FUNDAMENTALS OF LINEAR PROGRAMMING THEORY : Final paper

Linearno programiranje je način pronalaženja optimalnog rješenja za složeni problem koji se sastoji od funkcije cilja, varijabli i ograničenja (restrikcija). Razlikuju se standardni problemi linearnog programiranja, a to su standardni problem maksimuma i standardni problem minimuma; te opći problem. Specijalni problemi linearnog programiranja su transportni problem (otvoreni i zatvoreni) te problem asignacije. Linearno programiranje se može primijeniti za rješavanje raznih složenih problema za čije rješavanje je potrebno koristiti određene metode kako bi se došlo do optimalnog rješenja. Linearno programiranje se može koristiti u poduzećima kako bi se primjerice povećala dobit ili smanjio trošak. Kod specijalnih problema, poduzeće može koristiti linearno programiranje kako bi pronašli optimalni raspored zaposlenika na određeno mjesto na temelju njihove uspješnosti. Kod transportnog problema može se rješavati primjerice problem kako transportirati proizvode iz 2 ili više ishodišnih mjesta do 2 ili više odredišnih mjesta, a da se pri tome smanje troškovi po jedinici transporta. Na temelju objavljene literature i vlastitih zapažanja te primjera objasnit će se linearno programiranje. Prvo će se objasniti opća teorija o linearnom programiranju, te iznijeti što hrvatski i strani autori pišu o linearnom programiranju. Na kraju će se riješiti dva primjera linearnog programiranja te dati zaključak.Linear programming is a way of finding optimal solution for a complex problem which is made of objective function, variables and restrictions. Standard problems of LP are SP of maximum, SP of minimum and general problem. Special problems of LP are transportation problem (open and closed) and assignation problem. Linear programming can be applied to solve any complex problem that cannot be solved just like that, but it is necessary to come up with an optimal solution with certain methods. Linear programming can be used in companies when they want to increase profit or decrease cost. Those are the examples of SP of maximum and SP of6 minimum. With special problems, company can use linear programming to find an optimal timetable of employs to their designated workspace based on their accomplishment. With transportation problem, there can be a problem of how to transport products from 2 or more starting points to 2 or more destination points, but so that the cost per unit of transport decreases. Based on published literature and own observations and examples, we are going to explain linear programming and give a conclusion on everything that was processed in here. We are first going to explain a general linear programming theory, then we are going to present what Croatian and foreign authors are writing about linear programming. And finally, we are going to solve two examples of linear programming and then give a conclusion for this theme