Sample Syllabus for a Semester Introduction to
Deterministic Operations Research

using Optimization in Operations Research
by Ronald L. Rardin, Prentice Hall, 1998

Audience

This course is intended as a first course in Operations Research or Management Science for undergraduate or graduate students in engineering and mathematics, and graduate students in management, as well as a second course for management undergraduates with prior training in management science.

Background

This course assumes elementary background in multivariate differential calculus and in linear algebra, plus familiarity with vector/matrix notation and arithmetic.

Topics

Mathematical Modeling and the Operations Research Approach (Chapter 1)
Introduction to Formulation and Classification of Optimization Models (Chapter 2)
Elements of Improving Search-Based Optimization Algorithms (Sections 3.1-3.3, 3.5)
Formulation and Classification of Linear Programs (Sections 4.1-4.5)
Simplex Algorithms for Solving Linear Programs (Sections 5.1-5.3, 5.5-5.6)
Interior Point Algorithms for Solving Linear Programs (Sections 6.1-6.2, 6.4)
Duality and Sensitivity in Linear Programming (Sections 7.1-7.4)
Multiobjective Optimization and Goal Programming (Sections 8.1-8.2, 8.4)
Shortest Paths and CPM (Sections 9.1-9.3, 9.7)
Formulation and Structure of Network Flow Models (Sections 10.1-10.5)
Formulation and Classification of Discrete Optimization Models (Sections 11.1-11.3, 11.5-11.6)
Methods for Solving Discrete Optimization Models (Sections 12.1-12.2, 12.4)

Schedule (less one week of examinations)

Week	Topics	Reading
1	Class Organization Optimization Models and the O.R. Approach Tractability vs. Validity Modeling Tradeoffs	Sections 1.1-1.3 Sections 1.4-1.7
2	Form of Optimization Models, Graphic Solution Large-Scale Models, Linear vs. Nonlinear Programs Discrete vs. Continuous Optimization, Multiobjectives	Sections 2.1-2.2 Sections 2.3-2.4 Sections 2.5-2.7
3	Improving Search Paradigm, Local vs. Global Optima Search with Improving and Feasible Directions Conditions for Improving and Feasible Directions	Section 3.1 Section 3.2 Section 3.3
4	Starting Feasible Solutions Allocation and Blending LPs Operations Planning and Shift Scheduling LPs	Section 3.5 Sections 4.1-4.2 Sections 4.3-4.4
5	Time-Phased Models LP Standard Form Extreme-Points and Basic Solutions	Section 4.5 Section 5.1 Section 5.2
6	Simplex Search Two-Phase Simplex Degeneracy	Section 5.3 Section 5.5 Section 5.6
7	Interior Point Strategies for LP Affine Scaling of Solutions Log Barrier Interior Point Methods for LP	Section 6.1 Section 6.2 Section 6.4
8	Activities vs. Resources, Qualitative Sensitivity Quantitative Sensitivity and Duality Formulating Duals	Sections 7.1-7.2 Section 7.3 Section 7.4
9	Multiobjective Optimization Models Efficient Points and the Efficient Frontier Goal Programming	Section 8.1 Section 8.2 Section 8.4
10	Graphs and Networks, Shortest Path Models Dynamic Programming Approach and Bellman-Ford Longest Paths and CPM	Section 9.1 Section 9.2-9.3 Section 9.7
11	Network Flow, Transportation and Assignment Models Cycle Direction-Based Network Flow Search Integrality of Network Flows	Sections 10.1,10.5 Sections 10.2-10.3 Section 10.4
12	Lumpy LPs and Fixed Charge ILPs Knapsack and Capital Budgeting ILPs Set Packing, Covering and Partitioning ILPs	Section 11.1 Section 11.2 Section 11.3
13	Traveling Salesman and Routing Models Facility Location and Network Design ILPs Solving Integer Programs by Total Enumeration	Section 11.5 Section 11.6 Section 12.1
14	Relaxations of ILPs Branch and Bound	Section 12.2 Section 12.4

Variations

Instructors presenting this course to a chemical, mechanical or similar engineering audience may wish to substute nonlinear material for the shortest path and network topics of weeks 10 and 11. Such an alternative could be scheduled as follows:

Week Topics Reading

10' Formulation of Unconstrained NLPs
Golden Section Search
Gradient Search Section 13.1
Section 13.2
Section 13.5

11' Formulation of Constrained NLPs
Reduced Gradient Algorithms Sections 14.1-14.2
Section 14.6

Week	Topics	Reading
10'	Formulation of Unconstrained NLPs Golden Section Search Gradient Search	Section 13.1 Section 13.2 Section 13.5
11'	Formulation of Constrained NLPs Reduced Gradient Algorithms	Sections 14.1-14.2 Section 14.6

Computer Support

The course can be effectively conducted using only standard class optimization software such as GAMS, AMPL, or LINGO. It is strongly recommended that students use such software to solve all assigned formulations that have numbers.

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Sample Syllabus for a Semester Introduction to Deterministic Operations Research

using Optimization in Operations Research by Ronald L. Rardin, Prentice Hall, 1998