A Study of Linear and Linear Fractional Extreme Point Programming Problems

Abstract

An extreme point programming problems can be defined in which an objective function is optimized over a convex polyhedron with an additional requirement that optimal solution must also be an extreme point of another convex polyhedron.A zero-one integer programming problem can be converted into extreme point mathematical programming problem by replacing the requirement that each of the variables should be either zero or one. The chapter-wise summary of the thesis is as follows: Chapter 1 is introductory in nature. This chapter includes basic concepts used to find the extreme point solution of extreme point linear and linear fractional programming problem and its extension to bounded variables. In Chapter 2, an extreme point linear programming problem is studied and a procedure to solve extreme point linear programming problems has been discussed. In Chapter 3, a procedure to solve an extreme point linear fractional programming problem has been studied in which the concept of ranking of extreme point solutions has been used to find the best optimal extreme point solution. To illustrate the method used, a numerical example is solved. In Chapter 4, an extreme point linear fractional programming problem is extended to bounded variables and the procedure to solve linear fractional programming problem with bounded variables has been discussed. To illustrate the method, numerical example is also given.