For simplicity, we will consider only two integer variables. Lets start with the following MILP model. The red arrows indicates that the solution space goes further. When we know how the space of feasible solutions of MILP models looks like, we may start to reason about the general algorithm for MILP, its theoretical properties and possibly how to make more performant models. However, an understanding of the basic LP solution approach and the resulting properties are of fundamental importance. Linear Programming: The Simplex Method Initial System and Slack Variables Roughly speaking, the idea of the simplex method is to represent an LP problem as a system of linear equations, and then a certain solu-tion (possessing some properties we will de ne later) of the obtained system would be an optimal solution of the initial LP. a) If the feasible polytope described by the solution space of a linear programming problem is unbounded then there is no optimal solution b) If there are two basic optimal feasible solutions then there is an infinity of optimal feasible solutions. Complete coverage of LP solution approaches is beyond the scope of this book and is present in many other books. If you consider the inequalities the solution space looks like the yellow one. Linear programming solution has been the subject of many articles and books. The criteria for stopping the simplex algorithm is that the coefficients of the objective function must be non-positive. I'm taking an undergraduate course on Linear Programming and we were asked to solve the following problem using the Simplex Method: $$\max:~Z=3x+2y\\\text\Rightarrow z^*=55$
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |