This thesis aims to provide a reader with practical example of optimization achieved using the Lingo software. The main focus is improvement of efficiency and shortening of a production process in AKT, a company engaged in production of car parts. It is a software, which accommodates needs of the company as well as production requirements. The theoretical part is focused on detailed description of methods and procedures used in a practical part. These methods should help the reader to understand a nature of formulas relevant for the subject. Practical part focuses on the optimization using data obtained from the company AKT, evaluation of the data and subsequent consultations with a manager of production, followed by the assessment of practical relevance for the production.

The aim of the thesis is to create a model of timetable for primary school for all teachers and classes so that the timetable is in compliance with all teaching plans, the conditions of the Ministry of Education, Youth and Sports (general education program), the school's needs and requirements of teachers. The timetable is created for a particular school, ZŠ nám. Svobody in Prague. The first part of the thesis is focused on the theoretical description of methods and procedures for dealing with the problem of timetable. The second part describes the elementary school, for which the timetable is made, it's classes, teachers and conditions of the tuition. It is also formulated and described a mathematical model of the problem that is solved by using the program Lingo.

There are available various professional applications for the solving of optimization problems. This thesis deals with comparison of these optimization systems and simplicity of their connection with MS Excel through VBA. Problem of designing model together with his calculation in MS Excel or other systems connected via VBA, like MPL for Windows or LINGO, is demonstrated on concrete examples. Application in Visual Basic for Applications was created for this purpose. This application is easy to use and it is solving Knapsack Problem, Distribution Problem and also Quadratic Assignment Problem. Finally, comparison of these systems is made using Multi-criteria evaluation.

<p>This final-year project has been performed at Strix production Efterlyst. The task has been to make a page under their homepage, with a game application that’s supposed to be interesting and also have a strong connection to the TV- program. </p><p>In the first part of the report, the reader will learn about the preparing work that was done before the work with the final game began. It is in these two test versions all the technical problems were tested, to finally be used or thrown away. </p><p>When all this was done, a lot of effort was made to make an attractive design of the game. The different design alternatives that were made were sent to Strix, so that they could choose what they liked the most. </p><p>After the technical description and the design, comes a part that explains how each frame in the game is constructed. In this part you can also read about the programming that were made to make the game work as it’s supposed to. </p><p>In the end of this report you can follow the difficulties that came up during the project, and how they have been solved.</p>

This final-year project has been performed at Strix production Efterlyst. The task has been to make a page under their homepage, with a game application that’s supposed to be interesting and also have a strong connection to the TV- program. In the first part of the report, the reader will learn about the preparing work that was done before the work with the final game began. It is in these two test versions all the technical problems were tested, to finally be used or thrown away. When all this was done, a lot of effort was made to make an attractive design of the game. The different design alternatives that were made were sent to Strix, so that they could choose what they liked the most. After the technical description and the design, comes a part that explains how each frame in the game is constructed. In this part you can also read about the programming that were made to make the game work as it’s supposed to. In the end of this report you can follow the difficulties that came up during the project, and how they have been solved.

The pooling problem is an important optimization problem that is encountered in operation and scheduling of important industrial processes within petroleum refineries. The key objective of pooling is to mix various intermediate products to achieve desired properties and quantities of products. First, intermediate streams from various processing units are mixed and stored in intermediate tanks referred to as pools. The stored streams in pools are subsequently allowed to mix to meet varying market demands. While these pools enhance the operational flexibility of the process, they complicate the decisionmaking process needed for optimization. The problem to find the least costly mixing recipe from intermediate streams to pools and then from pools to sale products is referred to as the pooling problem. The research objective is to contribute an approach to solve this problem. The pooling problem can be formulated as an optimization program whose objective is to minimize cost or maximize profit while determining the optimal allocation of intermediate streams to pools and the blending of pools to final products. Because of the presence of bilinear terms, the resulting formulation is nonconvex which makes it very difficult to attain the global solution. Consequently, there is a need to develop computationally-efficient and easy-to-implement global-optimization techniques to solve the pooling problem. In this work, a new approach is introduced for the global optimization of pooling problems. The approach is based on three concepts: linearization by discretizing nonlinear variables, pre-processing using implicit enumeration of the discretization to form a convex-hull which limits the size of the search space, and application of integer cuts to ensure compatibility between the original problem and the discretized formulation. The continuous quality variables contributing to bilinear terms are first discretized. The discretized problem is a mixed integer linear program (MILP) and can be globally solved in a computationally effective manner using branch and bound method. The merits of the proposed approach are illustrated by solving test case studies from literature and comparison with published results.

