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Table 4 Upper level neutrosophic transportation problem Table 5 Lower level neutrosophic transportation problem

Table 4 Upper level neutrosophic transportation problem Table 5 Lower level neutrosophic transportation problem

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Fig. 1 Transportation route of vaccine through different modes
Fig. 1 Transportation route of vaccine through different modes
Table 1 Summary of literature related to transportation problem 3 Preliminaries
Table 1 Summary of literature related to transportation problem 3 Preliminaries
Table 2 Leader’s optimization problem for the best and the worst solution Using the above proposition on the constraint sets Eqs. 6 and 7 and taking [st , 83] = 1, we obtain the maximum possible feasible region (for best optimal solution) and minimum possible feasible region (for worst optimal solution) for both levels, respectively (Shaocheng 1994; Chinneck and Ramadan 2000). As we are dealing with minimizing an interval fractional objective function, its coefficients are adjusted appropriately for each level. The optimization problem to obtain the best & the worst solution for both the levels are shown in Tables 2 and 2
Table 2 Leader’s optimization problem for the best and the worst solution Using the above proposition on the constraint sets Eqs. 6 and 7 and taking [st , 83] = 1, we obtain the maximum possible feasible region (for best optimal solution) and minimum possible feasible region (for worst optimal solution) for both levels, respectively (Shaocheng 1994; Chinneck and Ramadan 2000). As we are dealing with minimizing an interval fractional objective function, its coefficients are adjusted appropriately for each level. The optimization problem to obtain the best & the worst solution for both the levels are shown in Tables 2 and 2
Table 3 Followers’s optimization problem for the best and the worst solution
Table 3 Followers’s optimization problem for the best and the worst solution
6 Numerical illustration of BLETP-NN
6 Numerical illustration of BLETP-NN
The source and demand constraints at upper level are:
The source and demand constraints at upper level are:
Table6 Best upper level optimization problem Taking I € [0,1] in the given problem we reduce the BLTP-NN into a BLTP with interval numbers. Tables 6 and 7 are the optimization problems obtained using Table 2 for finding best and the worst upper level solution, respectively. Similarly, we can obtain optimization problem for finding best and the worst lower level solution using Table 3. For finding the best and the worst solution, appropriate dummy source and destination are added to balance the transportation problem. The results are compiled in Table 8. Neyt we conctrict onal achievement fiinctinne far hoth the anhiective fiinctinne at hoth
Table6 Best upper level optimization problem Taking I € [0,1] in the given problem we reduce the BLTP-NN into a BLTP with interval numbers. Tables 6 and 7 are the optimization problems obtained using Table 2 for finding best and the worst upper level solution, respectively. Similarly, we can obtain optimization problem for finding best and the worst lower level solution using Table 3. For finding the best and the worst solution, appropriate dummy source and destination are added to balance the transportation problem. The results are compiled in Table 8. Neyt we conctrict onal achievement fiinctinne far hoth the anhiective fiinctinne at hoth
Table 7 Worst upper level optimization problem Table 8 Individual solutions
Table 7 Worst upper level optimization problem Table 8 Individual solutions
Table 10 Leader’s optimization problem for the best and the worst solution Table 11 Followers’s optimization problem for the best and the worst solution
Table 10 Leader’s optimization problem for the best and the worst solution Table 11 Followers’s optimization problem for the best and the worst solution
8 Numerical illustration of BLIQTP-NN
8 Numerical illustration of BLIQTP-NN
Table 12 Upper level neutrosophic transportation problem
Table 12 Upper level neutrosophic transportation problem
Table 13 Lower level neutrosophic transportation problem
Table 13 Lower level neutrosophic transportation problem
Table 14 Individual solutions
Table 14 Individual solutions
Table 15 Satisfactory solution of BLIQTP-NN
Table 15 Satisfactory solution of BLIQTP-NN
9 Flowchart for solving BLFTP-NN and BLIQTP-NN
9 Flowchart for solving BLFTP-NN and BLIQTP-NN
Table 16 Sensitivity analysis-I
Table 16 Sensitivity analysis-I
Lower level variables
Lower level variables
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Computer ScienceApplied Mathematics and Computational ScienceNarrative Transportation Theory
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