De senaste åren har en större mängd decentraliserad och variabel energiproduktion tagit plats inom elsystemet, mer specifikt vindkraft och solkraft, och etablering av mer distribuerad produktion kommer att fortsätta i enlighet med mål från nationer och världsorganisationer att fasa ut fossila bränslen och minska på växthusgasutsläpp. I takt med nedläggning av storskaliga kraftverk baserade på fossila bränslen påverkar detta möjligheterna att möta upp elbehovet med den tillgängliga produktionen. Mycket variabel produktion har samtidigt en negativ påverkan på elnätstabiliteten och kan skapa höga effekttoppar. Detta har skapat ett ökat behov av mer flexibilitet på kundsidan för att skapa balans på elnätet. Elektrokemiska batterilager kan lösa många av problemen som uppstår med intermittent förnybar energiproduktion. Batterilager har både utvecklats teknologiskt och minskats i pris avsevärt de senaste tio åren och kostnaderna kommer fortsätta att gå ned. För att batterilager på allvar ska bli intressant behöver aktörer som investerar i denna teknologi veta om det någon gång inom en snar framtid kommer att vara en positiv affär. Syftet med detta arbete har därför varit att undersöka lönsamheten med batterilager i kommersiella fastigheter idag och inom de närmsta 10 åren på den svenska marknaden. Studien har, med hjälp av blandad heltalsprogrammering (MILP) i MATLAB, tagit fram en modell som optimalt schemalägger energiflöden för en fastighet som har ett batterisystem och egen produktion installerat baserat på olika prisbilder. Modellen har i sin tur använts för att beräkna de ekonomiska möjligheterna som erbjuds på Sveriges elmarknad med ett batterisystem i en mängd olika scenarier både vad gäller pris på el, olika effektabonnemang, integration med solpaneler, olika batteristorlekar och systemlivslängd. Resultatet visar att det inte finns någon lönsamhet i att investera i batterier för de undersökta fastigheterna så som Sveriges elmarknad ser ut idag och någon hög lönsamhet kommer inte att ske även om pristrenden på batterier fortsätter nedåt. Ett mindre batterisystem på 28 kWh kan ge, beräknat med internräntan, en positiv avkastning på 1 % år 2020 men ju större batteriet är desto mindre blir avkastningen. Högst avkastningen som kan fås med dagens el- och nätpriser är 4-5 % om en investering görs med 2025-2030 års batteripriser. Om elnätsägarna går mot att endast erbjuda tidsdifferentierade nättariffer året om och det implementeras högre effektavgifter finns det möjligheter att avkastningen kan bli så hög som 15-18 % med 2025-2030 års batteripriser. Arbetet visar också att kapandet av effekttoppar med större batterilager än 28 kWh inte är kostnadseffektivt för de undersökta fastigheterna. / The world has seen a rapid deployment of distributed and time-varying renewable energy systems (RES) within the electricity grids for the past 20 years, especially from wind and solar power. The deployment RES is expected to increase even more as world organizations and nations will continue the phase-out of fossil fuels as the main source of energy for electricity production. As large scale power plants reliant on fossil fuels will shut down it will be harder for the system to balance production and demand. At the same time, time-varying production might have a negative effect on the grid stability which has spurred an increased interest in flexibility on the demand side and a call for technologies and strategies that can create balance on the grid. Energy storage, especially electrochemical battery storage, is seen as a part of a bigger solution to the problems that comes with intermittent energy production. Battery storage has had a fast technological development and a sharp downtrend in pricing the latest ten years and the costs are expected to keep on decreasing. For battery storage to be a serious contender on the electricity market there is a need to understand if and when an investment in this technology might give a positive outcome. The aim of this study has therefore been to analyse the profitability of battery storage within commercial real estate today, and in the oncoming 10-15 years on the Swedish electricity market. The study has, using mixed integer linear programming (MILP) within MATLAB, created a model which optimally schedules power flows for buildings that has a battery system and its own electricity production. The model has in turn been used to evaluate the economical possibilities that exist with a battery system within commercial real estate under various different scenarios that looks into pricing structures on electricity and demand, integration with and without solar panels, different battery sizes and system lifetimes. The results show that there is currently no profitability to invest in a battery system for the specific buildings analysed in this study. While break-even is possible just a couple of years from now, a high profitability will not be reached even with the future downtrend in battery prices under the current electricity market circumstances. A smaller battery system with a capacity of 28 kWh could give an internal rate of return (IRR) of 1 % year 2020. Larger battery systems are generally not cost-effective when compared to smaller battery systems when its primary purpose is utilized for demand reduction. Highest return with today’s electricity and utility pricing is 4-5 % somewhere between 2025 and 2030. However, if the market goes towards exclusively time-of-use billing structures on electricity and higher demand charges, the IRR can reach towards 15-18 % between 2025 and 2030.

