Articles you may be interested inParametric approach for an absolute value linear fractional programming with interval coefficients in the objective function AIP Conf.Abstract. In this paper, the linear fractional programming problem with interval coefficients in the objective function is considered. The aim of the paper is to show that a parametric approach, which is an iterative procedure, can be utilized to solve such problem. Questions of how to select the best coefficient through the intervals and also selecting the best value of decision variables are answered in this paper. Finally, the proposed method yields to the optimal solution. An example is given to show the efficiency of the method.

Optimizing the sum of linear fractional functions over a set of linear inequalities (S-LFP) has been considered by many researchers due to the fact that there are a number of real-world problems which are modelled mathematically as S-LFP problems. Solving the S-LFP is not easy in practice since the problem may have several local optimal solutions which makes the structure complex. To our knowledge, existing methods dealing with S-LFP are iterative algorithms that are based on branch and bound algorithms. Using these methods requires high computational cost and time. In this paper, we present a non-iterative and straightforward method with less computational expenses to deal with S-LFP. In the method, a new S-LFP is constructed based on the membership functions of the objectives multiplied by suitable weights. This new problem is then changed into a linear programming problem (LPP) using variable transformations. It was proven that the optimal solution of the LPP becomes the global optimal solution for the S-LFP. Numerical examples are given to illustrate the method.

According to the positivity or negativity of the function ݃ሺ‫ݔ‬ሻ, two linear programming problems are resulted to be solved to achieve the optimal solution. Combination of the two linear programming problems finally yields a mixed 0-1 linear programming problem which can be used to obtain the optimal solution of an absolute value linear fractional programming problem with interval coefficients in the objective function. A numerical example is given to illustrate the efficiency and the feasibility of the method.

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of α - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly ɛ - efficient solution. Two examples are given to illustrate the method.

Finding efficient solutions for the multi-objective linear fractional programming problem (MOLFPP) is a challenging issue in optimization because more than one target has to be taken into account. For the problem, we face the concept of efficient solutions which is an infinite set especially when the objectives are in conflict. Since a classical method generally comes out with only one efficient solution, thus introducing new efficient approaches is helpful and beneficial for the decision makers to make their decisions according to more possibilities. In this paper, we aim to consider the MOLFPP with fuzzy coefficients (FMOLFPP) where the concept of α - cuts is utilized so as to transform the fuzzy numbers into closed intervals and rank the fuzzy numbers as well. Consequently, the fuzzy problem is changed into an interval valued multi-objective linear fractional programming problem (IV-MOLFPP). Subsequently, the IV-MOLFPP is further changed into linear programming problems (LPPs) using a parametric approach, weighted sum and max-min methods. It is demonstrated that the solution obtained is at least a weakly ɛ - efficient solution, where the value of ɛ helps a decision maker (DM) to make his decision appropriately i.e. DMs chose more likely the solutions with the lowest value of ɛ. Numerical examples are solved to illustrate the method and comparison are made to show the accuracy, and the reliability of the proposed solutions.