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In this study, the resilience of farm production plan through different management adjustments was analyzed. For this purpose, a farm model based on mathematical programming was applied. Through organized workshops typical farms focusing on dairy production were defined through qualitative and quantitative classification. Data were obtained from various databases and expert assessments from the agricultural sector. Analysis of resilience was carried out for three of these typical dairy farms. Using the farm model, the production plan of each farm was reconstructed in the first step and then tested for possible deviations from the baseline. Gross margin was used as the main economic indicator. The results show that the typical farms have very different levels of efficiency and potential for improvement. Furthermore, it was found that all farms can achieve significantly higher gross margin only with improved feed quality, which indirectly leads to a lower need for purchased feed and consequently to lower variable costs and higher gross margin. The level of the latter is also significantly affected by the milk yield achieved, especially on larger farms. However, on smaller farms they can improve profitability more significantly by keeping dairy cows on pasture to a greater extent, which results in a reduction in harvesting costs., V študiji smo analizirali odpornost proizvodnih načrtov kmetij z različnimi prilagoditvami upravljanja. V ta namen smo uporabili model kmetijskih gospodarstev, ki je temeljil na matematičnem programiranju. Z organiziranimi delavnicami smo s kvalitativno in kvantitativno klasifikacijo definirali tipična kmetijska gospodarstva usmerjana v prirejo mleka. Podatke smo pridobili iz različnih podatkovnih zbirk in strokovnih ocen. Analizo prožnosti smo opravili na treh tipičnih kmetijah. V prvem koraku smo z modelom rekonstruirali proizvodni načrt vsake kmetije in nadalje analizirali morebitna odstopanja od izhodišča. Kot glavni ekonomski kazalnik smo uporabili bruto dodano vrednost (BDV). Ugotovili smo, da imajo analizirane kmetije zelo različne stopnje učinkovitosti, kot tudi možnosti za izboljšanje. Nadalje smo ugotovili, da lahko vse kmetije dosežejo pomembno višje pokritje zgolj z izboljšano kakovostjo pridelane krme, kar posredno privede do manjših potreb po kupljeni krmi in posledično nižjih spremenljivih stroškov ter višje bruto dodane vrednosti. Na višino slednje pomembno vpliva tudi dosežena mlečnost, zlasti je ta vpliv izrazit na večjih kmetijah. Na manjših kmetijah pa lahko ekonomičnost izboljšajo predvsem z vključevanjem večjega obsega paše krav molznic, kar vpliva predvsem na znižanje stroškov spravila.

V Sloveniji je že dlje časa samooskrba s hrano pomembna tema, ki je na nizki ravni. Posebej nizko je ta stopnja vidna pri zelenjavi, zato smo se odločili pristopiti k analizi problematike. V raziskavi smo k problematiki pristopili »od spodaj navzgor« in sicer z namenom, da najdemo empirične rešitve, ki kmetovalcem omogočajo pogoje, s katerimi bi dvignili nizko samooskrbo. V ta namen smo razvili 5 matematičnih modelov, s katerimi se bo analizirala problematika samooskrbe. 1. model je namenjen analizi ekonomske upravičenosti v raziskavo vključenih kultur, kot tudi posameznih sort in hibridov. Rezultati le-tega predstavljajo vhodne podatke za naslednje faze razvoja modelov. Rezultati analize modela 1 kažejo ekonomsko upravičenost vseh analiziranih zelenjadnic. V 2. fazi smo razvili 2 modelni orodji. S prvim ocenjujemo potrebne količine zelenjadnic za zagotovitev oskrbe po zelenjavi za določen teden v letu, v naboru razpoložljivih kultur. Drugo modelno orodje 2. faze pa izmed razpoložljivih kultur in njihovih hibridov/sort oceni potrebne površine, s čimer zadovoljimo želene potrebe po oskrbi z zelenjavo. 3. faza je namenjena izboru ustrezne metode ciljnega programiranja, na podlagi katere bi lahko ocenili ustrezne sorte/hibride. Za oceno problema smo uporabili 3 metode ciljnega programiranja (tehtano ciljno programiranje, prioritetno ciljno programiranje in Čebiševo ciljno programiranje). Kot najustreznejše se je pokazalo tehtano ciljno programiranje, ki je doseglo nekoliko slabše rezultate v primerjavi s prioritetnim ciljnim programiranjem, ki pa je med izračunom doseglo večje število napak. Kot najslabše se je pokazalo Čebiševo ciljno programiranje. V fazi 4 je sledilo načrtovanje kolobarja znotraj posameznega koledarskega leta. S pomočjo razvitega orodja smo sestavili 538 letnih scenarijev, ki jih potem v fazi 5 združimo v 183 5-letnih kolobarjev. Rezultati kažejo, da na 874,66 ha obdelovalnih površin zagotavljamo popolno samooskrbo z zelenjavo za območje Pomurja od 1. maja do 13. novembra. V nadaljevanju raziskave na osnovi s. w. o. t. analize stanja trga na organizacijske strani pridelave in prodaje predlagamo ukrepe, ki stimulirajo pridelavo. Prva je uvedba indeksa izkoriščenosti njivskih površin kot ukrepa, s katerim bi lahko stimulirali pridelavo preko neposrednih plačil, ki so drugače razdeljena. Drugi ukrep predstavlja povezovanje pridelovalcev. Tretji ukrep je organiziranje skupnega prostora, kjer se srečata ponudba s strani pridelovalcev in povpraševanje s strani odkupa. Kot ključen ukrep pa je seveda ureditev cen. In Slovenia food self-sufficiency which is at a low level is an important topic for a long time. Especially low this rate is visible in the case of vegetables, so we decided approach to the analysis of the problem. We approach to the study from bottom to the top with the aim of finding empirical solutions that enable farmers conditions that would raise low self-sufficiency. With this purpose, we have developed 5 mathematical models to analyze the problem of self-sufficiency. 1st model is intended for the analysis of economic viability in research involved cultures, as well as individual varieties and hybrids. The results of this are input data for the next stages of model development. The results of the analysis of model 1 show the economic viability of all analyzed vegetables. In the second phase we developed 2 modeling tools. The first estimates the necessary quantities of vegetables to ensure the supply with vegetables for a certain week of the year from the range of available crops. The second phase of 2nd modeling tool estimates the required area from all available cultures and their hybrids/varieties in order to meet the desired needs for vegetable supply. Phase 3 is intended to select an appropriate goal programming method, on the basis where it could be possible to evaluate relevant varieties/hybrids. In order to evaluate the problem, we used the 3 methods of goal programming (weighted goal programming, lexicographic goal programming, and Chebyshev goal programming). Weighted goal programming was shown to be the most appropriate, which achieved somewhat poorer results compared to lexicographic goal programming, which resulted in more errors during the calculation. Chebyshev goal programming was the worst. In phase 4, the planning of the crop rotation within each calendar year was designed. With the help of the developed tool, we compiled 538 annual scenarios, which are then combined in 183 5-year coils in phase 5. The results show that 874,66 ha of cultivated areas provide complete self-sufficiency with vegetables in the Pomurje region from 1st May to November 13. In the continuation of the study, based on s.w.o.t. analysis of the state of the market on the organizational side of production and sale we propose measures that stimulate production. The first step is to introduce an arable land use index as a measure that could stimulate production through direct payments which are otherwise distributed. The second measure is connection of growers. The third measure is in organization of a common space where the supply and demand meet. Of course, price regulation is a key measure.

