Operations Research Methods

The operations research analyst has a wide variety of methods available for problem solving. For mathematical programming models there are optimization techniques appropriate for almost every type of problem, although some problems may be difficult to solve. For models that incorporate statistical variability there are methods such as probability analysis and simulation that estimate statistics for output parameters. In most cases the methods are implemented in computer programs. It is important that at least some member of an OR study team be aware of the tools available and be knowledgeable concerning their capabilities and limitations.

In this section we include a number of topics that relate to the methods of operations research. The contents of this section are arranged by problem type. This Methods section includes the documentation for the teaching add-ins.

 Linear Programming We provide three units to demonstrate and teach linear programmming solution algorithms. Primal Simplex Demonstrations are implemented using Flash to illustrate basic concepts of the primal simplex technique. The Teach Linear Programming Add-in implements three different algorithms for solving linear programming models. Several text presentations using the pdf format described more advanced concepts of linear programming. Network Flow Programming We provide five units to demonstrate and teach linear programmming solution algorithms. The Teach Network Add-in implements the network primal simplex method for both pure and generalized minimum cost flow problems. A graphical demonstration using Flash illustrates and contrasts algorithms for finding the minimal spanning tree and shortest path tree. The Transportation primal simplex method is implemented in the Teach Transportation Add-in. A graphical demonstration using Flash illustrates the network primal simplex method. A text presentation of the network primal simplex algorithm using the pdf format. The Teach NLP Add-in demonstrates direct search algorithms for solving nonlinear optimization problems. Integer Programming The Teach IP Add-in implements two methods for solving linear integer programming problems. The add-in provides demonstrations and hands-on practice for branch and bound and cutting plane methods. Dynamic Programming The Teach Dynamic Programming Add-in has features that allow almost any system appropriate for dynamic programming to be modeled and solved. The program includes both backward recursion and reaching.