Matrices, Determinant and Body Volume

Ve své bakalářské práci popisuji základní vlastnosti matic, determinantu a jejich využití v otázkách zobrazení mezi vektorovými prostory. V závěrečných kapitolách se věnuji determinantu a jeho aplikacím, kde ukazuji vztah mezi determinantem a výpočtem objemu. Následně popisuji použití determinantu při výpočtu těles pomocí vícenásobných integrálů. Další možnou aplikací je pak tzv. Cramerovo pravidlo, které nám umožnuje rešení soustav n lineárních rovnic o n neznámých.In his thesis describes the basic properties of matrices, determinants and their use in display issues between vector spaces. In the final chapters devoted to determinants and its applications, which indicates the relation between determinants and calculation of volume. Subsequently determinanti describes how to use in calculating the elements using multiple integrals. Another possible application is the so-called Cramerovo rule which allows us to solving systems of linear equations.

Application of stochastic programming methods for the purpose of energy producing system

Diplomová práce se zabývá vyhodnocením strategického investování do výstavby zařízení pro energetické využití odpadů s možností napojení na síť CZT (centrální zásobování teplem). Cílem je najít ekonomicky výhodné řešení pro obecně neznámý vývoj odpadového hospodářství a energetického trhu. Podstatným faktorem ovlivňující strategické rozhodnutí je množství tepla, které lze v síti CZT uplatnit. Problém formulujeme jako úlohu dvoustupňového stochastického programování, založenou na scénářích. Pro výpočet řešení využíváme program GAMS. Výsledkem je stanovení podstatných parametrů navrhovaného zařízení.This thesis deals with the evaluation of the strategic investment in the waste-to-energy plant development. The central supply of heat and the incineration plant connection can be provided for example by the distribution network. The objective is to find financially feasible solution regarding uncertain development of waste management and energy market. A heat supplies to district heating network significantly influences the strategic decision. A two-stage stochastic programming based on the scenarios and the GAMS software were applied to solve this task. The main contribution of this thesis is decision on crucial parameters of the waste-to-energy plant.

Effective Investment Planning in Waste-to-Energy Systems

Disertační práce se zabývá aplikací simulačních a optimalizačních metod v oblasti energetického využití odpadů. V úvodu práce je popsán současný stav v oblasti odpadového hospodářství v EU se zaměřením na ČR. Následující kapitola pojednává o hodnotících kritériích investičních záměrů a základních principech stochastického programování. Jádrem práce jsou matematické modely zaměřené na plánování a provoz jednotlivých zařízení a problematiku spojenou se svozem odpadu. Dopravní úloha dává do souvislostí všechny uvažované projekty v hodnoceném zájmovém území a je možné díky ní simulovat toky odpadu mezi producenty a zpracovateli. Přístup je demonstrován na pěti případových studiích. V prvních třech studiích byly uvedeny výpočty pro potenciálního investora. Hlavním výstupem bylo určení míry atraktivity investice a identifikace největších rizik. Další případová studie byla věnována analýze z pohledu statní koncepce. V poslední případové studii je detailně analyzována problematika nakládání s odpadem z pohledu producentů.PhD thesis deals with the application of the simulation and optimization methods in the waste-to-energy field. An introduction describes the current state of the waste management in the EU with the focus on the Czech Republic. In the following chapter the evaluation criteria for investment intentions and the basic principles of stochastic programming are discussed. The core of the work lays in the mathematical models for the planning and operation of the process plants as well as in the mathematical models for the waste collection. The transportation problem involves all considered technological elements and therefore it is possible to simulate the waste streams between the producers and processors. This approach is demonstrated with five case studies. In the first three studies the calculations for the potential investor are presented. The main outcome of these case studies is the determination of the level of attractiveness of investment and the identification the greatest risks. Another case study is devoted to an analysis with the focus on perspective of government policies and in the last case study the issue of the waste management is analyzed in detail from the perspective of the waste producers. Developed computational tools are flexible and can be further developed and adapted based on the objectives of the specific tasks.