In the article we define a quantity which measures the quality of the approximation of a function, given by a table, with a function from a certain family D of nonconstant functions. For this purpose one has to find the infimum and the supremum of the set of correlation coefficients between the given function and functions from D.We do this for the family of all nonconstant functions and for the family of growth functions. V članku je definirana količina, ki meri kvaliteto aproksimacije tabelarično podane funkcije družine D nekonstantnih funkcij. V ta namen je treba poiskati infimum in supremum množice korelacijskih koeficientov med dano funkcijo in funkcijami iz D. Tu je to storjeno za družino vseh nekonstantnih funkcij in za družino rastnih funkcij.

Za iskanje možnosti učinkovitejšega gospodarjenja na živinorejskih kmetijah je prehrana živali zagotovo področje, ki to dopušča. Četudi se številni raziskovalci lotevajo raziskav pridelave travniške krme z njiv le s tehnološkega vidika, se ugotovitve navezujejo tudi na ekonomiko pridelave. Za ocenjevanje ekonomske upravičenosti uporabe tehnologij ali odločitev zanje si pomagamo z uporabo simulacijskih modelov, programskih orodij ter primernih metod. Pri računanju krmnih obrokov prehranske strokovnjake pretežno zanima pokritost potreb živali glede na intenzivnost proizvodnje, medtem ko agrarne ekonomiste zanima zlasti stroškovni vidik v razmerju s prihodki. V nalogi z vidika pogojev za pridelavo travniške krme z njiv ugotavljamo njihov vpliv na sestavo in vrednost krmnih obrokov za krave molznice. Razvito je orodje, ki poleg ocenjevanja ekonomskih vplivov omogoča tudi načrtovanje pridelave krme ter ocenjevanje primernosti tehnologij s stroškovnega vidika. Pri tem je uporabljena metoda klasičnega determinističnega linearnega programiranja. V nalogi je pristop testiran na primeru ravninskega kmetijskega gospodarstva, ki je specializirano v prirejo mleka. Dobljeni rezultati kažejo prednosti in slabosti linearnega programiranja. Hkrati je ugotovljeno, da je linearno programiranje lahko primerno orodje za načrtovanje pridelave krme in ocenjevanje tehnologij, a je pri tem kakovost rezultatov in razpoložljivost vhodnih podatkov pomembna omejitev. In the quest for more effective management of livestock farms, animal nutrition is an area that offers a wide range of possibilities. Although numerous researches focus on the production of forage on temporary grassland (which is part of arable land) only in technological terms, their findings always relate to the economics of production, too. Simulation models, software tools and suitable methods are applied to assess the economic viability of using or deciding for specific technologies. In calculating feed rations, nutrition experts primarily examine the coverage of animal needs in relation to the intensity of production, while agricultural economists are interested in the lowest cost of feed rations. In the thesis, we examine these topics in terms of conditions for the production of temporary grassland forage and their impact on the composition and value of feed rations for dairy cows. We developed a model which, in addition to impact assessment, also helps us plan forage production and assess the suitability of technologies. The method of traditional linear programming is applied. In the thesis, the model and the method are tested for a flatland dairy farm. Based on the results obtained we presented both advantages and disadvantages of linear programming. We found that linear programming can be a suitable tool for the planning of forage production and assessing technologies, with the quality of results and availability of input data being an important limiting factor.

Kmetijstvo danes deluje v poslovnem okolju, za katerega so značilni spreminjanje cen pridelkov, deregulacija trgov in nestabilnost dohodkov. Sooča se s številnimi tveganji, na eni strani povezanimi z vremenskimi vplivi, škodljivci, kot tudi vse pogostejšimi boleznimi živali. Na strani spreminjajočega okolja imajo pomembno vlogo tudi ukrepi skupne kmetijske politike. Zaradi slednjega so nosilci kmetijske proizvodnje pri svojih proizvodnih in organizacijskih odločitvah pogosto v dilemi in se soočajo s številnimi izzivi. Pri njihovih odločitvah so jim v pomoč različna orodja. Med kompleksnejšo skupino metod sodi matematično programiranje, znotraj katere je najpogosteje uporabljeno linearno programiranje. Tako smo tudi v nalogi uporabili modelno orodje, katerega metodološki pristop temelji na matematičnem programiranju. Z njim smo želeli raziskati, na kakšen način v danih ekonomskih razmerah optimirati ekonomski položaj v govedoreji na določenem omejenem območju. Tako smo v prvem koraku definirali tipe kmetijskih gospodarstev in jim na podlagi dejanskih podatkov določili fizični obseg proizvodnje. Vsi tipi predstavljajo govedorejske kmetije, usmerjene v prirejo mleka, rejo bikov pitancev oziroma kombinacijo obeh. Nato smo na podlagi oblikovanih scenarijev na danih tipih kmetijskih gospodarstev z metodo delne optimizacije definirali trenuten ekonomski položaj. V nadaljevanju smo z metodo omejene optimizacije iskali optimalen proizvodni načrt s ciljem doseženega čim boljšega ekonomskega rezultata. Pri tem smo s postopkom optimizacije spreminjali proizvodne omejitve in dodajali ali odvzemali posamezne aktivnosti, ki lahko vstopajo v optimalno rešitev. V primeru, ko smo dobili rezultate, ki so iz ekonomskega in tehnološkega vidika korektni, vendar nerealni, smo postopek optimizacije ponovili z dodajanjem dodatnih omejitev. Na podlagi uporabe modelnega orodja smo prišli med drugim do rezultatov, da samostojno obravnavanje živinorejskih aktivnosti vpliva na optimalen proizvodni načrt in posledično na višje pričakovano pokritje in višji pričakovani dohodek. Rezultati kažejo, da kmetijske površine niso optimalno izkoriščene, saj bi lahko na vseh treh tipih kmetijskih gospodarstev na obstoječih površinah redili več živali in s tem dosegali tudi boljše ekonomske rezultate. Agriculture nowadays operates in a business environment characterized by changing crop prices, deregulation of markets and income instability. It faces many risks from weather, pests and increasing occurrence of animal diseases. In such changing environment common agricultural policy plays an important role. That is the reason for a dilemma for carriers of agricultural production who are facing many challenges. There are many tools and methods to help them in decision making. Among the complex group of methods is mathematical programming, within which is the most commonly used linear programming. In our thesis we used a model tool where methodological approach is based on mathematical programming. With it, we wanted to explore how to optimize the economic situation of the cattle breeding farm in the current economic conditions in certain area. The first step was to define types of agricultural holdings and set their physical output on the basis of actual data. All chosen types represent cattle farms focused on milk production and breeding of fattening bulls or a combination of both. Then, we defined current economic situation formed by partial optimization on the basis of given scenarios for chosen types of agricultural holdings. With limited optimization method we were looking for the optimal production plan with the objective to achieve the best possible economic result. We changed the procedure of optimization of production constraints and added or subtracted different activities, which can enter the optimal solution. In the case when we got the results that are in economic and technological point of view correct, but unrealistic, we repeated the optimization process by adding additional constraints. Based on the use of modelling tools we have reached the results which inter alia show that independent planning of livestock activities affects the optimal production plan and, consequently magnifies the expected coverage and income. The results indicate that agricultural areas are not optimally used, as it could be in the case if all three types of holdings were breeding more animals and thus achieve better economic results.

