Linear-fractional programming

Linear-fractional programming (LFP) formally is almost the same as Linear programming but instaed of linear objective function we have a ratio of two linear fuctions, subject to linear equality and linear inequality constraints. Informally, if linear programming determines the way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model and given some list of requirements represented as linear equations, in linear-fractional programming model we can achieve the best (highest) ratio outcome/cost. i.e. highest efficiency.

For example, if in the frame of LP we maximize profit = income - cost and obtain maximal profit of 100 units (=1100$ of income - 1000$ of cost), then using LFP we can obtain only 10$ of profit which requires only 50$ of investment. Thus, in LP we have efficiency 100$/1000$=0.1, at the same time LFP provides efficiency equal to 10$/50$=0.5.

Linear-fractional programming can be used in the same real-wolrd applications as LP, in various fields of study. Most extensively it is used in business and economic situations, especially in the situations of deficit of financial resources. Also LFP can be utilized for wide range of engineering problems. Some industries that use linear programming models including transportation, energy, telecommunications, and manufacturing may use LPF as well as LP.