Linear-fractional programming: Difference between revisions

Revision as of 01:38, 7 April 2021

Revision as of 15:03, 10 March 2022

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==Relation to linear programming==

Both linear programming and linear-fractional programming represent optimization problems using linear equations and linear inequalities, which for each problem-instance define a [[feasible set]]. Fractional linear programs have a richer set of objective functions. Informally, linear programming computes a policy delivering the best outcome, such as maximum profit or lowest cost. In contrast, a linear-fractional programming is used to achieve the highest ''ratio'' of outcome to cost, the ratio representing the highest efficiency. For example, in the context of LP we maximize the objective function '''profit = income − cost''' and might obtain maximum profit of \$100 (= \$1100 of income − \$1000 of cost). Thus, in LP we have an efficiency of \$100/\$1000 = 0.1. Using LFP we might obtain an efficiency of \$10/\$50 = 0.2 with a profit of only \$10, but only requiring \$50 of investment.

==Definition==