Restricted flow in a non linear Capacitated Transportation Problem with Bounds on Rim Conditions

This paper discusses restricted flow in a fixed charge capacitated transportation problem with bounds on total source availabilities and total destination requirements. The objective function is the sum of two linear fractional functions consisting of variable costs and fixed charges respectively. Sometimes, situations arise when one wishes to keep reserve stocks at the sources for emergencies, thereby restricting the total transportation flow to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve non linear capacitated transportation problem with restricted flow. Numerical illustration is included in support of theory.