Methods of Optimization in Operations Research: Mathematical Programming and Its Related Theorems

For decision making optimization plays the central role. In our time to take any decision, we use most modern scientific methods based on computer implementations. We know that, for solving Mathematical Programming problem various algorithms can be used, but only few of the methods will be affective for solving problems. Usually none of the algorithms have no relation with others and there is no universal algorithm to solve the problems. In this book first, we have shown how to formulate a business problem into a Mathematical Programming problem and next compare some methods of solving such problems and computer implementation for solving Mathematical Programming problem has been developed. Here we have shown that by graphical method using MATLAB programming for all kinds of programming problem, we can determine a particular plan of action from amongst several alternatives in very short time and we develop computer program (FORTAN) of Swarup's Simplex type method for solving Linear Fractional Programming (L. F. P) Problems more easily. It also has been discussed how to find out a initial basic feasible of a Transportation problem to minimize the transportation cost.