[pt] As doenças vasculares são enfermidades graves e seus tratamentos são complexos e necessitam de procedimentos cirúrgicos. Para a realização desses procedimentos, são necessários equipamentos, equipes qualificadas e unidade de terapia intensiva (UTI) equipada para o pós-operatório. Hospitais de ensino devem atender à legislação vigente que preconiza um número mínimo de cirurgias para aprovação do residente no programa de formação. Assim, propõe-se, via otimização, encontrar soluções eficientes para o planejamento e programação de cirurgias eletivas que atendam à legislação. Este problema é tratado em 2 níveis. O primeiro é relativo ao planejamento e é chamado de Master Surgical Schedule (MSS) que consiste em definir os recursos necessários para a realização de um conjunto de procedimentos. O segundo se refere à programação e é chamado de Surgical Case Assigment Problem (SCAP) e tem por objetivo alocar o médico a cada cirurgia. Assim, foram propostos dois modelos de programação matemática, um para o MSS e outro para o SCAP. Estes modelos foram aplicados no caso real da alocação de residentes para cirurgias vasculares no Hospital Universitário Pedro Ernesto. Como resultado do modelo MSS, identificou-se a necessidade de mais anestesistas e maior disponibilidade de equipamentos para atender à legislação de formação de residentes. Por fim, como resultado do SCAP, o quantitativo de cirurgias foi distribuído entre os cirurgiões de forma balanceada. / [en] Vascular diseases are serious diseases and their treatments are complex and require surgical procedures. In order to perform these procedures, is required equipment, qualified teams and an intensive care unit (ICU) equipped for the postoperative period. Teaching hospitals must comply with current legislation that recommend a minimum number of surgeries for the resident s approval in the training program. Thus, it is proposed, through optimization, to find efficient solutions for the planning and programming of elective surgeries that comply with the legislation. This problem is dealt with on two levels. The first is relative to planning and is called the Master Surgical Schedule (MSS), which consists of defining the necessary resources to perform a set of procedures. The second one refers to programming and is called Surgical Case Assigment Problem (SCAP) and aims to allocate the doctor to each surgery. Thus, two models of mathematical programming were proposed, one for MSS and another for SCAP. These models were applied in the real case of residents allocation for vascular surgeries at Pedro Ernesto University Hospital. As a result of MSS model were identified the need for more anesthesiologists and greater availability of equipment ensure the cover of resident training legislation. Finally, as a result of SCAP, the quantity of surgeries was distributed equitably distributed among surgeons.

This diploma thesis deals with optimization models with design of a new waste management infrastructure in the Czech Republic, such that combustible waste, which is not utilized by the material recovering, can be used by energy recovering. This task is handled by optimization models, including trac and mixing problems. First of all, the concepts of graph theory and optimization are presented in this paper. Subsequently, some of the GAMS functions are discussed, and later the VBA programming language used to handle the larger data quickly is presented. In the main part, three gradually expanding models are developed. At the end the data from the waste management information system are implemented into them.

No description available.