V doktorski disertaciji obravnavamo tematiko s področja rekonstruiranja obstoječih industrijskih procesov. Pri tem podrobneje predstavljamo predlagan koncept za rekonstrukcijo, ki zajema ključne aktivnosti za doseganje izboljšav nerentabilnih kemijskih procesov. Aktivnosti so zajete v predvidenih korakih, kot so spoznavanje procesa, matematično modeliranje, optimiranje, generiranje alternativ in ocena ustreznosti generiranih alternativ. Kompleksna infrastruktura, veliko število nemerljivih podatkov in alternative, ki jih je potrebno v naprej preučiti, so omejitve, ki zahtevajo kompleksen pristop k rekonstrukcijskemu načrtovanju. Obrati v preteklosti niso bili prilagojeni tipičnim rekonstrukcijskim zahtevam, ki bi omogočale večjo energijsko učinkovitost, zadovoljivo produktivnost in rentabilnost. Z ustreznimi modifikacijami se lahko bistveno izboljšajo omenjeni dejavniki in podaljša življenjska doba obstoječih kemijskih procesov. Pri tem imajo ustrezno razviti rekonstrukcijski načrti pomembno vlogo za doseganje konkurenčnosti ob upoštevanju negotovosti, trendov prihodnjih cen in zanimanj po tržnih produktih. Znotraj koncepta sta v prvem delu generiranja alternativ predlagana preprosti in kompleksni sklop tehnoloških izboljšav, ki temeljita na rekonstrukciji obstoječega procesa v smeri novih produktov. Drugi del generiranja alternativ zajema modifikacije v smeri surovinskih, produktnih in tehnoloških izboljšav. Za preprosti in kompleksni sklop izboljšav smo razvili matematične modele na podlagi simulacij kemijskih procesov in matematičnega programiranja za vsako izmed predlaganih alternativ posebej. Sintezni pristop je omogočal hkratno optimiranje procesnih parametrov in koriščenje morebitnih interakcij med procesnimi podsistemi, ki so na videz ločeni. Za surovinske, produktne in z njimi povezane tehnološke izboljšave smo razvili drevesno in mrežno superstrukturo z matematičnimi modeli, ki predstavljajo ustrezno orodje za simultano iskanje najprimernejše procesne alternative glede na optimizacijski kriterij. Razviti koncept za rekonstrukcijsko načrtovanje in prenovo obstoječih kemijskih procesov ter ustvarjene matematične modele smo aplicirali na realnem industrijskem procesu proizvodnje metanola. Rezultati kažejo, da je predlagani rekonstrukcijski koncept na podlagi matematičnih modelov privedel do izboljšav v primeru proizvodne novega produkta dimetil etra z neposredno potjo sinteze iz zemeljskega plina in višjo tržno ceno novega produkta. Prispevek raziskav lahko umestimo na področje rekonstrukcijskega načrtovanja v procesni sistemski tehniki. Načrtovanje zajema veliko količino podatkov na podlagi realnih kemijskih procesov, simulacij, hevrističnih pravil in spoznanj dobljenih tekom generiranja procesnih alternativ. Disertacija ne temelji na strateškem odločanju, temveč na razvoju orodij in tehnik za rekonstruiranje obstoječih procesov in procesnih linij v kemičnih in procesnih industrijah. This doctoral dissertation deals with the topic in the field of reconstruction of the existing industrial processes. It represents in details the proposed concept for the retrofit, which includes key activities for achieving improvements for non-profitable chemical processes. Activities are included within several steps, which are obtaining the knowledge about the process, mathematical modelling, optimization, generation of alternatives and the assessment of the appropriateness of generated alternatives. A complex infrastructure, a large number of non-measurable data and alternatives, which need to be studied in advance, are restrictions that require a complex approach to reconstruction. In the past, chemical plants were not adapted to typical reconstruction requirements that would lead to greater energy efficiency, satisfactory productivity and profitability. By suitable modifications these factors could be significantly improved and the lifetime of chemical processes could be prolonged. Taking into account uncertainty, future price trends and interests for commercial products, suitably developed reconstruction plans play an important role in achieving competitiveness. The first part of generating alternatives proposes simple and complex set of technological improvements. Both sets are based on reconstruction of the existing process so to produce the new products. The second part of generation of alternatives includes modifications in the direction of improvements in raw materials, products and technologies. For simple and complex set of improvements, mathematical models were developed on the basis of simulations of chemical processes and mathematical programming for each proposed alternative separately. Synthesis approach enables simultaneous optimization of process parameters and utilization of potential interactions between those process subsystems that seem to be separated. For improvements in raw materials, products and related technological improvements, a superstructure-based model was developed as a tool for simultaneously determining the most suitable alternative with regard to optimization criterion. The developed concept for reconstruction planning and retrofit of existing chemical processes, and developed mathematical model were applied to an industrial process of methanol production. The results show that the proposed concept of retrofit on the basis of mathematical models led to improvements in the case of production of a new product that has higher price in the market. The contribution of this research may be placed on the field of reconstruction planning in process system engineering. Planning includes a large amount of data on the basis of realistic chemical processes, simulations, heuristic rules and knowledge during generation of alternatives. This dissertation is not based on strategic decision-making, but on the development of tools and techniques for retrofitting of industrial processes.

