Linear programming is widely used to solve various complex problems with many variables, subject to multiple constraints. Expert systems are created to provide expertise on complex problems through the application of inference procedures and advanced expert knowledge on facts relevant to the problem. The diet problem is well-known for its contribution to the development of linear programming. Over the years many variations and facets of the diet problem have been solved by means of linear programming techniques and expert systems respectively. In this study the feasibility of combining expert system technology and linear programming techniques to solve a diet problem topical to South Africa, is examined. A computer application is created that incorporates goal programming- and multi-objective linear programming models as the inference engine of an expert system. The program is successfully applied to test cases obtained through knowledge acquisition. The system delivers an eating-plan for an individual that conforms to the nutritional requirements of a healthy diet, includes the personal food preferences of that individual, and includes the food items that result in the lowest total cost. It further allows prioritization of the food preference and least cost factors through the use of weights. Based on the results, recommendations and contributions to the linear programming and expert system fields are presented. / MSc (Computer Science), North-West University, Potchefstroom Campus, 2014

Linear programming is widely used to solve various complex problems with many variables, subject to multiple constraints. Expert systems are created to provide expertise on complex problems through the application of inference procedures and advanced expert knowledge on facts relevant to the problem. The diet problem is well-known for its contribution to the development of linear programming. Over the years many variations and facets of the diet problem have been solved by means of linear programming techniques and expert systems respectively. In this study the feasibility of combining expert system technology and linear programming techniques to solve a diet problem topical to South Africa, is examined. A computer application is created that incorporates goal programming- and multi-objective linear programming models as the inference engine of an expert system. The program is successfully applied to test cases obtained through knowledge acquisition. The system delivers an eating-plan for an individual that conforms to the nutritional requirements of a healthy diet, includes the personal food preferences of that individual, and includes the food items that result in the lowest total cost. It further allows prioritization of the food preference and least cost factors through the use of weights. Based on the results, recommendations and contributions to the linear programming and expert system fields are presented. / MSc (Computer Science), North-West University, Potchefstroom Campus, 2014

The purpose of this thesis is to efficiently solve real life problems. We study LPs. We study an NLP and an MINLP based on what is known as the generalised pooling problem (GPP), and we study an MIP that we call the cattle mating problem. These problems are often very large or otherwise difficult to solve by direct methods, and are best solved by decomposition methods. During the thesis we introduce algorithms that exploit the structure of the problems to decompose them. We are able to solve row-linked, column-linked and general LPs efficiently by modifying the tableau simplex method, and suggest how this work could be applied to the revised simplex method. We modify an existing sequential linear programming solver that is currently used by Format International to solve GPPs, and show the modified solver takes less time and is at least as likely to find the global minimum as the old solver. We solve multifactory versions of the GPP by augmented Lagrangian decomposition, and show this is more efficient than solving the problems directly. We introduce a decomposition algorithm to solve a MINLP version of the GPP by decomposing it into NLP and ILP subproblems. This is able to solve large problems that could not be solved directly. We introduce an efficient decomposition algorithm to solve the MIP cattle mating problem, which has been adopted for use by the Irish Cattle Breeding Federation. Most of the solve methods we introduce are designed only to find local minima. However, for the multifactory version of the GPP we introduce two methods that give a good chance of finding the global minimum, both of which succeed in finding the global minimum on test problems.

The aim of this thesis is to analyse lifestyle changes and their impact on tourism. Goal to zoom in on the changing trend in the area of lifestyle, nutrition and wellness toward health. The theoretical part explains the lifestyle as a term and characterizes the wellness concept and worldwide trends in the field of wellness. It also represents the alternative methods, therapies and wellness services. It also deals with the problems of nutrition and nutritional alternative styles and introduces some of the results of the World Health Survey in the Czech Republic. The main part of the thesis includes own research on the preferences of the Czech population in the area of lifestyle, which is based on a questionnaire.

Aujourd'hui, l'alimentation représente plus de 70% du coût de production en engraissement porcin et dans le contexte économique actuel, il est important de parvenir à réduire ce coût. L'alimentation utilisée actuellement utilise des phases et est représentée par un modèle linéaire. L'alimentation par mélanges introduite récemment est représentée par un modèle bilinéaire. Nous introduisons ici une nouvelle formulation qui est une combinaison des alimentations traditionnelle par mélanges: la méthode hybride. Nous montrons qu'elle permet de réduire le coût de plus de 5%. L'étude principale porte sur l'optimisation globale du problème bilinéaire, non convexe, modélisant l'alimentation par mélanges. La bilinéarité apparaît dans la fonction objectif et dans les contraintes. Ce problème peut posséder plusieurs minima, mais nous souhaitons obtenir un minimum global. Il est équivalent à un problème de pooling et nous montrons qu'il est fortement NP-difficile. Après de premiers résultats, nous énonçons la conjecture que tout minimum local est global pour ce problème bilinéaire appliqué à l'industrie porcine. Nous la prouvons sur un exemple de dimension réduite. Notre problème ne pouvant pas être résolu avec des solveurs globaux à cause de sa dimension, nous utilisons des approches telle que la pénalisation, la discrétisation, et techniques de relaxation lagrangienne ou convexe. Toutes ces approches supportent notre conjecture. Nous faisons également une étude de la robustesse des modèles à la variation des prix des ingrédients ainsi qu'une étude multicritère nous permettant d'obtenir des résultats numériques réduisant considérablement les rejets, autres enjeux importants. / Today, feed represents more than 70% of the production cost in growing-finishing pig industry and in the current economic context, it is important to reduce it. The feeding system currently used uses phases and is expressed as a linear model. The feeding system using feeds introduced more recently is represented by a bilinear model. We introduced here new feeding system which is a combination offeeding systems using phases and feeds: the hybrid method. We show that it can reduce the feed cost by more than 5%. The main part of this manuscript is about global optimization of the bilinear problem, and non convex, problem modeling feeding system using feeds. The objective function and some constraints are bilinear. This problem can have several local minima but we would like to have a global one. It is equivalent to a pooling problem and we prove that it is a strongly NP-hard problem. After a study of first results, we enounce the conjecture that any local minimum is a global minimum for that problem applied in the pig industry. We prove it for a small size example. Our problem cannot be solved by using global solver due to its size, then we applied some relaxation methods such as penalization of bilinear terms, their discretization and Langrangian and convex relaxations. All these approaches support our conjecture. Then we study the robustness of the models on the ingredient price variations and a multicriteria study reducing phosphorus and nitrogen excretion.

The thesis describes a way of searching the best bill of fare for certain patient in hospital. The target is to set up and then to solve an optimization model. Criterion of performance is to minimize spending on selected foodstuff. The first part describes a theory of optimization models, the second is about nutrition and the third aims to solve a model and to interpret the results.

This thesis is based on the theory of mathematical programming, on the fastfood diet problem in particular. The aim is to find an optimal menu with accordance to nutritional limitations for various groups of fastfood customers and with minimal overall prize. This model is applied on the group of foods and beverages offered in selected fastfood chains in the Czech Republic.