OPTIMUM COST-TIME TRADE-OFF PAIRS IN A FRACTIONAL PLUS FRACTIONAL CAPACITATED TRANSPORTATION PROBLEM WITH RESTRICTED FLOW

Abstract

This paper provides the optimum cost-time trade-off pairs to the manager of a trading firm, D. M. Chemicals, who deals in the trade of soap stone. The problem of the manager is to determine the quantity (in tons) of soap stone that the firm should purchase from different sellers and sell to the different buyers such that the ratio of actual cartage to standard cartage plus ratio of purchasing cost to profit is minimized provided the demand and supply conditions are satisfied keeping the reserve stocks for emergency situations. Moreover, the manager wishes to minimize the maximum time of transporting goods. The problem under consideration is modeled as a fractional plus linear fractional capacitated transportation problem with restricted flow. The data is taken from the account keeping books of the firm. The solution so obtained by using the developed algorithm is compared with the
existing data. Moreover, the solution obtained is verified by a computing software Excel Solver.