Quadratic fractional transportation problem with additional impurity restrictions

Abstract

The transportation problems with impurities in commodity are very important from practical point of view. In many real life transportation situations in industries of coal, iron, cement etc., the commodity does vary in some characteristics according to it source and the final commodity mixture reaching the various destinations may then be required to meet known specifications. In this paper a transportation problem is considered where the objective function is quadratic fractional and the commodity can have different types of impurities. Using simplex multipliers technique, an optimality criterion is derived and an algorithm is developed for its solution. The algorithm takes into account the special structure of the problem and heavily depends on the optimality conditions. A real life example of Bharat Ispat Industries Limited (BIIL), Bihar, India is included to illustrate the Algorithm.