The development of sustainable business models is a challenging task since various factors might influence the results of an assessment. Given the complexity at the municipal level, system interdependencies between different alternatives need to be considered. One possibility to support decision makers is to apply energy system optimization models. Existing optimization models, however, ignore the roles different actors play and the resulting impact they have. To address this research issue, this thesis presents an integrated techno-economic optimization framework called IRPopt (Integrated Resource Planning and Optimization). A proven graph-based energy system approach allows the accurate modeling of deployment systems by considering different energy carriers and technical processes. In addition, a graph-based commercial association approach enables the integration of actor-oriented coordination. This is achieved by the explicit modeling of market actors on one layer and technology processes on another layer as well as resource flow interrelations and commercial agreements mechanism among and between the different layers. Using the optimization framework, various optimization problems are solvable on the basis of a generic objective function. For demonstration purposes, this thesis assesses the business models demand response and community storage. The applied examples demonstrate the modeling capabilities of the developed optimization framework. Further, the dispatch results show the usefulness of the described optimization approach.

In the aftermath of the liberalization of European Energy Markets in the 2000s, Power Exchange platforms have constantly evolved towards more integrated and competitive designs, where quality forecasts and effective optimization strategies play decisive roles. This study presents the development of a hydropower scheduling optimization algorithm for the Day-Ahead spot market using Mixed Integer Linear Programming (MILP). This work was supported by the hydro asset management team of ENGIE Global Energy Markets (GEM) located in Brussels.  The model developed is focusing on the optimization of Coindre Hydraulic Power Plant (HPP), located in the highlands of Massif Central in France. With the combined water discharge of its two interconnected reservoirs, Grande-Rhue and Petite-Rhue, the powerhouse can reach up to 36 MW of power output capacity. The two reservoirs are located kilometres apart from each other and have different storage capacities and catchment areas. The reservoirs naturally exchange water due to the level difference along an interconnection pipe. Maximum power output is limited by water level differences in both reservoirs, which makes modelling complicated. These operational constraints are a limiting factor in terms of operability, as a result the scheduling process is a non-trivial task and is time-consuming.  A framing study of the power plant was conducted over a hydraulic year to identify the governing parameters of the model. The multi-reservoir nature of the optimization problem oriented the model development towards a Mixed Integer Linear Formulation. After experimenting with different solvers, Gurobi 28.1.0 was chosen for its performance in the Branch and Cut Algorithm for the power scheduling task.  The performance of the new model has been validated by re-running the model on past production plans, results show that reservoir volume errors are less than 5% of their respective capacities on a 5 days’ time-horizon. After backtesting it was found that the new optimization strategy results in higher revenue for the plant due to the optimized operation at higher average energy prices. The results also bring out the importance of proper valve actuation in the optimization strategy, as well as the need for future studies. / Till följd av liberaliseringen av de europeiska energimarknaderna under 2000-talet har energiföretagen och elbörserna ständigt utvecklats mot mer integrerade och konkurrenskraftiga lösningar, där kvalitetsprognoser och effektiva optimeringsstrategier spelar avgörande roller. Detta examensarbete presenterar utvecklingen av en algoritm för optimering av vattenkraftplaneringen på Day-Ahead elmarknaden med hjälp av en matematisk modell av typen Mixed Integer Linear Programming (MILP). Arbetet initierades av och utfördes hos ENGIE Global Energy Markets (GEM) i Bryssel.  Modellen som utvecklats är tänkt att optimera Coindre vattenkraftverk, som ligger på höglandet inom Massif Central i Frankrike. Med det kombinerade vattenutsläppet från dess två fördämningar, Grande-Rhue och Petite-Rhue, kan kraftverket leverera upp till 36 MW el netto till elnätet. Vattenreservoarerna ligger flertalet kilometer ifrån varandra och har mycket olika kapacitet och upptagningsområden. Båda reservoarerna är kopplade till varandra genom det gemensamma tilloppsröret till kraftverket, där en reglerventil finns endast vid Petite-Rhue. Vatten kan växlas naturligt mellan de två dammarna när ventilen är öppen på grund av skillnaden i varderas vattennivå. Den maximala effekten från kraftverket är begränsad av vattennivåerna i båda reservoarerna vilket gör optimeringsmodelleringen komplicerad. Dessa operationella begränsningar är mycket hindrande vad gäller valet av driftsregim, eftersom kalkylering av driftsplaneringen blir en svår och tidskrävande uppgift.  