A priority based time minimization transportation problem

Bindu Kaushal, Shalini Arora
2018 Yugoslav Journal of Operations Research
This paper discusses a priority based time minimizing transporation problem in which destinations are prioritized so that the material is supplied, based upon the priorities of the destinations. All the destinations, which are at priority, are served first in Stage-I while the demands of the secondary destinations are met in Stage-II. It is assumed that secondary transportation can not take place until the primary transportation is done. The purpose is to transport in such a manner that the sum
more » ... of the transportation time of primary and secondary destinations is minimum. To achieve this, two approaches are proposed. In the first approach, primary destinations are served optimally by giving weights while in the second approach, lexicographic optimization is used. From the generated pairs, the minimum sum of times corressponding to Stage-I and Stage-II times is picked up as the optimal solution. It is also shown, through Computational Details, that the lexicographic optimization converges to the optimal solution faster than the first approach as reported in Table 4 . Step 6 Set t ij = M ∀t ij > T r . End While Loop Step 7 Stop. For each pair of lexicographic solution, we find M inf r = M in[T r + T r ] = T, r = 1, 2, . . . , p Hence, T = (T r , T r ) is the lexicographical optimal solution. NUMERICAL ILLUSTRATION Consider the following 6X8 priority based time minimization transportation problem as shown in Table 1 . Each cell represents the time of transportation between every source destination pair. Entries which are marked bold show primary destinations, and others show secondary destination. I = {1, 2, 3, 4, 5, 6}=Number of given sources J = {1, 2, 3, 4, 5, 6, 7, 8}=Number of given destinations J 1 = {1, 3, 4, 6, 8}=Primary destinations J 2 = {2, 5, 7} = Secondary destinations Now, partition various time entries given as t 1 (= 13) > t 2 (= 12) > t 3 (= 10) > t 4 (= 9) > t 5 (= 8) > t 6 (= 7) > t 7 (= 6) > t 8 (= 5) > t 9 (= 4) > t 10 (= 3) > t 11 (= 2) > t 12 (= 1). Here, t p = t 12 , so p = 12 Let M l = {(i, j) : t ij = t l }, l = {1, 2, . . . , p} and λ p−l+1 be the weights attached to the set M l shown in