An analytical study on different methods for solving transportation and assignment problem in fuzzy environment

Abstract

The transportation problem is one of the subclasses of linear programming problem where the newlineobjective is to transport various quantities of a single homogeneous product that are initially newlinestored at various origins, to different destinations in such a way that the total transportation is newlineminimum. In the beginning it was formulated for determining the optimal shipping pattern, so it newlineis called transportation problem. The basic transportation problem was originally developed by newlineHitchcock [15]. The transportation can be modeled as a standard linear programming problem, newlinewhich can then we solved by simplex method. The conventional and very well known newlinetransportation problem consists in transporting a certain product from each of n origins newlinei=1,2,3,......n to any of m destinations j=1, 2,3,.....m The origins are production facilities with newlinerespective capacities and#119886;1. and#119886;2 . . and#119886;and#119898; and the destinations are warehouses with required levels of newlinedemands and#119887;1, and#119887;2 . and#119887;and#119899; For the transport of a unit of the given product from the and#119894;and#119905;and#119893; source to the newlineand#119895;and#119905;and#119893;destination a cost and#119888;and#119894;and#119895; is given for which, without loss of generality, we can assumeand#119888;and#119894;and#119895; and#8805; 0 newlineHence, one must determine the amounts and#119909;and#119894;and#119895; to be transported from all the origins newlinei=1,2,3,......n to all the destinations j=1, 2,3,.....m in such a way that the total cost is newlineminimized. newline