En ramstudie av vattenkraftverket genomfördes under ett typiskt hydrauliskt år för att identifiera modellens styrparametrar. Den möjliga vattenöverföringen mellan de två dammarna orienterade modellutvecklingen mot en Mixed Integer Linear Programming (MILP) formulering. Efter att ha experimenterat med olika kalkylverktyg valdes Gurobi 28.1.0 för sin bra prestation i lösningen av Branch and Cut-algoritmen.  Systemets hydraulik har validerats genom att injicera realiserade produktionsplaner som input till modellen. Resultaten visar att volymfelet är mindre än 5% av deras respektive kapacitet under en 5-dagars tidshorisont. Efter tvärstester mot historiska data konstaterades det att den nya optimeringsstrategin resulterar i bättre genomsnittliga elpriser på varje kWh inmatad till nätet och högre intäkter för kraftverket. Resultaten visar också på vikten av korrekt ventilmanövrering i optimeringsstrategin.  Modellen körs i rimliga beräkningstider och redan används i den dagliga optimeringen av Coindre kraftverket, vilket sparar mycket tid. Specifika exempel på den optimerade prestandan och framtida förbättringar hittas i slutet av denna rapport.

[pt] O Problema de Roteirização de Veículos (Vehicle Routing Problem - VRP) é um problema clássico combinatório bem conhecido. Este trabalho apresenta um novo fator no modelo de otimização matemática de otimização do VRP, considerando restrições que abordam a probabilidade de roubo de cargas nas regiões visitadas, além das restrições tradicionais, tais como o número de veículos, janelas de tempo, a capacidade do veículo e tempo de ciclo dos veículos. O modelo desenvolvido é testado em um estudo de caso real, considerando uma empresa de distribuição de produtos farmacêuticos do Rio de Janeiro. As soluções de rota com e sem risco de roubo de carga são comparadas. O modelo é resolvido usando o software AIMMS, para análises com instância pequenas, e resolvidas executando a Metaheurística Simulated Annealing, para o estudo de caso, onde se utiliza de duas instâncias. / [en] The Vehicle Routing Problem (VRP) is a classic well-known combinatorial problem. This paper introduces a new factor in the VRP mathematical optimization model, considering restrictions that address the probability of cargo theft in the regions visited, beyond the traditional constraints such as the number of vehicles, time windows, the capacity of the vehicle and the vehicle s cycle time. The paper proposes a mixed integer linear model that minimizes total transportation costs and cargo theft costs. The model is tested in a real-life case study, a company that distributes pharmaceutical products in Rio de Janeiro. The route solutions with and without cargo theft risk are compared. The model is solved using AIMMS software for analysis with small instance, and resolved by running the Simulated Annealing Metaheuristic, for the case study, which uses two instances.

[pt] Este trabalho trata do problema real de avaliar a capacidade de processamento de pátios ferroviários planos de classificação. Nesses pátios, os vagões são recebidos em trens e movimentam respeitando a disposição dos trilhos e a formação sequencial do trem de saída. Movimentações ineficientes implicam em uma capacidade de processamento inferior à potencial do pátio dado seu layout. O objetivo desta pesquisa é descrever o problema e incitar um método capaz de calcular a capacidade de processamento de pátios ferroviários planos de classificação no horizonte estratégico, indicando se existe ou não a necessidade de um projeto de expansão para garantir atendimento à demanda prevista. O problema foi modelado através de programação linear inteira mista (MILP) baseado na teoria de sequenciamento de produção. O modelo foi aplicado em instâncias de teste, reproduzindo movimentações reais de vagões, e provou avaliar diferentes layouts adequadamente, porém com elevado tempo de execução. A inicialização de algumas variáveis binárias do modelo permitiu um incremento de tamanho nas instâncias, porém ainda inviável para aplicação na prática. / [en] This work deals with the real problem of evaluating the processing capacity of flat rail classification yards. In these yards, the railway cars are received on trains and move respecting the car sequence of the outgoing train. Inefficient movements imply a lower processing capacity than the yard s potential given its layout. The objective of this research is to describe the problem and to incite a method capable of calculating the processing capacity of flat rail classification yards in the strategic horizon, indicating whether or not there is a need for an expansion project to ensure meeting the expected demand. The problem was modeled using mixed integer linear programming (MILP) based on production scheduling theory. The model was applied to test instances, reproducing real railway car movements, and proved to evaluate different layouts properly, but with a high execution time. The initialization of some binary variables of the model allowed an increase in the size of the instances, however it is still unfeasible for practical application.

