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ROWAN
UNIVERSITY

Department
of Mathematics

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Syllabus

**Math 03.411
Deterministic Models in Operations Research
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**Catalog Description**

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**Math 03.411 Deterministic Models in Operations Research 3
s.h.
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(Prerequisites:
(Math 01.230 Calculus III or Math 01.141 Accelerated Calculus II) and
(Math 01.210 Linear Algebra **or **Math 01.235
Math for Engineering Analysis I) with a C- or better in all prerequisites.)

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, inventory theory, assignment and transportation problems, dynamic programming and sensitivity analysis. 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. 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**

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

7.
Deterministic
Inventory Theory

Continuous-Review Models

Periodic-Review Models

Modeling Corporate “Goodwill”

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 prepare solutions to class projects and be required
to make a brief presentation at the end of the semester. Additional methods,
such as journal reviews, may also be used.

d)
**Course Evaluation**

The course will be evaluated through customary
student evaluations as well as regular departmental review.