Abstract
In this paper, a transportation problem with an objective function as the sum of a linear and linear fractional function is considered. We present an algorithm to solve the above transportation problem. In addition, we consider two special cases of the problem, where the transportation flow is either restricted or enhanced. The first case deals with when one wishes to keep reserve stocks at the sources for emergencies, thereby restricting the total flow to a known specified level. The second case deals with when extra demand in the market compels some of the factories to increase their production, thereby enhancing the total flow to meet the customer demands fully. For the above special cases, we formulate a related linear plus linear fractional transportation problem. We present a numerical example to illustrate the proposed algorithm for the different cases. We show that the solution obtained is a local minimum occurring at an extreme point of the convex set of feasible solutions.
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