Abstract
Abstract Zimmermann (Int. J. Gen. Syst. 2:209-215, 1976) first introduced the concept of fuzzy inequality in the field of linear programming problem (LPP). But this concept is hardly used in any real life applications of LPP. So, in this paper, a multi-objective multi-item solid transportation problem (MMSTP) with fuzzy inequality constraints is modeled. Representing different preferences of the decision maker for transportation, three different types of models are formulated and analyzed. Fuzzy inequality solid transportation problem is converted to parameter solid transportation problem by an appropriate choice of flexible index, and then the crisp solid transportation problem is solved by the algorithm (Cao in Optimal Models and Methods with Fuzzy Quantities, 2010) for decision values. Fuzzy interactive satisfied method (FISM), global criterion method (GCM) and convex combination method (CCM) are applied to derive optimal compromise solutions for MMSTP by using MatLab and Lingo-11.0. The models are illustrated with numerical examples and some sensitivity analysis is also presented.
Highlights
The solid transportation problem (STP) is a generalization of the traditional transportation problem in which three-dimensional properties are taken into account in the objective and constraint set instead of source and destination
If more than one objective is to be optimized in an STP, the problem is called multiobjective solid transportation problem (MOSTP)
8 Conclusion The multi-objective multi-item solid transportation problem in fuzzy inequality constraints has been explored in this paper
Summary
The solid transportation problem (STP) is a generalization of the traditional transportation problem in which three-dimensional properties (supply, demand, convenience) are taken into account in the objective and constraint set instead of source and destination. If more than one objective is to be optimized in an STP, the problem is called multiobjective solid transportation problem (MOSTP). If we consider more than one item and more than one objective at a time in an STP, it is called a multi-objective multiitem solid transportation problem (MMSTP). Step : Solve linear programming (LPα∗ ), and we can obtain an optimal solution xα∗ and an optimal value zα∗. By solving (LPα ), we obtain the optimal solution as x = . (viii) xpijk = the amount to be transported from ith origin to jth destination by means of kth conveyance of pth item (decision variables). (ix) Citjpk = per unit transportation cost from ith origin to jth destination by kth conveyance of pth item and tth objective. (i) Homogeneous product should be transported from sources to destinations. (ii) During transportation no items are damaged, i.e., the amount of received items in destination is the same as the one sent from sources
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