V magistrskem delu smo analizirali in s supertrukturnim pristopom poiskali predloge za rekonstrukcijo omrežij toplotnih prenosnikov za posamezne obrate in več obratov oz. celotna območja ob upoštevanju spremenljivih obratovalnih pogojev. Za posamezne obrate in celotna območja smo z namenom znižanja porabe energije ob upoštevanju nedoločenih obratovalnih pogojev temperature, pretokov in sestav vhodnih surovin najprej s programom TransGen ugotavljali potencial za zmanjšanje energije. Nato smo s postopkom matematičnega programiranja s programom TransGen predlagali modifikacije za zmanjšano porabo energije v posameznih obratih in celotnih območjih. Z uporabo multiperiodnega modela smo za dane scenarije za modifikacije pridobili fleksibilne rešitve. Z metodo Monte Carlo smo za podatke ob spremenljivih obratovalnih pogojih procesov in celotnih območij procesov pridobili pričakovane in nominalne vrednosti spremenljivk in njihove frekvenčne in kumulativne porazdelitve. Na štirih primerih smo analizirali potencial zmanjšanja porabe pogonskih sredstev v odvisnosti od števila modifikacij in izračunali ekonomsko upravičenost. V vseh primerih smo ugotovili precejšen potencial za zmanjšanje energije: v prvem primeru 21 %, v drugem 17,4 %, v tretjem 75,9 % in v četrtem primeru 72,4 %. Poraba pogonskih sredstev se skoraj linearno zmanjšuje v odvisnosti od števila modifikacij, dobiček pa se s številom modifikacij povečuje. Doba vračanja je v vseh primerih manjša od enega leta: v prvem primeru znaša 2,4 mesece, v drugem 3 mesece, v tretjem 3,6 mesecev in v četrtem 7,8 mesecev. The aim of this Masters Dissertation is to analyse and identify possible modifications for retrofitting heat exchanger networks for both individual process plants and Total Sites, by considering flexible operating conditions using a super-structural approach. We first identified potentials for the reduction of energy consumption by considering uncertain operating conditions, such as temperatures, flow-rates, and compositions of raw materials. We then suggested retrofitting modifications for obtaining this reduction of energy consumption within individual process plants and Total Sites, by using mathematical programming approach and software tool TransGen. For different operating scenarios, modelled as multi-period formulation, we obtained flexible solutions regarding modifications. By using the Monte Carlo method, we obtained the expected and nominal values of the variables, their frequencies and cumulative distributions under the flexible operating conditions of individual process plants and Total Sites. We analysed the potential for utilities’ consumption reduction depending on the number of modifications regarding the four case studies, and for all the cases we calculated the economic viabilities. In all the cases we obtained considerable potential for energy consumption reductions - in the first case it was 21 %, in the second case 17.4 %, 75.9 % in the third case, and 72.4 % in the fourth case. The results indicated that with the number of modifications the consumptions of the utilities decreased and profit increased almost linearly. The payback periods in all the cases were less than a year - 2.4, 3.0, 3.6 and 7.8 months, respectively.

Namen diplomske naloge je ugotoviti morebitne prednosti hkratne toplotno integrirane proizvodnje biodizla in bioetanola. Preučevali smo proizvodnjo bioetanola z uplinjanjem koruzne slame in nadaljnjo fermentacijo sinteznega plina in pridelavo biodizla s homogeno bazično katalizo olja oljne repice brez predpriprave. Optimizacijo proizvodnje biodizla smo izvedli na podlagi vnaprej pripravljenih modelov s programskim paketom GAMS z manjšimi spremembami. Dobiček smo preučevali pri letni proizvodnji 20 000 ton in 40 000 ton biodizla pri različnih stopnjah toplotne integracije tako znotraj procesa kot tudi med procesoma. Proizvodnjo bioetanola smo optimizirali s programskim paketom MIPSYN pri 40 000 ton letno. Za analizo toplotne integracije smo uporabili program TransGen, s katerim smo preučili razlike v stroških pogonskih sredstev glede na stopnjo toplotne integracije s pesimistično oceno cen pogonskih sredstev. Končni rezultati so pokazali velike prihranke pri toplotno integriranih procesih v primerjavi s toplotno neintegriranimi procesi. V primeru procesa proizvodnje bioetanola je toplotna integracija znotraj samega procesa zmanjšala stroške pogonskih sredstev za 90 % in v primeru proizvodnje biodizla za 46 %. Toplotna integracija znotraj procesa je stroške še dodatno zmanjšala, vendar je bilo za preboj potrebno za doseganje dobičkonosnosti v proces vključiti cenejša pogonska sredstva. Rezultati so tudi pokazali, da je medprocesna toplotna integracija stroške pogonskih sredstev še dodatno zmanjšala, in sicer za majn kot 7 % pri kapaciteti proizvodnje biodizla 20 000 t/a, in za majn kot 8 % pri kapaciteti proizvodnje biodizla 40 000 t/a. Proizvodnja bioetanola je v obeh primerih potekala pri kapaciteti 40 000 t/a. The purpose of this study was to analyse the economic performances of biodiesel and bioethanol production processes whilst performing heat integration. Bioethanol was produced through gasification of maize stover and subsequent fermentation of the generated syngas into bioethanol. Biodiesel was produced using homogeneous alkaline catalysis from rapeseed oil without pre-treatment. Optimisation of the biodiesel production was carried out using previously formulated models with minor changes by using the ‘GAMS’ software package. Profits were studied for biodiesel production at capacity of 20 000 t/y and 40 000 t/y at different stages of integration, between processes and within each process itself. Production of biodiesel was optimised using the software package ‘MIPSYN’ by fixed production at 40 000 t/y. The software tool ‘TransGen’ was used for heat integration. We then studied the differences in utility costs according to the degree of heat integration, utilising a pessimistic assessment of utility prices. The final results showed significant savings when integrating the processes versus non-heat integrated processes. In the case of bioethanol production, the utility cost was reduced by 90 %, and in the case of biodiesel production by 46 %. Heat integration within the process reduced utility cost significantly, however for the processes to be profitable, it was necessary to include cheaper utilities besides high pressure steam and cooling water. The results have also demonstrated that when heat integration was performed between the processes, rather than merely within the individual processes, the cost of utilities was additionally reduced. The reduction amounted to less than 7 % for biodiesel production with a capacity of 20 000 t/y, and less than 8 % for biodiesel production with capacity of 40 000 t/y. The capacity of ethanol production was 40 000 t/y, in both cases.

