Linear-fractional programming: Difference between revisions

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Linear-fractional programming (LFP) formally is almost the same as [[Linear programming]] but instaedinstead of linear objective function we have a ratio of two linear fuctionsfunctions, 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$/50$=0.2.