LINEAR PROGRAMMING PROBLEMS IN MECHANICAL ENGINEERING AND RELATED FIELDS

U ovom završnom radu prikazani su problemi linearnog programiranja u strojarstvu. Linearno programiranje je grana matematike koja se bavi problemom optimizacije sustava unutar zadanih ograničenja. U strojarstvu se linearno programiranje najčešće koristi za: određivanje količina proizvoda s kojima se postiže maksimalna dobit, određivanje plana proizvodnje s kojima se postižu minimalni troškovi, određivanje količine sirovine uz maksimalnu dobit itd. U ovom završnom radu prikazani su neki od tih problema. Prvo su obrađeni problemi optimiranja proizvodnje i iskorištenja materijala, a zatim problem modeliranja smjesa, optimiranja transporta i raspored radnika. Navedeno je teoretsko objašnjenje zadanih problema i definirani su matematički modeli. Ovisno o vrsti problema cilj može biti različit; neki od najčešćih ciljeva su: maksimalna dobit, minimalan trošak, minimalan otpad, maksimalno iskorištenje resursa, minimalno vrijeme proizvodnje.In this bachelor thesis, problems of linear programming in mechanical engineering are presented. Linear programming is a branch of mathematics that deals with the problem of system optimization within the given constraints. Linear programming is the most commonly used in mechanical engineering: determining the amount of product to achieve maximum profit, determining a production plan to achieve minimum costs, determining the amount of raw material with maximum profit etc. In this bachelor thesis, some of these problems are shown. First, the problems of optimizing the production and utilization of materials were discussed, and then the problem of modeling the mixture, optimizing the transport and the assignment problem. The theoretical explanation of the given problems was specified and mathematical models were defined. Depending on the type of problem, the objective function may be different; some of the most common objective functions are: maximum profit, minimal cost, minimal waste, maximum material utilization, minimum production time