An Experimental Study on Linear Fractional Programming Problems

Abstract

Much effort has been concentrated on transportation problems (TP) with equality constraints. In real life, however, most problems have mixed constraints accommodating many applications that go beyond transportation related problems to include job scheduling, production inventory, production distribution, allocation problems, and investment analysis. A literature search revealed no systematic method for finding an optimal solution or addressing more-for-less situations in transportation problems with mixed constraint. Here we consider modified VAM method to solve TP with mixed constraints to find out more-for-less situations in transportation problems. Several numerical examples have been considered to justify the effectiveness of the method. On the other hand Linear Fraction Programming (LFP) (i.e. ratio objective that have numerator and denominator) have attracted the interest of many researches due to its application in many important fields such as production planning, financial and corporate planning, health care and hospital planning. Also various optimization problems in engineering and economics involve maximization (or minimization) of the ratio of physical or economical function, for instances cost/time, cost/volume, cost/benefit, profit/cost or other quantities measuring the efficiency of the system. This study presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The LFP problem is converted it into a regular linear programming (LP) problem by an efficient way. The proposed approach is able to reduce some significant limitations of the existing methods. To test the effectiveness and efficiency of the algorithm some hard instances are considered. The proposed approach is able to solve the problem efficiently whereas in some cases the existence approaches are failed to solve the problems.