Sustainable model integration of waste production and treatment process based on assessment of GHG

The paper presents a new model for supporting strategic decision-making in the area of municipal solid waste management. The effort is to integrate the assessment of greenhouse gas (GHG) to a sustainable economy. The goals are (in the following order) to reduce the waste produced, recycle at the highest rate as possible (material recovery) and to use the resultant residual waste for energy recovery. These features will be implemented through both pricing and advertising-like principles. The resulting mathematical model proposes multi-objective approach considering GHG and cost minimisation. The aim is to design the optimal waste management strategy, where stakeholders decide about the investment to the propagation of waste prevention and to advertising of waste recycling, and investors decide about new facility location and technological parameter. The availability of waste is projected in pricing method as well as the location of the facility. The mathematical model will utilise randomness in the form of waste production. All of the non-linearities (advertising and pricing) in the objective function will be replaced by piecewise linear approximation. The results of the work are applicable to the area of waste treatment infrastructure planning and to support decision-making at the micro-regional level with regard to the GHG impact. The original obtained solution will further be utilised for analyses dealing with all types of combustible waste. Copyright © 2018, AIDIC Servizi S.r.l

Circular economy implementation in waste management network design problem: a case study

The paper presents a new approach to support the strategic decision-making in the area of municipal solid waste management applying modern circular economy principles. A robust two-stage integer non-linear program is developed. The primary goal tends to reduce the waste production. The generated waste should be preferably recycled as much as possible and the resultant residual waste might be used for energy recovery. Only some waste residues are appropriate for landfilling. The aim is to propose the near-optimal waste allocation for its suitable processing as well as waste transportation plan at an operational level. In addition, the key strategical decisions on waste treatment facilities location must be made. Since waste production is very often hard to predict, it is modeled as an uncertain decision-dependent quantity. To support the circular economy ideas, advertising and pricing principles are introduced and applied. Due to the size of available real-world data and complexity of the designed program, the presented model is linearized and uncertainty is handled by a robust optimization methodology. The model, data, and algorithm are implemented in MATLAB and Julia, using the state-of-the-art solvers. The computational result is a set of decisions providing a trade-off between the average performance and the immunization against the worst-case conditions. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature

Pricing and advertising strategies in conceptual waste management planning

The paper presents a new model for integration of circular economy strategies into the municipal solid waste management. The goals are to reduce the waste produced, recycle at the highest rate as possible (material recovery) and to use the resultant residual waste for energy recovery. Such a strategy utilizes both pricing and advertising principles in the mixed integer linear programming model while accounting two criterions - assessment of greenhouse gas (GHG) and cost minimization. The aim is to design the optimal waste management grid to suggest a sustainable economy with environmental concerns. The government, municipalities and/or authorized packaging company decide about the investments to the propagation of waste prevention and to advertising of waste recycling, while investors decide about new facility location and technological parameter. The availability of waste is projected in pricing method as well as in the location of the facility. The mathematical model will consider randomness in the form of waste production. The suggested non-linear functions of pricing and advertising are replaced by piecewise linear approximation to reduce computational complexity. The proposed multi-objective model is applied in a case study for the Czech Republic in the area of waste treatment infrastructure planning to support decision-making at the micro-regional level. The integration of circular economy principles, considering also the total amount of produced GHG, revealed the existing potential in waste prevention. On the other hand, the increase of recycling is limited, landfills are not supported and the energy recovery is preferred. However, the planning of the complex system relies on the decision-maker. © 2019 Elsevier LtdCzech Republic Operational Programme Research and Development, Education, Priority 1: Strengthening capacity for quality research [CZ.02.1.01/0.0/0.0/15_003/0000456]; Operational Programme Research, Development and Education, Priority axis 1: Strengthening capacity for high-quality research [CZ.02.1.01/0.0/0.0/16 026/0008392

