Abstract
For both in economical and social development of country transportation system plays a vital role. As it is directly involved with financial growth of the country, for that a complete well planned transportation infrastructure is necessary. Most of the transportation models are formulated with minimization of transportation cost as the basic objective. But consideration of transportation system with a single objective is not able to meet the various requirements of transportation industry for which it may not lead to the practical optimal solution. It bounds the decision makers (DMs) to consider several objectives at a time instead of single objective. To handle a multi-objective transportation problem with fixed parameters is a challenging issue; rather it is easy to consider all parameters in terms of linguistic variables. In this paper, a multi criteria multi-objective transportation models is formulated based on fuzzy relations under the fuzzy logic with several objectives like (i) minimization of total transportation cost and (ii) minimization of total transportation time. Another objective, maximization of the transported amount from a source to a destination is determined on the basis of previous two objectives. All the objectives are associated with multiple numbers of criteria like breakable items, shipping distance, service charge, mode of transportation etc. These relations are imprecise in nature and represented in terms of verbal words such as low, medium, high and very high. The fuzzy rule based multi-objective transportation problem is formulated and result is discussed.
Highlights
Mathematical FormulationConsider the m-supply points S1, S2...Sm and n-demand points D1, D2 ...Dn with kobjectives Z1, Z2 ...Zk. Without any loss of generality it is assume that, all the objectives are of minimization type
Introduction known as Transportation ProblemThe transportation problem is a special case of Linear programming problem, in which all theThe basic objective of decision making process is, to identify and choose the best alternative as per the requirement of decision maker
From the analysis it is observed that the input parameter breakable item has less impact on both the outputs transportation cost and transportation time whereas there is an increase in transportation cost in case of more shipping distance and maximum breakable items (See Fig 5a)
Summary
Consider the m-supply points S1, S2...Sm and n-demand points D1, D2 ...Dn with kobjectives Z1, Z2 ...Zk. Without any loss of generality it is assume that, all the objectives are of minimization type. Suppose the supply point Si has an availability ai (i = 1, 2 ...m) and the demand point Dj has the requirement (k) bj (j = 1, 2 ....n). Let for each objective Zk, the penalty Cij associated with transporting a single unit from supply point Si to demand point Dj. Let the variable xxiiii represents the unknown quantity transported from supply point Si to destination Dj
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