Langerová, M. Optimization of logistic flows in the brewing industry. Diploma the-sis, Brno. Mendel University, 2014. The diploma thesis deals with logistic flows in the brewing industry. The main aim of this thesis is to determine problem fields of logistic processes and evaluation commonly used optimization methods. Then the best method is chosen for optimization in fields warehousing and distribution in brewing companies. Different parts of the logistic flows are described in this thesis -- supplier relationships, production, warehousing, transportation and distribution. Subse-quently logistic flows in brewery Vyškov are analyzed and found problem fields. The transportation and distribution are assessed as unsuitable in this brewery therefore the system of distribution was suggested by using the program LINGO. The example of brewery Vyškov is used for the generalization in the brewing industry.

Tato diplomová práce zabývající se matematickou optimalizací rozvrhu na střední škole si klade za cíl prošetřit, zda je vhodné k optimalizaci středoškolského rozvrhu použít dělící problém. Veškeré výpočty jsou dokumentovány ve třech různých úlohách, které se zakládají na reálných datech skutečné střední školy. Z optimalizačních softwarů byly zvoleny programy Lingo a Xpress na kterých byly ověřeny dva rozdílné způsoby formulace matematického modelu. Práce obsahuje sedm příloh, které jsou obsaženy v hlavním dokumentu a speciální přílohy obsahující formulace modelů a interpretační tabulky v programu MS Excel s využitím VBA na přiloženém CD.

Flights and revisions planning is the problem of assigning flights and revisions to aircrafts in such a way that constraints are satisfied, and some objective function is optimized. Objective function can be to minimalize the number of aircrafts. The intention of my thesis is to find the optimum solution in the problem of flights and revisions planning to aircrafts. In this work, I am using linear programming, which is important and irreplaceable in everyday practical use.

Det är allt vanligare inom tredjepartslogistik att kunder hyr en yta för lagring. För den uthyrande parten, i detta fall Delta Terminal, är arean den begränsande faktorn för hur stor yta som kan hyras ut. Idag använ-der sig Delta Terminal av beslutsunderlag i form av lokalernas area och erfarenhet vart gods ska placeras och har inget hjälpmedel för att beräkna vart och hur mycket gods som kan allokeras för att använda så liten yta som möjligt. Studiens syfte har därför varit att ta fram ett faktabaserat hjälpmedel som kan användas som beslutsunderlag. För att uppnå syftet har en matematisk modell utvecklats för att optimera hur gods kan placeras till olika lokaler för att använda så liten area som möjligt och även kunna simulera förändringar. Modellen testades genom att jämföra den maximala godsvolym som lagrades 2012 mot optimeringsmodellens lösning baserat på samma gods- och lokaldata. De vanligaste godstyperna hos Delta terminal var bulk, storsäck och pall och användes i modellen. För dessa så approximerades den förväntade area- och volymåtgång vilket också gav beslutsfattaren en förväntad volymkapacitet för respektive lokal och gods. Resultatet i den optime-rade lösningen visade att ett av godsen skulle kunna flyttas till en annan lokal vilket skulle innebära att ungefär 25 procent mindre area används jämfört med den area som godsets placering upptar idag. Dessutom innebar den optimerade lösningen att tre lokaler frigjordes. Resultatet från simulering av volymkapaciteten för respektive gods och lokal kan hjälpa till vid en beslutssituation om en viss godsvolym får plats i lokalen eller inte och kan därmed hjälpa till att anpassa lokalens kapaci-tet mot godsets volym. Modellen fungerar teoretiskt och skulle kunna implementeras som ett användbart verktyg för beslutsfattaren i frågor som rör optimering eller simulering av ytorna. Vid en implementering gäller det emellertid att modellen valideras och jämförs mot verkliga utfall. / An increasingly common part in third party logistics is that customers rent an area for storage. For the party that leases out the area, in this case Delta Terminal, the area is the limiting factor for the amount of how much can be let out to lease. Today Delta Terminal uses decision sup-port in the form of premises area and experience where goods should be placed and have no means to calculate where and how much goods that can be allocated to use as small space as possible. The purpose of this study was therefore to develop a data based tool that can be used as support in the decision process. To achieve the objective a mathematical model was developed to optimize how freight can be placed at different locations to use as small an area as possible and also be able to simulate changes. The model was tested by comparing the maximum amount of cargo during 2012 against optimization model solution based on the same freight and local data. The most common goods handled at Delta Terminal were bulk, big bags and EUR-pallets and were used in the optimization model. For those goods an approximation of the expected area and volume was made that gave the decision maker an expected volume capacity for each local and goods. The result showed with the optimized solution that one of the goods could be moved to another storage place which would release approximate 25 percent reduction in area compared to where the goods are placed today and also three of the local spaces were released. The result from simulation of the volume capacity of each goods and local can help in a decision situation if a given volume of goods will fit in the local space and thus help to adapt the local capacity against the goods volume. Theoretically the model works and could be implemented as a useful tool for decision-makers on issues related to optimization or simulation of surfaces. However, when implementing the optimization model it is important to validate and compare the model’s result against actual outcomes.