Robust facility location problem for bio-waste transportation

The article presents an optimisation tool for bio-waste facility allocation. The quantity of bio-waste produced in individual territorial units is a key factor for the selection of localities when constructing a new facility. Bio-waste production changes over the course of the year and differs between various types of housing developments. Separation rate is a determining factor for bio-waste production. Readiness to separate the waste reflects the total quantity of bio-waste produced. Predicting the future of bio-waste production is a complex problem, and it would be suitable to consider more developed scenarios. The introduced tool takes into consideration additional possible scenarios for production and provides a robust solution from the point of view of a locality suggestion for the construction of the processing facility. The optimisation model is based on the two-stage stochastic programming approach. The decision regarding the locality for the construction of a new facility is made during the first stage. This method is called the "Here-and-Now" approach. The results are presented in a case study for a selected region in the Czech Republic. Since changes to the legislation in 2014, municipalities are now supposed to provide the possibility to collect the bio-waste of citizens. This has caused significant growth in production - about 20 % annually over the past few years. At this point, it is very complicated to estimate a future trend based on the historical data. Due to this reason, it would be appropriate to consider future bio-waste production across more scenarios. In order to enable the applicability of the tool on a large area with many nodes, it would be necessary to adapt the computation method according to its computational complexity. Copyright © 2017, AIDIC Servizi S.r.l

Cooking oil and fat waste management : a review of the current state

Waste management is a continuously growing area connecting industry and academia nowadays. There are, however, still many issues and sub-areas requiring in-depth analysis and development of new approaches and solutions. One of them is the management of waste cooking oils and fats originated from households. While most of the solid waste is addressed within the circular economy proposal, the fat waste recycling consideration is still in its early stage, as the relevant European Union legislation has only recently been adopted. Disposing of oil and fat waste in a traditional way often leads to sewage problems. However, if utilised, this waste may be a valuable source of energy and material recovery. While maintaining the reverse supply chain viewpoint (from waste producers through the collection to treatment and utilisation), this paper reviews the current state of the waste cooking oils and fats management and identifies the drawbacks in existing collection and handling methods. The review shows that current approaches have shortcoming mainly due to poorly organised collection container networks and provides insights into the importance of effective prognosis of the cooking oil and fat waste whose collection and handling is still in the development. The Czech Republic current state and the future outlook is discussed and commented with regards to the expected growth of production and separation of these wastes. The review stresses the challenges of establishing and coordinating the supply chain segments, which will benefit from applying mathematical modelling to facilitate decision-making.publishedVersio

The L-shaped method for large-scale mixed-integer waste management decision making problems

It is without a doubt that deciding upon strategic issues requires us to somehow anticipate and consider possible variations of the future. Unfortunately, when it comes to the actual modelling, the sheer size of the problems that accurately describe the uncertainty is often extremely hard to work with. This paper aims to describe a possible way of dealing with the issue of large-scale mixed integer models (in term of the number of possible future scenarios it can handle) for the studied waste management decision making problem. The algorithm is based on the idea of decomposing the overall problem alongside the different scenarios and solving these smaller problems instead. The use of the algorithm is demonstrated on a strategic waste management problem of choosing the optimal sites to build new incineration plants, while minimizing the expected cost of waste transport and processing. The uncertainty was modelled by 5,000 scenarios and the problem was solved to high accuracy using relatively modest means (in terms of computational power and needed software)

Quantity-predictive vehicle routing problem for smart waste collection

The current trends in the field of waste management involves the use of modern technologies such as wireless sensors. The smart waste management with Sensor Technology involves an integration of the so-called smart trash bins and containers into existing network by using sensors that fill level of the bins and containers. Apart from the technological aspects of the problem, this arrangement points to the need of development of new decision-making tools that allow collectors to make fast and smart operative decisions on the waste collection. The sensors from the waste containers read the current fill-height once a day and send the information to the central database. The central decision-maker appraises the data and makes the waste collection plan for an entire (e.g., one week) collection period; note that this improves existing models on the data available and used. The aim of this paper is to present complex modelling ideas, develop a simple mathematical model, discuss its complexity and propose/discuss a computational approach in order to solve the collection problem. The objective is to optimize the dynamic planning on daily garbage-truck schedules with respect to minimization of transportation costs that also reflects a positive environmental impact presented by savings in transportation/routing distance. The secondary objective is to optimally decide on early collection of partly-filled containers, especially those directly on or close to the optimum route linking the full ones considering waste production rates in the next days. The paper outlines some directions for further research such as the need of modifying the old-existing models into a form utilizing the newly available data. This leads to specific vehicle routing problems that request appropriate computational time requirements and the need of suitable heuristic methods development. Copyright © 2019, AIDIC Servizi S.r.l