Swedish home care industry has been facing both external and internal problems, such as ageing population, varying quality and unsatisfactory continuity. Accordingly, workforce scheduling system, as one of the most common and useful software within home care planning nowadays, is in need of constant improvement and upgrading. This master’s thesis aimed to explore and analyze improvement potential of an established workforce scheduling system for an IT-company. The thesis was divided into two phases, of which a pre-study in Phase I tried to understand the planning process for planners and identify the perceived problems and shortcomings of the current system from a planner’s perspective. Based on the analysis from the pre-study, the caregiver continuity was chosen as the research area for Phase II. The current system was re-implemented and was modelled as an optimization problem. Furthermore, the system mainly consisted of two key parts, mixed integer linear programming (MILP) and heuristics. Different approaches in terms of modifications in both MILP and heuristics were applied to the re-implemented system. The performance of the modifications was measured by multiple evaluation indicators. The test results showed that there was a potential to improve caregiver continuity with 1.2% to almost 13% depending on the modification type. The modifications were lastly suggested for further examination regarding their practical appropriateness by applying them to the current running algorithm. / Den svenska hemtjänsten möter både yttre och inre problem såsom åldrande befolkning, varierande kvalitet och bristande kontinuitet. Schemaläggningssystemet som är en av de vanligaste och användbaraste programvarorna inom hemtjänsten behöver därmed en ständig förbättring och uppgradering som bemöter de existerande utmaningarna. Detta examensarbete hade som syfte att utforska och analysera förbättringspotentialen av ett etablerat schemaläggningssystem för ett ITföretag. Arbetet var indelat i två faser, varav förstudien i Fas I försökte förstå planerarnas planeringsprocesser och identifiera upplevda problem och brister i det nuvarande systemet utifrån ett planerares perspektiv. Baserat på analysen från förstudien, personalkontinuitet valdes som ett forskningsområde för Fas II. Nuvarande systemet implementerades om och det modellerades som ett optimeringsproblem. Systemet bestod huvudsakligen av två nyckeldelar, blandat heltalslinjärprogrammering (MILP) och heuristik. Olika metoder i form av modifieringar i både MILP och heuristik tillämpades på det omimplementerade systemet. Modifieringarnas prestanda mättes sedan med flera utvärderingsindikatorer. Testresultaten visade att, beroende på vilken modifiering det gäller, fanns det en potential att förbättra personalkontinuiteten med 1,2% till nästan 13%. Det föreslogs slutligen att modifieringarnas praktiska lämplighet behövs undersökas ytterligare genom att applicera det på det nuvarande systemet som är i drift.

