Goal programming and generalieed inverse approaches in the multi-objective analysis and application in feed industry

This study aimed to optimize the nutritional balance of selected feed mixes which were described in the Turkish Feed Regulation, by means of goal programming and generalized inverse approaches. Crude protein, crude cellulose, crude ash, calcium and phosphorus contents of some feedstuffs for livestocks and in addition to these nutrient metabolical energy for poultry were considered according to the data obtained from General Directorate of Feed Industry. Goal programming is a relatively new tool that has been proposed as a model and approachfor the analysis of problems involving multiple and conflicting objectives. This method modification and extension of linear programming which can be used to optimize the nutritional balance of a selected mix of feedstuffs. It achieves this through replacement of cost minimization in the objective function by the total deviation of the goal from pre- specified levels required for optimum balance. Following the goal programming approach to multiple goals we try to secure further perspective and insight by approaching this same topic in a different way by using the generalized inverse of a matrix. Goal programming and generalized inverse approaches both derive solutions which minimize the "distance" from the set of goals. The distance in the goal programming approach is measured by the sum of absolute value of the deviations from each goal. But the distance in the generalized approach is measured by the square root of the sum of squares of the deviation from each goal. In some cases the difference between distance functions in the two approaches gives us an advantage in favour of generalized inverse. Solutions to the two approches were obtained at the Computing Center of the Faculty of Art and Sciences of Gazi University by using the programs we prepared.