3 - Further Topics in Linear Programming

Abstract

This chapter discusses several topics in linear programming that have important computational consequences. The concept of duality shows how to associate a minimization problem with each linear programming problem in standard form. The chapter highlights the types of problems associated with duality—dual problems and primal problems. It shows the economic interpretation of the dual problem, the duality theorem, computational relations between the solutions to the primal and dual problems, and how to compute a solution to the dual problem from the final tableau of the primal problem. The dual simplex method and the reverse dual simplex method are explained. A linear programming problem is just one part of mathematically modeling a situation. After the problem is solved, it is necessary to find out whether the solution makes sense in the actual situation or not. It is also very likely that the numbers that are used for the linear programming problem are not known exactly. In most cases they will be estimates of the true numbers, and many times they will not be very good estimates. The sensitivity of the solution to changes in the values that specify the problem should be measured, which is called “sensitivity analysis.”