210, 0.8221, 0.8105) (0.9438, 0.9354, 0.9336) | (45.8, 62, 83.6) (75.3, 96, 123) (33, 51, 69) | \({x_{13}}\) \({x_{111}}\) | \(x_{24}\) | \(x_{35}\) | \({x_{46}}\) \({x_{49}}\) | \({x_{51}}\) \({x_{52}}\) \({x_{58}}\) | \({x_{67}}\) \({x_{610}}\) | |
6 | 0.8093 | (0.9096, 0.9167, 0.9066) (0.9590, 0.9615, 0.9575) (0.8577, 0.8236, 0.8093) | (50.8, 67, 88.6) (76.2, 96, 123) (19, 37, 56.8) | \({x_{14}}\) \({x_{111}}\) | \({x_{21}}\) \({x_{23}}\) | \({x_{35}}\) \({x_{37}}\) | \({x_{46}}\) \({x_{48}}\) \({x_{49}}\) | \({x_{62}}\) \({x_{610}}\) | ||
Jobs-13 | 1 | 0.8118 | (0.9098, 0.9265, 0.9127) (0.8518, 0.8248, 0.8118) (0.9182, 0.9110, 0.9014) | (83.4, 105, 137.4) (71, 98, 128.6) (24.1, 43, 66.4) | \({x_{13}}\) \({x_{113}}\) | \({x_{210}}\) \({x_{211}}\) | \({x_{31}}\) \({x_{36}}\) | \({x_{44}}\) \({x_{48}}\) \({x_{49}}\) | \({x_{55}}\) \({x_{512}}\) | \({x_{62}}\) \({x_{67}}\) |
2 | 0.8636 | (0.8734, 0.8705, 0.8837) (0.9086, 0.9056, 0.9031) (0.8824, 0.9713, 0.8636) | (87.9, 114, 142.8) (61.4, 83, 110) (29.2, 49, 71.5) | \({x_{13}}\) \({x_{14}}\) \({x_{113}}\) | \({x_{21}}\) \({x_{26}}\) \({x_{29}}\) | \({x_{38}}\) \({x_{312}}\) | \({x_{45}}\) \({x_{47}}\) \({x_{411}}\) | \(x_{52}\) | \(x_{610}\) | |
3 | 0.8170 | (0.9598, 0.9672, 0.9550) (0.8469, 0.8305, 0.8170) (0.9109, 0.8985, 0.8872) | (73.2, 93, 125.4) (71.8, 97, 127.6) (25.2, 45, 68.4) | \({x_{11}}\) \({x_{14}}\) \({x_{111}}\) | \({x_{23}}\) \({x_{210}}\) | \({x_{36}}\) \({x_{37}}\) | \({x_{48}}\) \({x_{412}}\) | \({x_{55}}\) \({x_{513}}\) | \({x_{62}}\) \({x_{69}}\) | |
4 | 0.8260 | (0.8260, 0.8322, 0.8364) (0.8727, 0.8786, 0.8586) (0.9708, 0.9609, 0.9542) | (52.9, 70, 89.8) (67.1, 86, 113.9) (26.1, 45, 64.8) | \({x_{13}}\) \({x_{111}}\) | \(x_{21}\) | \({x_{36}}\) \({x_{37}}\) \({x_{38}}\) | \({x_{44}}\) \({x_{45}}\) \({x_{49}}\) | \({x_{62}}\) \({x_{610}}\) | ||
5 | 0.8296 | (0.8380, 0.8421, 0.8296) (0.8778, 0.8786, 0.8630) (0.9830, 0.9773, 0.9740) | (51.9, 69, 90.6) (66.2, 86, 113) (21, 39, 58.8) | \({x_{13}}\) \({x_{111}}\) | \(x_{21}\) | \(x_{38}\) | \({x_{46}}\) \({x_{47}}\) \({x_{49}}\) | \(x_{55}\) | \({x_{62}}\) \({x_{67}}\) \({x_{610}}\) | |
6 | 0.8186 | (0.8438, 0.8540, 0.8352) (0.9749, 0.9726, 0.9684) (08619, 0.8347, 0.8186) | (74.3, 95, 125.6) (82.8, 108, 139.5) (30.3, 51, 73.5) | \({x_{15}}\) \({x_{111}}\) \({x_{113}}\) | \({x_{23}}\) \({x_{24}}\) | \(x_{37}\) | \({x_{46}}\) \({x_{48}}\) | \({x_{51}}\) \({x_{512}}\) | \({x_{62}}\) \({x_{69}}\) \({x_{610}}\) | |