Glavni cilj magistrskega dela je določitev optimalne strukture kolobarja pod določenimi pogoji za modelno zelenjadarsko kmetijo. V ta namen so bila razvita 3 glavna podporna orodja, ki obsegajo naslednje delovne faze: 1. faza obsega razvoj tehnološko-ekonomsko simulacijskega modela 'Pr.KALK', s katerim se tehnološki podatki o posamezni pridelavi prenesejo v numerološko obliko, ki definira upravičenost pridelave. Izbrani podatki posamezne pridelave so nato preneseni v 2. fazo, za katero je zgrajen model 'Pr.OPTI'. Ta je namenjendoločitvi optimalne strukture kolobarja. Sestava kolobarja se nato prenese v 3. fazo, kjer s pomočjo orodja 'Pr.GANTT' na pregleden način upravljamo s planiranjem proizvodnje na kmetiji. V raziskavi sta predpostavljena 2 scenarija, po katerih se določa omejitev stroškov ročnega in strojnega dela ter strošek gnojenja. V prvem scenariju se omejitve postavijo 'ročno'. V drugem scenariju pa so omejitve določene s pomočjo metode linearnega programiranja, kjer so stroški predmet minimiranja in nato preneseni v model tehtanega ciljnega programiranja, nadgrajenega s kazensko funkcijo kot omejitvijo. Primerjava obeh postopkov nam kaže, da dobljeni rezultati s pomočjo metodologije po 2. scenariju v treh primerih od štirih generiranih v primerjavi s 1. scenarijem dosegajo višji finančni rezultat, kateri je opredeljen kot glavni cilj v modelnem orodju. Gantogramska tehnika je vpeljana v metodologijo načrtovanja kolobarja, kjer na pregleden način prikažemo tako celotni kolobar, kakor tudi časovne dogodke. The main goal of the master's thesis is to determine an optimal cropping plan for a model vegetable farm. For this purpose,three main support tools were developedincluding the following operations: the first stage is the development of a technological and economic simulation model 'Pr.KALK' with which individual pieces of technological data relating to the individual production are transferred into the numerological form, thus justifying the production. The selected pieces of data of each production are then transferred to the second phase for which the model 'Pr.OPTI' was developed with a view to determining an optimal cropping plan. The structure of the cropping plan is transferred to the third phase of the thesis where, with the assistance of the 'Pr.GANTT' model, we transparently manage the planning of the production on the farm. The researchpresents two possible scenarios to limit the costs of manual and mechanical labor and fertilizer costs. In the first scenario, the limit is set 'by hand'. In the second scenario, however, the limits are determined by the method of linear programming, where the costs are subject to minimization, and then transferred to the weighted goal programming model with penalty function as a restriction. The comparison of the two procedures shows that the results obtained using the methodology from the second scenario in three out of four generated cases compared to thefirst scenario achieve a higher financial result, which has been defined as the main goal. Gantogramic technique is introduced into themethodology of the designing process of the cropping plan where the whole cropping plans as well as temporal events are shownin a transparent way.

Economically viable process designs should be, in addition to other criteria, profitable over their entire process lifetimes not only at the present time. An improved process design can be achieved by establishing an appropriate trade-off between product income, raw material, operating costs, and investment. The full lifetime of the processes and future prices have to be considered rather than optimising them on a yearly basis using current prices. Single-period optimisation and synthesis models for processes reflects current prices only. The prices can fluctuate rather quickly and the optimal solution may be very different from one year to the another. Therefore, the traditional superstructural synthesis approach applying a mixed-integer nonlinear programming model was upgraded: i) over time, by considering an entire lifetime, which can be described by a multi-period model and ii) the whole field of variation regarding uncertain future prices. A stochastic approach considering the statistical distribution of price projections over an entire lifetime was used on different case studies instead of the traditional deterministic approach accounting for nominal future price projection. The objective was the maximisation of the expected net present value of a process or the expected incremental net present value of different process subsystem. The heat exchanger network has been one of the subsystem, which can significantly contribute to operating costs due to savings of external utility consumption. For this subsystem a deterministic and stochastic multi-period mixed-integer nonlinear programming (MINLP) synthesis models have been developed in order to account for future price projections. Considering higher energy prices gives rise to larger initial investments compared to solutions obtained with current prices. However, due to the uncertainties of utility prices' forecasts, retrofitting using an extension of HEN during future years of the lifespan might be a better strategy. The objective is to identify a design that is the most suitable for effective future extensions and preferably with the lowest sensitivity to energy price fluctuations, as there can be various designs featuring similar initial investment. The results supports that it is economically beneficial to consider future utility prices as the incremental investment is not only paid-off but additional savings are achieved. Process-to-process Heat Integration can also significantly affect the trade-off between investment and operating cost. The aim of Total Site (TS) HEN synthesis was to develop a model synthesis for the TS that, besides many other important features, would also consider future utility prices. Two strategies for TS synthesis have been developed: i) sequential, when HI is performed within a process during the first step and then after a process-to-process HI has been performed, and ii) simultaneous, where the HI is performed within and between processes simultaneously. The second strategy can reveal additional opportunities for heat recovery that might not be identified when applying the first strategy. Comparison of the results obtained at consideration of current utility prices and forecasted utility prices indicates that is worth to account for future utility prices. The separation processes also consume a significant amount of energy. The synthesis of a distillation column sequence integrated within its heat exchanger network was used as a case study for the separation of a multi-component stream into pure component products by considering future utility prices. This analysis has been performed in order to evaluate the magnitude of the influence of forecasted utility prices. It can be concluded that forecasted utility prices can be beneficial, however, the technical limits of the systems should be carefully observed. The price fluctuation can also be observed for other prices not only utility prices, e.g. raw material cost, product price, etc Ekonomično upravičeni načrti morajo biti, poleg ostalih kriterijev, tudi dobičkonosni skozi celotno življenjsko dobo procesa, ne samo v sedanjem času. Z vzpostavitvijo primernega trženja med prihodki produkta, stroški surovin, obratovalnimi stroški in investicijo v celotni življenski dobi lahko dosegamo izboljšan načrt procesa. Zato je optimizacija za celotno življenjsko dobo procesa z upoštevanjem napovedanih cen primernejša od optimizacije na letni osnovi. Enoperiodno optimiranje in sinteza za procese odraža le sedanje cene. Optimalna rešitev, dosežena za eno leto, se lahko znatno razlikuje od rešitve za drugo leto, saj se cene spreminjajo precej hitro. Običajni superstrukturni sintezni pristop z uporabo mešano-celoštevilskega nelinearnega programiranja smo zato nadgradili 1) z upoštevanjem celotne življenjske dobe, kar lahko opišemo z večperiodnim modelom in 2) z območjem spreminjanja negotovih prihodnjih cen. Namesto običajnega determinističnega pristopa pri nominalnih projekcijah prihodnjih cen smo uporabili stohastični pristop z upoštevanjem statistične porazdelitve napovedovanja cen za celotno življenjsko dobo. Namen je bil maksimiranje pričakovane neto sedanje vrednosti procesa oz. pričakovane inkrementalne neto sedanje vrednosti izboljšave različnih procesnih podsistemov. Podsistem, ki znatno prispeva k obratovalnim stroškom zaradi prihrankov pri porabi zunanjih pogonskih sredstev, je omrežje toplotnih prenosnikov. Za sintezo tega podsistema smo razvili tako deterministični kot stohastični večperiodni celoštevilski nelinearni programirni (MINLP) model ob upoštevanju prihodnjih cenovnih projekcij. Z upoštevanjem višjih cen energentov se povečajo začetne investicije v primerjavi z rešitvami, ki jim dosežemo pri sedanjih cenah. Zaradi negotovosti napovedovanja cen se je smiselno povečanju začetne investicije izogniti z načrtovanjem možnosti razširitve omrežja toplotnih prenosnikov v kasnejšem obdobju. Namen je doseči načrt, ki je kar najbolj primeren za učinkovito razširitev v prihodnosti, po možnosti z najmanjšo občutljivostjo na spreminjanje cen. Toplotna integracija med različnimi procesi lahko tudi znatno vpliva na trženje med investicijo in obratovalnimi stroški. Tako je bil eden od ciljev sinteze omrežja toplotnih prenosnikov prav upoštevanje prihodnjih cen pogonskih sredstev. Razvili smo dve strategiji za sintezo celotnega območja (ang. Total Site), in sicer: i) zaporedno, pri kateri toplotno integracijo izvajamo najprej na nivoju procesa in potem na nivoju celotnega območja, in ii) sočasno, pri kateri izvajamo toplotno integracijo na nivoju procesa in na nivoju celotnega območja hkrati. Slednja strategija omogoča dodatne možnosti prihranka toplote, kar potrjuje primerjava rezultatov doseženih pri sedanjih in prihodnjih cenah pogonskih sredstev. Separacijski procesi so lahko veliki porabniki energije. Sintezo zaporedja destilacijskih kolon integriranih z lastnim omrežjem toplotnih prenosnikov smo uporabili kot študijski primer za ločevanje večkomponentnega toka v čiste produkte. Analizo smo izvedli tudi z namenom določitve obsega vpliva napovedanih prihodnjih cen pogonskih sredstev. Zaključimo lahko, da z upoštevanjem napovedanih cen lahko dosegamo ekonomsko učinkovitejše procese ali procesne podsisteme, vendar je pri tem potrebno skrbno upoštevati tehnološke omejitve študiranega sistema. Nihanje cen razen pri pogonskih lahko opazimo tudi pri drugih cenah, npr. pri cenah surovin, in produktov. Pričakujemo lahko, da trženje v postopku optimiranja poskuša kompenzirati ta nihanja cen, npr. višje cene pogonskih sredstev bodo izravnane s povečanjem investicije, s čemer se zmanjšajo prihodnji obratovalni stroški. Vendar, ko upoštevamo vse stroške in prihodke hkrati, so lahko trendi vplivov različni od posameznega vpliva le teh, kar smo pokazali tudi s študijskim primerom.

