Abstract

Production and stock optimization in supply chains is a complex problem because it determines the optimum quantity production in time. Due to their multileveld nature, those problems are mostly solved by different methods and models of dynamic programming. The problem discussed in this paper refers to the determination of optimum quantity of production and stocks within the supply chain in a certain period of time, as well as in each sub-interval of a period, but with the condition that the production and stock expenditure remains minimal and that the predetermined demand in every sub-interval and throughout the entire observation period remains satisfied. Optimalizacija proizvodnje i zaliha u opskrbnim lancima predstavlja iznimno složen problem, jer se radi o određivanju optimalne količine proizvodnje u vremenu. Takvi problemi se zbog svoje više-etapnosti najčešće rješavaju primjenom raznih metoda i modela dinamičkog programiranja. Problem koji se obraduje o ovoj znanstvenoj raspravi, odnosi se na određivanje optimalne količine proizvodnje i zaliha unutar opskrbnog lanca u određenom razdoblju, kao i u svakom pod-intervalu toga razdoblja, pod uvjetom da troškovi proizvodnje i zaliha, budu minimalni i da se zadovolji unaprijed zadana potražnja u svakom pod-intervalu, a tako i u cijelom promatranom razdoblju.

Abstract

This paper deals with issues of shaping and functioning of computer programs in the modelling and solving of multimodal transportation network problems. A methodology of an integrated use of a programming language for mathematical modelling is defined, as well as spreadsheets for the solving of complex multimodal transportation network problems. The paper contains a comparison of the partial and integral methods of solving multimodal transportation networks. The basic hypothesis set forth in this paper is that the integral method results in better multimodal transportation network rationalization effects, whereas a multimodal transportation network model based on the integral method, once built, can be used as the basis for all kinds of transportation problems within multimodal transport. As opposed to linear transport problems, multimodal transport network can assume very complex shapes. This paper contains a comparison of the partial and integral approach to transportation network solving. In the partial approach, a straight forward model of a transportation network, which can be solved through the use of the Solver computer tool within the Excel spreadsheet interface, is quite sufficient. In the solving of a multimodal transportation problem through the integral method it is necessary to apply sophisticated mathematical modelling programming languages which support the use of complex matrix functions and the processing of a vast amount of variables and limitations. The LINGO programming language is more abstract than the Excel spreadsheet, and it requires a certain programming knowledge. The definition and presentation of a problem logic within Excel, in a manner which is acceptable to computer software, is an ideal basis, for modelling in the LINGO programming language, as well as a faster and more effective implementation of the mathematical model. This paper provides proof for the fact that it is more rational to solve the problem of multimodal transportation networks by using the integral, rather than the partial method. U radu je obrađena problematika oblikovanja i funkcioniranja računalnih programa u modeliranju i rješavanju problema multimodalnih transportnih mreža. Definirana je metodologija integrirane uporabe programskog jezika za matematičko modeliranje i proračunske tablice u rješavanju problema složene multimodalne transportne mreže. Uspoređene su parcijalna i integralna metoda rješavanja multimodalnih transportnih mreža. Temeljna hipoteza postavljena u ovom radu je da se integralnom metodom postižu bolji učinci racionalizacije multimodalnih transportnih mreža, pri čemu se jednom izgrađeni model multimodalne transportne mreže temeljen na integralnoj metodi, može koristiti kao temelj za sve vrste transportnih problema u multimodalnom transportu. Za razliku od linearnih transportnih problema multimodalna transportna mreža može poprimiti vrlo složene oblike. U radu su uspoređeni parcijalni i integralni pristup rješavanja transportne mreže. Kod parcijalnog pristupa dovoljan je jednostavniji model transportne mreže koji se može riješiti uporabom računalnog alata Solver u sučelju proračunske tablice Excel. U rješavanju multimodalnog transportnog problema integralnom metodom, potrebno je koristiti sofisticirane programske jezike za matematičko modeliranje koji podržavaju uporabu složenih matričnih funkcija i procesiranje velikog broja varijabli i ograničenja. Programski jezik LINGO je apstraktniji u odnosu na proračunsku tablicu Excel i zahtijeva određena znanja o programiranju. Definiranje i prezentacija logike problema u Excelu na način prihvatljiv računalnom programu predstavlja idealnu osnovu za modeliranje u programskom jeziku LINGO, te bržu i učinkovitiju implementaciju matematičkog modela. U radu je dokazano da je problem multimodalne transportne mreže racionalnije rješavati integralnom, nego parcijalnom metodom.