In a generic wireless network where the activation of a transmission link is subject to its signal-to-noise-and-interference ratio (SINR) constraint, one of the most fundamental and yet challenging problem is to find the maximum number of simultaneous transmissions. In this thesis, we consider and study in detail the problem of maximum link activation in wireless networks based on the SINR model. Integer Linear Programming has been used as the main tool in this thesis for the design of algorithms. Fast algorithms have been proposed for the delivery of near-optimal results time-efficiently. With the state-of-art Gurobi optimization solver, both the conventional approach consisting of all the SINR constraints explicitly and the exact algorithm developed recently using cutting planes have been implemented in the thesis. Based on those implementations, new solution algorithms have been proposed for the fast delivery of solutions. Instead of considering interference from all other links, an interference range has been proposed. Two scenarios have been considered, namely the optimistic case and the pessimistic case. The optimistic case considers no interference from outside the interference range, while the pessimistic case considers the interference from outside the range as a common large value. Together with the algorithms, further enhancement procedures on the data analysis have also been proposed to facilitate the computation in the solver.

The theme of this thesis is high school timetabling. The built mathematical model is based on bivalent programming. The model uses multicriteria linear programming too, because a timetable has to fill legal and school's requests and student's and teacher's wishes. Firstly, there are given theoretical basics. Then there is described economic model with school's characteristics and it continues by mathematical model. For optimization, tool MPL for Windows with using Gurobi. Finally, export of optimization is transferred using VBA to form for end users.

This report considers an application of mixed-integer disjunctive programming (MIDP)where a theoretical robot can jump from one point to another and where the number ofjumps is to be minimized. The robot is only able to jump to the north, south, east andwest. Furthermore, the robot should also be able to navigate and jump around or across anypotential obstacles on the way. The algorithm for solving this problem is set to terminatewhen the robot has reached a set of end coordinates. The goal of this report is to find amethod for solving this problem and to investigate the time complexity of such a method.The problem is converted to big-M representation and solved numerically. Gurobi is theoptimization solver used in this thesis. The model created and implemented with Gurobiyielded optimal solutions to problems of the form above of varying complexity. For most ofcases tested, the time complexity appeared to be linear, but this is likely due to presolvingperformed by Gurobi before running the optimization. Further tests are needed to determinethe time complexity of Gurobi’s optimization algorithm for this specific type of problem.

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This paper explores strategies in portfolio optimization, focusing on integrating mean-variance optimization (MVO) frameworks with cardinality constraints to enhance investment decision-making. Using a combination of quadratic programming and mixed-integer linear programming, the Gurobi optimizer handles complex constraints and achieves computational solutions. The study compares two mathematical formulations of the cardinality constraint: the Complementary Model and the Big M Model. As cardinality increased, risk decreased exponentially, converging at higher cardinalities. This behavior aligns with the theory of risk reduction through diversification. Additionally, despite initial expectations, both models performed similarly in terms of root relaxation risk and execution time due to Gurobi's presolve transformation of the Complementary Model into the Big M Model. Root relaxation risks were identical while execution times varied slightly without a consistent trend, underscoring the Big M Model's versatility and highlighting the limitations of the Complementary Model.

Goal programming is an approach for solving decision problems. The aim of this doctoral thesis is to show the practical use of this approach for solving real problems. The first chapter brings a brief introduction to multicriteria decision making. The second chapter is devoted to goal programming, its history, theory, criticism and also to its practical applications. The third chapter deals with description of a model for optimisation of white mass production. This model utilises the goal programming principle to deal with measuring deviations of raw materials' composition. A part of this chapter is a presentation of OPTIPROT, an application that implements the mentioned model. In the fourth chapter there are described three mathematical models for timetabling at a department level; two multistage models and one complex model. All three models are formulated utilising goal programming. In this chapter there is also described an application that implements the complex model for timetabling.