U radu se razmatra utjecaj zračnosti u spojevima na reakcijske sile spoja u mehanizmima. Pomoću matematičkog programiranja, uspješno se mogu dobiti optimalni parametri kinematičkih lanaca primjenom determinističkog pristupa. Međutim, situacija postaje složenija ako se moraju uzeti u obzir slučajni učinci tolerancije dužine poluge (kraka) i slučajni položaji svornjaka. U ovom se radu utjecaj zračnosti na spojne sile izračunao pomoću Taylor aproksimacije i Monte Carlo metode. Implementacija modela ilustrirana je na dva primjera. Prvi primjer razmatra lanac zatvorene petlje, predstavljajući mehanizam s četiri šipke kao sastavnog dijela hidrauličkog nosača, korištenog u rudarstvu. Drugi primjer razmatra reaktivne sile spoja u mehanizmu automobilskog brisača., This paper discusses the influence of the clearance in joints on the joint reaction forces in mechanisms. By using mathematical programming, the optimal parameters of kinematic chains can be efficiently obtained by using the deterministic approach. However, the situation becomes more sophisticated if random effects of tolerances of the arm lengths and the random pin positions have to be considered. In this work the influence of clearances on joint forces is calculated by using the Taylor approximation and the Monte Carlo method. The implementation of the model is illustrated with two examples. The first example considers a closed loop chain, representing a four-bar mechanism being an actual part of a hydraulic support, employed in mining industry. The second example considers joint reaction forces of car wiper mechanism.

V članku je definirana količina, ki meri kvaliteto aproksimacije tabelarično podane funkcije družine D nekonstantnih funkcij. V ta namen je treba poiskati infimum in supremum množice korelacijskih koeficientov med dano funkcijo in funkcijami iz D. Tu je to storjeno za družino vseh nekonstantnih funkcij in za družino rastnih funkcij. In the article we define a quantity which measures the quality of the approximation of a function, given by a table, with a function from a certain family D of nonconstant functions. For this purpose one has to find the infimum and the supremum of the set of correlation coefficients between the given function and functions from D.We do this for the family of all nonconstant functions and for the family of growth functions.

