Planar three-index transportation problems with dominating index

Abstract

Zusammenfassung. Es Summary." A class of planar three-index transportation problems is described which can be reduced to classical transportation problems. Moreover an example of a polytope with full dimension having this property is given.

Time Minimizing Multi-Index Bulk Transportation Problem

“…The problem is extended into MITP by considering commodities or modes of transportation as additional indices.MITP was first introduced by Schell [16] and Galler and Dwyer [17] in literature. Several other authorslike Haley [18], Junginer [19], Korsnikov [20], Pandian and Anuradha [21], Patel and Tripathy [22] studied MITP using different approaches. Latha [23] studied MIBTP with time minimizing objective using Lexi-Search algorithm.…”

Pareto Optimal Solutions of the Fuzzy Multi-Index, Bi-Criteria Fixed Charge Transportation Problem

“…He further solved the MITP with North-West corner rule and an extension of the modified distribution (MODI) method. Haley [13], Haley [14], Moravek and Vlach [23], Smith [30], Vlach [34], Korsnikov [20], Bandopadhyaya and Puri [6], Junginger [16], Pandian and Anuradha [26], Bulut and Bulut [10], Zitouni [37], Djamel et al [11] are names of few researchers who considered MITP.…”

“…The fuzzy fixed charges are given as f 111 = (4,6,10,20) f 121 = (14,16,30,60) f 131 =(9,11,20,40) f 112 = (9,11,20,40) f 122 = (9,11,20, The total fuzzy fixed charge for fuzzy initial basic feasible solution is calculated from Table 4. Then eMODI method as explained in step ( 6) is applied to Table 4 which gives the allocations corresponding to the first Pareto Optimal cost as shown in Table 5.…”