Linear-fractional programming: Difference between revisions

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{{article issues|intromissing=May 2009|unreferenced=May 2009|wikify=May 2009}}

'''Linear-fractional programming''' (LFP) formally is almost the same as [[Linear programming]] but instead of linear objective function we have a ratio of two linear functions, subject to linear 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.