Rowan
University

Syllabus

**1703.511
Operations Research I**

**Catalog
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.