Linear programmingProgramminglinear (LP) represents the best-developed family of methods solving specific constrained optimization problems. These tasks consider a linear objective multivariable function with constraintsConstraint composed of linear inequalities. They represent models of various real-lifeProblemsreal-life and economic problemsProblemeconomic. For instance, a possible task can be determining the production level to maximize the revenues when constraining resources, storage facilities, employees, working hours, etc. The goal can also be to minimize the costsCosts to reach the desired guaranteed minimal production level. Another modelModel can represent the so-called mixing problem: making the cheapest mixture containing minimal portions of necessary substances. Using LP, one can also solve problems of material parting, i.e., producing the required number of pieces of particular products with a minimumMinimum of the given material resources. Last but not least, some transportation (traffic) problems can be solved using LP techniques to distribute products to the shops at a minimum costCostminimum.

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Linear Programming

  • Libor Pekař

摘要

Linear programmingProgramminglinear (LP) represents the best-developed family of methods solving specific constrained optimization problems. These tasks consider a linear objective multivariable function with constraintsConstraint composed of linear inequalities. They represent models of various real-lifeProblemsreal-life and economic problemsProblemeconomic. For instance, a possible task can be determining the production level to maximize the revenues when constraining resources, storage facilities, employees, working hours, etc. The goal can also be to minimize the costsCosts to reach the desired guaranteed minimal production level. Another modelModel can represent the so-called mixing problem: making the cheapest mixture containing minimal portions of necessary substances. Using LP, one can also solve problems of material parting, i.e., producing the required number of pieces of particular products with a minimumMinimum of the given material resources. Last but not least, some transportation (traffic) problems can be solved using LP techniques to distribute products to the shops at a minimum costCostminimum.