This master thesis in optimization and systems theory is a development of two different optimization models formulated to schedule multi-skilled agents for contact centers depending on the forecasted demand, assigned by Teleopti. Four mixed integer linear programming models are created with the optimization programming language GAMS and solved by the internet based solver NEOS. Two of the models are formulated to perform an optimal scheduling that matches a forecasted demand per skill and day and the remaining two models are formulated to perform an optimal scheduling that matches a forecasted demand per skill, day and half hour. The first two models are referred to as the Basic Models and the second two are referred to as the Complex Models. The Basic Models includes seven constraints and the Complex Model includes nine constraints, describing regulations at the contact center. The main goal of the project is to find an optimal solution that results in an as even distribution of under or over scheduling. The scheduling optimization covers a period of 28 days, starting on a Monday which results in four weeks. The optimization models are based on two sets of data, there are 104 assigned agents that possesses one, two or three of the skills Channel, Direct and Product. All agents are bound to work according to a contract specified through the constraints. In the Basic Model the forecasted demand is given in amount of hours per day and skill, the demand is non-cyclical. In the Complex model the forecasted demand is given in amount of half hours per day, skill and half hour. Each day is scheduled from 7 a.m. to 11 p.m. resulting in 32 available half hours. All optimization models are developed to correctly mathematically formulate the constraints specified by Teleopti. Any non-linear equation that arises are linearized to maintain linearity, this is favourable in the sense of computational time solving the models. The objective functions in this thesis are formulated to describe the main goal of even distribution as correctly as possible. The result for the Basic Model shows that an optimal solution is achieved after 34 seconds. This model contains 169,080 variables and 39,913 equations. In the Complex Models integer solutions are achieved, but no optimal solution is found in 8 hours of computational time. The larger Complex Model contains 9,385,984 variables and 1,052,253 equations and the smaller Complex Model contains 5,596,952 variables and 210,685 equations. Teleopti’s scheduler produces an integer solution matching the Complex Model in 4 minutes. / Detta examensarbete i optimering och systemteori är framtagningen av två olika optimeringsmodeller formulerade för att schemalägga multikompetenta agenter för kontaktcenters beroende av den förväntade efterfrågan, tilldelad av Teleopti. Fyra blandade heltals linjära programmeringsmodeller skapas med optimeringsprogrammeringsspråket GAMS och löses av den internetbaserade lösaren NEOS. Två av modellerna är formulerade för att utföra en optimal schemaläggning som matchar en prognostiserad efterfrågan per skicklighet och dag och de återstående två modellerna är formulerade för att utföra en optimal schemaläggning som matchar en prognostiserad efterfrågan per färdighet, dag och en halvtimme. De två första modellerna i detta arbete benämns de Grundläggande Modellerna och de resterande två benämns de Komplexa Modellerna. Grundmodellerna inkluderar sju bivillkor och de Komplexa modellerna innehåller nio bivillkor, vilka beskriver arbetsvillkoren på kontaktcentret. Projektets huvudmål är att hitta en optimal lösning som resulterar i en jämn fördelning av under- eller överschemaläggning. Den schemalagda optimeringen täcker en period av 28 dagar, vilken börjar på en måndag vilket resulterar i fyra veckor. Optimeringsmodellerna är baserade på två uppsättningar data, det finns 104 tillgängliga agenter vilka har en, två eller tre av kompetenserna Channel, Direct och Product. Alla agenter är bundna att arbeta enligt det kontrakt som specificeras genom bivillkoren. I grundmodellen anges den prognostiserade efterfrågan i timmar per dygn och kompetens, efterfrågan är icke-cyklisk. I den komplexa modellen anges den beräknade efterfrågan i mängd halvtimmar per dag, kompetens och halvtimme. Varje dag är schemalagd från kl. 07.00 till 23.00 vilket resulterar i 32 tillgängliga halvtimmar. Alla optimeringsmodeller är utvecklade för att matematiskt beskriva de begränsningar som Teleopti specificerar. Alla icke-linjära ekvationer som uppstår linjäriseras för att upprätthålla linjäritet, detta är gynnsamt i avseendet mängd tid beräkningen av modellerna tar. Målfunktionerna i detta arbete är formulerade för att beskriva huvudmålet för jämn distribution så korrekt som möjligt. Resultatet för grundmodellen visar att en optimal lösning uppnås efter 34 sekunder. Denna modell innehåller 169,080 variabler och 39,913 ekvationer. I de komplexa modellerna uppnås heltalslösningar, men ingen optimal lösning hittas på 8 timmars beräkningstid. Den större komplexa modellen innehåller 9,385,984 variabler och 1,052,253 ekvationer och den mindre komplexa modellen innehåller 5,596,952 variabler och 210,665 ekvationer. Teleoptis schemaläggare producerar en heltalslösning som matchar den komplexa modellen på 4 minuter.