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AMS 341, Operations Research I: Deterministic Models

Catalog Description: Linear programming with a view toward its uses in economics and systems analysis. Linear algebra and geometric foundations of linear programming; simplex method and its variations; primal dual programs; formulation and interpretation of linear programming models, including practical problems in transportation and production control. Optional computer projects. AMS 341 and  AMS 342 may be taken in either order, though it is recommended that AMS 341 be taken first.

PrerequisiteAMS 210 or MAT 211

3 credits

Textbooks: Introduction to Mathematical Programming, Fourth Edition, by Wiston and Venkataramanan, John Wiley and Sons; ISBN: 9780534359645

Effective Fall 2013, this course will now be offered during the Fall semesters only 

AMS 341 Webpage 

1.  Sample linear  programming problems with geometric solution. (Chap. 1) –  3 class hours
2.  Simplex Method and variations (Chap. 2) –  9 class hours
3.  Sensitivity Analysis and Economic Applications (Chap. 3) – 6 class hours
4.  Linear Algebra and the Revised Simplex Method (Appendices) – 4 class hours 
5.  Duality Theory and Its Applications (Chap 4) – 5 class hours
6.  Transportation and Transshipment Problems (Chap 8) – 5 class hours 
7.  Integer Programming (Chap.9) – 2 class hours
8.  Dynamic Programming (Chapter 11) - 3 class hours
9.  Examinations and Review – 5 class hours

 

Learning Outcomes for AMS 341, Operations Research- Deterministic Models

1.) Become familiar with the many optimization problems arising in diverse settings that can modeled as linear programs, and construct mathematical models for an array of such optimization problems.
        * Maximizing income subject to supply constraints;
        * Minimizing costs subject to minimum requirements;
        * Scheduling problems;
        * short-term and long-term financial planning problems;
        * blending problems;
        * multi-period planning problems.

2.) Learn the simplex algorithm and use it to solve linear programss
        * putting linear programs in standard form with slack and excess variables;
        * finding an initial basic feasible solution (using big M or two-phase simplex for min problems);
        * choosing which variable enters and which variable leaves the basis;
        * handling unbounded and infeasible problems.

3.) Apply sensitivity analysis to optimal solutions
        * shadow prices and reduced costs;
        * range for objective function coefficients and right-hand sides;
        * connections to the dual linear programs and complementary slackness.

4.) Learn and use specialized algorithms for solving network problems:
         * transportation problems;
         * assignment problems;
         * critical path problems.

5.) Demonstrate an understanding of integer programs and how to solve them.
        * model various discrete optimization problems as integer programs;
        * solve integer programs using a branch-and-bound strategy.

6.) Demonstrate an understanding of dynamic programming and solution techniques.
        * model a class of discrete optimization problems as dynamic programs;
        * solve simple dynamic programs using a sequential solution technique.

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