This thesis deals with optimization problems of the parcels distribution. This issue can be solved on the ground of traveling salesman problem whose mathematical and economic model, including their modifications, are presented in the theoretical part of the thesis. We can solve these problems by using exact methods, heuristic and metaheuristic algorithms. In the theoretical part are described traveling salesman problem, traveling salesman problem with time windows, traveling salesman problem with multiple time windows and dynamic traveling salesman problem including possible ways of solution. In the practical part we can find application of problems on the real example, when we are finding the shortest possible route for the PPL's employee under different assumptions. The solution is obtained by using solver Gurobi within the modelling system MPL for Windows. In conclusion of the thesis the results are summarized and models are compared with each other.

The functionality to both charge and discharge energy from and to the power grid to a Battery Electric Vehicle (BEV) is referred to as Vehicle-to-Grid (V2G). This allows the customer to buy energy when the spot price is low and sell energy when the price is high to make a profit, called energy arbitrage. However, when the battery is charging, discharging, or idling for storage, battery degradation occurs due to chemical properties and reactions. This thesis developed a mathematical optimisation model in Python, using the modelling language Pyomo. Mathematical equations are used to integrate energy arbitrage and degradation data to reduce the total cost in terms of degradation and energy by finding an optimised charge and discharge pattern. The model allows different user scenarios to be analysed by changing inputs such as charger power, battery cost or daily driving distance. When using V2G technology, the State-of-Charge (SoC) level of BEVs battery packs can be adjusted to find SoC levels which minimise the battery degradation, while allowing the user to make a profit from energy arbitrage. The result shows that the V2G charging protocol, compared to protocols without a bidirectional charger could be beneficial for the simulated time periods, by both reducing degradation and the total energy cost. The results also indicate that the degradation cost of the battery is often the determining factor in the decision of when to charge or discharge, i.e., the substantial cost-saving strategy is to control the storage and cycle degradation to reduce the total degradation, rather than controlling the energy arbitrage. The model and the result of this thesis can be used by car manufacturers to learn more about how battery cell types behave in V2G mode and influence further work on V2G control.

This project aimed to evaluate the effectiveness of the Auto Regressive Exogenous(ARX) model in forecasting stock prices and contribute to research on statisticalmodels in predicting stock prices. An ARX model is a type of linear regression modelused in time series analysis to forecast future values based on past values and externalinput signals. In this study, the ARX model was used to forecast the closing pricesof stocks listed on the OMX Stockholm 30 (OMXS30*) excluding Essity, Evolution,and Sinch, using historical data from 2016-01-01 to 2020-01-01 obtained from YahooFinance. The model was trained using the least squares approach with a control signal that filtersoutliers in the data. This was done by modeling the ARX model using optimizationtheory and then solving that optimization problem using Gurobi OptimizationSoftware. Subsequently, the accuracy of the model was tested by predicting prices in aperiod based on past values and the exogenous input variable. The results indicated that the ARX model was not suitable for predicting stock priceswhile considering short time periods.

This paper presents the development and mathematical implementation of a production scheduling model utilizing mixed-integer linear programming (MILP). A simplified model of a real-world multi-product batch plant constitutes the basis. The paper shows practical extensions to the model, resulting in a digital twin of the plant. Apart from sequential arrangement, the final model contains maintenance periods, campaign planning and storage constraints to a limited extend. To tackle weak computational performance and missing model features, a condensed mathematical formulation is introduced at first. After stating that these measures do not suffice for applicability in a restrained time period, a novel solution strategy is proposed. The overall non-iterative algorithm comprises a multi-step decomposition approach, which starts with a reduced scope and incrementally complements the schedule in multiple subproblem stages. Each of those optimizations holds less decision variables and makes use of warmstart information obtained from the predecessor model. That way, a first feasible solution accelerates the subsequent improvement process. Furthermore, the optimization focus can be shifted beneficially leveraging the Gurobi solver parameters. Findings suggest that correlation may exist between certain characteristics of the scheduling scope and ideal parameter settings, which yield potential for further investigation. Another promising area for future research addresses the concurrent multi-processing of independent MILPs on a single machine. First observations indicate that significant performance gains can be achieved in some cases, though sound dependencies were not discovered yet.