Namen diplomskega dela je eksperimentalna preiskava vpliva mešalnega časa, mešalne hitrosti in koncentracije površinsko aktivne snovi na porazdelitev velikosti kapljic ter uporabnost modela PBE (populacijski bilančni model), ki smo ga preizkusili za omenjene spremembe v procesu priprave koncentriranih emulzij. Preiskovali smo koncentrirane emulzije, kjer je vodna faza vodna raztopina kalcijevega klorida in organska faza mešanica stirena in divinilbenzena. Sorbitol oleat smo uporabljali kot stabilizator koncentriranih emulzij. Eksperimentalne meritve porazdelitve velikosti kapljic smo izvedli s pomočjo optičnega mikroskopa. Model PBE smo reševali z uporabo programske opreme GAMS/CONOPT. Uporaba modela PBE zahteva eksperimentalno določevanje modelnih parametrov s pomočjo meritev za osnovni sistem. Zbrane eksperimentalne podatke za druge sisteme smo primerjali z rešitvami modela PBE. Postopek reševanja je bil poenostavljen in poenostavitve smo kvantitativno ovrednotili. Ugotovili smo, da se učinkovitost modela PBE veča, če se razlika med obravnavanim sistemom in osnovnim sistemom manjša. Pokazali smo, da uporaba modela PBE omogoča zaznavanje napak v eksperimentalni proceduri. Rezultati eksperimentalnih meritev kažejo, da se tekom procesa priprave koncentriranih emulzij ne vzpostavi stacionarno stanje niti po 20 urah mešanja. Aim of the investigation was the experimental determination of influences regarding the stirring time, the stirring rate of rotation, and the concentration of surface active material on the drop size distributions of concentrated emulsions, as well as testing the applicability of the PBE (population balance equation) model for predicting various drop size distributions. Concentrated emulsions were prepared from an aqueous phase, which was a water solution of calcium chloride, and from an organic phase containing styrene and divinylbenzene. Sorbitol oleate was used as a system stabilization agent. Experimental determination of drop size distributions was performed using an optical microscope. The PBE model was solved using GAMS/CONOPT. Determination of model parameters was performed using the experimental results for a base case system. Experimentally determined drop size distributions for other systems were compared with the predicted ones, those representing the solutions of the PBE model. The solution procedure was simplified and the simplifications quantitatively evaluated. It was shown that the applicability of the PBE model was higher if the difference between the studied and base case system was lower. Furthermore, the use of the PBE model allows determining any gross errors of the experimental results. Finally, it could be stated that steady state is not achieved during the preparation of concentrated emulsions, even after 20 hours of mixing.

V doktorski disertaciji predstavljamo študijo določitve stroškovno optimalnih obratovalnih pogojev za razbarvanje in čiščenje vodne raztopine barvila C. I. Reactive Blue 268 z naprednimi procesi čiščenja. Najprej predstavljamo rezultate laboratorijskih eksperimentov in matematične modele procesov UV/H2O2 in Fe2+/H2O2. Rezultati kažejo, da lahko z uporabo metodologije odzivnih površin razvijemo ustrezna matematična modela, ki statistično zadostno opišeta odvisnost merjenih odzivov od izbranih (vplivnih) obratovalnih parametrov. Nato prikazujemo študijo optimiranja energijsko intenzivnega procesa UV/H2O2. Kot vplivne parametre smo upoštevali koncentracijo barvila, koncentracijo vodikovega peroksida, pH, čas obdelave in temperaturo. Stroške elektrike, stroške vodikovega peroksida in stroške vode za uravnavanje koncentracije barvila smo upoštevali kot relevantne obratovalne stroške. Čeprav so minimalni stroški čiščenja ocenjeni na visokih 17 €/m3, dobljeni rezultati jasno kažejo, da moramo, če želimo zagotoviti obratovalno in ekonomsko učinkovitost, proces optimirati z obeh vidikov hkrati. Ekonomsko učinkovitost lahko dodatno izboljšamo z integracijo naprednih procesov čiščenja. Kot alternative v integriranem sistemu smo upoštevali proces UV/H2O2, proces Fe2+/H2O2 in membransko filtracijo. Procesno shemo integriranega procesa in vrednosti obratovalnih parametrov, pri katerih sistem obratuje pri minimalnih stroških, smo določili s pristopom, ki temelji na matematičnem programiranju. Iz rezultatov je razvidno, da lahko z ustrezno integracijo izbranih procesov znatno znižamo povprečne stroške čiščenja. V primerjavi s procesom UV/H2O2 so ocenjeni povprečni stroški čiščenja integriranega proces približno 75 % nižji (2,4 €/m3). Many processes have been proposed as an effective treatment technology for remediation of colored wastewaters. However, it has frequently been noted that some of them are economically unacceptable due to high operating cost. This thesis provides studies on approaches to determine cost-effective decoloration and mineralization of C. I. Reactive Blue 268 using advanced treatment technologies. First, the results of laboratory experiments and mathematical models of UV/H2O2 and Fe2+/H2O2 processes are presented. The results indicate that the processes can be modeled in a sufficient way by using the response surface methodology. Second, a study on optimization of an energy intensive UV/H2O2 process is presented. Dye concentration, hydrogen peroxide concentration, pH, treatment time, and temperature were considered to be influential operating parameters. Cost of electricity, cost of hydrogen peroxide, and cost of water needed to adjust the dye concentration were considered to be relevant operating costs. Although the minimal treatment cost were estimated to 17 €/m3, the results obtained clearly indicate that, in order to assure effective and economically efficient operation any given process should be simultaneously optimized from the perspective of both operational and economic efficiency. The latter can, however, be improved further by integration of advanced treatment technologies. UV/H2O2, Fe2+/H2O2 and membrane filtration were considered as alternatives for the integrated system. The integrated process flow sheet and values of operating parameters yielding minimal operating cost were determined. The results indicate that for the system studied significant reduction in average treatment cost can be achieved by proper integration of the denoted alternatives. Compared to the treatment cost of UV/H2O2, the estimated average treatment cost of an integrated system is approximately 75 % lower (2,4 €/m3).

