Rowan
University
Department of Mathematics
Syllabus
1703.511
Operations Research I
Catalogue Description
1703.511Operations
Research I 3
s.h.
(Prerequisites:
an undergraduate course in linear algebra and an undergraduate course in
multivariate calculus or permission of the instructor.)
This course is an introduction to mathematical modeling, analysis, and solution procedures applicable to decision-making problems in deterministic environment. Methodologies covered include the simplex and interior point methods of solving linear programming models, project planning, network optimization, assignment and transportation problems, dynamic programming and game theory. Solutions will be obtained using theoretical methods and software packages.
a)
Objectives in Relation to
Student Outcomes
Students in this course will become familiar with
the process of Operations Research: learning how to create and validate a
mathematical model, as well as the processes and optimization/sub-optimization. They will learn how to determine solutions
using linear and dynamic programming.
They will also learn how to make an optimal set of assignments, based on
a set of costs or demands. They will
learn how to determine optimal shipping and inventory policies. Students will also learn how to determine
optimal project scheduling plans and strategies in "games." All of
the types of modeling covered in this course will be deterministic, that is,
lacking any uncertainty. Reliance on
the tools in the Calculus and Linear Algebra will be substantial, but we will
also examine the reasons why these tools provide us with an optimal solution in
each scenario. In addition, we will
examine how multiple modeling procedures can be used to arrive at the same
result, as well as the benefits and pitfalls of the different techniques. Furthermore, students will learn a procedure
called sensitivity analysis, which is
used to determine what types of changes are necessary for our optimal solution
to become sub-optimal. Use of some of the leading software in the field, which
is included in the text, will be required.
b)
Topical Outline (Additional graduate topics denoted by *)
1.
History
of Operations Research
2.
Operations
Research Modeling Approach
Model Formation
Solution Derivation
Model Validation and Implementation
3.
Linear
Programming
Graphical Methodology
Simplex Method
Shadow Prices
Slack and Surplus Variables
Post-Optimality Analysis
Selected Interior-Point Algorithms
Duality Theory
Dual-Primal Simplex Algorithm
Sensitivity Analysis
Computer Implementation
4.
Transportation
and Assignment Problems
Using Dummy Variables
Big-M Method
Linear Programming Representation
Computer Implementation
5.
Integer
Programming
Binary Integer Programming Problems
Mixed Integer Programming Problems
Branch-and-Bound Algorithm
Computer Implementation
6.
Deterministic
Dynamic Programming
Characteristics of Dynamic Programming Problems
Development of Algorithms to Solve DP Problems
Polynomial, Non-Polynomial (NP) Complete and NP Hard
Algorithms*
Solving Linear Programming Models Using Dynamic
Programming*
Curse of Dimensionality*
7.
Deterministic
Inventory Theory
Continuous-Review Models
Periodic-Review Models
Modeling Corporate “Goodwill”
8.
Game
Theory*
Two-Player, Zero-Sum Games
Games with Mixed Strategies
Solving Using Linear Programming
9.
Network
Optimization*
Shortest Path Problems
Minimum Spanning Tree
Minimum Cost Problems
Maximum Flow Problems
10.
Project
Management Using Program Evaluation and Review Technique (PERT) and Critical
Path Method (CPM)*
Project Scheduling
Time-Cost Tradeoffs
c)
Evaluation and Grading
Students will be evaluated by traditional methods of
homework, which will include analytic and computer-based problems, and written
exams. Students will also be required
to devise and complete a substantial project.
Possible projects can come from applied problems in the student’s major,
an application from the individual’s place of employment, applications in
relevant journals, theoretical derivations of solutions, research on a topic
not covered in the course, or in the form of annotated bibliographies. A presentation on the project will be
required.
d)
Course Evaluation
The course will be evaluated through customary
student evaluations as well as regular departmental review.