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.
Prerequisite: AMS 210 or MAT 211
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
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.