This thesis presents two different approaches to the synthesis of regional networks for biomass and biofuel production and supply: Mathematical Programming and Graph Theoretic approach. The optimisation criterion for both approaches is the maximisation of profit. The first approach is based on a generic optimisation model of biomass production and supply networks. This superstructure approach is based on a flexible number of network layers: plantation, collection using a pre-treatment, process, and consumption. A Mixed Integer Linear Programming (MILP) model has been successfully developed during this work. However, the solution of this biomass production network model is very challenging due to the large sizes of the networks and the number of interconnections. The huge number of redundant variables reduces model efficiency (time taken to solve the model and the interpretation of the results). This model when representing very large size networks cannot be solved over a reasonable time even by professional mathematical programming software tools. Several model-size reduction techniques are therefore proposed for the solution of large-scale networks. In particular, methods are proposed for (i) reducing the connectivity within a biomass supply chain network by setting the maximum allowable distance between the supply zones to the collection centres, (ii) eliminating unnecessary variables and constrains to reduce the zero-flows in the full model, and (iii) aggregating the network and hence the synthesis process by merging the collection centres. The network synthesis is also carried out by P-graph (Process Graph) tools. P-graph is a directed bipartite graph, having two types of vertices — one for operating units and another for those objects representing material or energy flows/quantities. In this procedure, firstly a maximum feasible superstructure for biomass production network is generated from which the optimal structure is then selected by the Branch and Bound method. This graph-based method clearly shows where, how, and what kind of material and energy carriers will be transferred from one supply chain layer to another. In order to test the efficiency of the model, a small regional renewable network problem was solved using both methods. Their performances were tested and the results confirmed the applicability on a regional scale. The proposed model-size reduction techniques were also tested. A large-scale regional case study was created to demonstrate these techniques. The results are very positive and some suggestions for future work are given in the conclusion. V doktorski disertaciji predstavljamo dva različna pristopa k sintezi regionalnih omrežij za proizvodnjo in dobavo biomase in biogoriv: matematično programiranje in pristop, ki temelji na teoriji grafov. Uporabljen kriterij optimiranja pri uporabi obeh pristopov je maksimiranje dobička. Prvi, superstrukturni pristop temelji na splošnem optimizacijskem modelu omrežja za proizvodnjo in dobavo biomase in biogoriv. Pri tem superstrukturo sestavljajo štiri ravni dobavne verige: nivo proizvodnje obnovljivih surovin, nivo zbiranja s pred-obdelavo, nivo proizvodnje in nivo povpraševanja. S to raziskavo smo uspešno razvili mešano celoštevilski linearni programirni (MILP) model. Vendar pa predstavlja reševanje tega modela zaradi obsežnosti regionalnih omrežij z velikim številom povezav precejšen izziv. Veliko število odvečnih spremenljivk zmanjšuje učinkovitost reševanja (čas reševanja in razlago rezultatov). Obsežnih regionalnih omrežij tako pogosto ni mogoče rešiti v realnem času, četudi pri tem uporabljamo profesionalna matematično programirna računalniška orodja. Zato predlagamo nekatere tehnike za zmanjševanje velikosti mrežnih modelov. Predlagane tehnike so namenjene predvsem i) zmanjševanju števila povezav v omrežju z definiranjem največje dovoljene razdalje med dobavnimi conami in zbirnimi centri, ii) odpravi nepotrebnih ničelnih spremenljivk in pogojev in iii) zmanjšanju razvejanosti omrežja in s tem zmanjšanju sinteznega problema z združitvijo zbirnih centrov v manjše število centrov. Sintezo omrežja smo izvedli tudi z uporabo orodja P-graf ('procesni graf'). P-graf je usmerjeni dvopartitni graf z dvema vrstama oglišč – ena so za procesne enote in druga za objekte, ki predstavljajo snovne ali energijske tokove oz. količine. V tem postopku se za omrežje proizvodnje in porabe biomase najprej generira maksimalna dopustna superstruktura, nakar se z metodo vejanja in omejevanja (Branch-and-Bound) izbere optimalna struktura. Pri tej metodi grafov je jasno razvidno, kako in kateri snovni in energijski nosilci se prenašajo iz enega na drugi nivo dobavne verige. Z namenom preizkušanja učinkovitosti modela smo najprej za regionalno omrežje rešili računsko manj zahteven problem in pri tem uporabili obe metodi ter preizkusili njuni zmogljivosti. Dobljeni rezultati potrjujejo uporabnost obeh metod za reševanje problemov na regionalni ravni. Preizkusili smo tudi učinkovitost predlaganih tehnik za zmanjšanje obsežnosti modela in za ta namen razvili obsežnejši primer. Dobljeni rezultati so zelo obetavni. V zaključkih dodajamo tudi nekaj predlogov za nadaljnje delo.

V tem diplomskem delu je predstavljena osnovna teorija matematičnih programov. V začetnem delu so zajeti predvsem pojmi in izreki v povezavi s konveksnimi in konkavnimi funkcijami na konveksni množici, ki vodijo do pomembnih ugotovitev, povezanih z lokalnimi in globalnimi ekstremi. Ti izreki so pomembni v matematičnem programiranju, saj nam ob določenih posebnih predpostavkah, kot sta konveksnost in linearnost, omogočajo preprostejše načine iskanja optimalne rešitve danega programa. Kot pomemben primer matematičnega programiranja je predstavljen linearen program in njegov dual. Opisan je postopek pretvorbe linearnega programa v dualni program in izrek o dualnosti, ki pravi, da imata primarni in dualni program enaki optimalni vrednosti kriterijske funkcije, če optimalna rešitev obstaja. Prav tako je opisana ekonomska vloga dualnih spremenljivk in z njimi povezane senčne cene. Predstavljeni so Kuhn-Tuckerjevi pogoji za optimalnost rešitve matematičnega programa, ki so potrebni pogoji za lokalni ekstrem in pri posebnih predpostavkah zadostni pogoji za globalni ekstrem. V drugem delu sledi kratka predstavitev trga električne energije in njegovih udeležencev. Predstavljeni so modeli proizvajalcev, odjemalcev, trgovcev in borza električne energije. Pomembni vprašanji, s katerima se proizvajalci, odjemalci in trgovci soočajo, sta, koliko energije kupiti (prodati) preko dvostranskih pogodb in koliko preko borze električne energije. Običajno se za daljše obdobje udeleženci odločijo za dvostranske pogodbe, ki zagotavljajo zadostno količino električne energije po nespremenjenih cenah, kar pa nujno ne prinaša maksimalnega dobička. V primerih povečanega povpraševanja oz. padca cen električne energije, pa se zatekajo k nakupu na organiziranem trgu. Opisani so matematični programi, ki maksimirajo dobiček posameznih udeležencev, glede na dane omejitve. In this diploma thesis, we present a theoretical basis of mathematical programming. At the beginning, we describe notation and theorems related to convex and concave functions on convex sets, which is the basis of important results about local and global extremes. These theorems are important in mathematical programming, because they allow for more efficient methods of finding the optimal solution of a mathematical program, under suitable convexity and linearity assumptions. Next, we present an important basic case of mathematical programming that is linear program and its dual program, including a procedure of how to find the dual of normal linear program and the dual theorem, which says if the optimal value exists, it’s the same for both the primal and the dual program. We also present the economical interpretation of the dual variables as shadow prices. At the end of the theoretical part, we describe the Kuhn-Tucker conditions. These are the necessary conditions for local optimality for a mathematical program. Under suitable restrictions, they are also sufficient conditions for global optimality. In the second part of this diploma thesis, we continue with a short presentation of electricity markets and their participants. We describe the viewpoints of the main participants including producers, consumers, energy service companies, and a pool operator. A decision problem that we investigate is how much energy to buy (sell) with bilateral contracts and how much energy to buy from or sell in the power pool. It turns out that participants decide on bilateral contracts in longer terms, because of their reliability and fixed price in advance, but this does not necessarly give the maximal profit. In case of lower prices in the power pool and increased demand for electrical energy, the participants decide to buy energy from or sell it in the pool. According to this, we describe mathematical programs that maximize profits for all participants under certain constraints.