Multiple Objectives Mathematical Programming Using Payoff Techniques

Optimization is a decision Science which helps managements to take better decisions and refers to finding the values of decision (or free) variables. It is ubiquitous in daily life people use optimization, often without actually realizing, for simple things such as traveling from one place to another and time management, as well as for major decisions such as finding the best combination of study, job and investment. Similarly, optimization finds many applications in engineering, science, business, economics, etc. except that, in these applications, quantitative models and methods are employed unlike qualitative assessment of choices in daily life. Without optimization of design and operations, manufacturing and engineering activities will not be as efficient as they are now. Even then, scope still exists for optimizing the current industrial operations, particularly with the ever changing economic, energy and environmental landscape. Mostly we have three methods priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a-posteriori methods convey much more information to the decision maker. Especially, the a-posteriori (or generation) methods inform the Decision Maker (DM) about the whole context of the decision alternatives before his/her final decision. However, the generation methods are the less popular due to their computational effort and the lack of widely available software. The basic step towards further penetration of the generation methods in MMP applications, is to provide appropriate codes for Mathematical Programming (MP) solvers that are widely used by people in engineering, economics, agriculture etc. The present work is related with the Payoff Matrix and augmented ε -constraint method in which the Decision Maker (DM) plays important roll. Finally a program to find the Payoff Matrix have been designed .