An algorithm to find optimum cost time trade off pairs in a fractional capacitated transportation problem with restricted flow

This paper presents an algorithm to find optimum cost - time trade off pairs in a fractional capacitated transportation problem with bounds on total availabilities at sources and total destination requirements. The objective function is a ratio of two linear functions consisting of variable costs and profits respectively. Sometimes, situations arise where either reserve stocks have to be kept at the supply points say, for emergencies or there is a shortfall in the production level. In such situations, the total flow needs to be curtailed. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and the efficient cost- time trade off pairs to the given problem are shown to be derivable from this related transportation problem. Moreover, it is established that special type of feasible solution called corner feasible solution of related transportation problem bear one to one correspondence with the feasible solution of the given restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. Numerical illustration is included in support of theory.