COM 3504 Management Science


This course provides an overview of the nature and applications of Management Science/ Operations Research (MS/OR).  After surveying a variety of small and large practical problems which can be approached using the methods of management science, students will be able to formulate mathematical models of practical problems, then to solve them and finally to interpret the results, as they might have to do, as managers and business executives of large enterprises making decisions.

 

The major topics covered are Introduction to Management Science, Linear Programming: Model formulation and applications, Graphical Method, Simplex Method, Transportation Problem, Assignment problem, Network Flow Models, Project Scheduling: PERT/CPM Network, Decision analysis, and Dynamic programming.

  • Introducing some of the techniques, methodologies and models used in Operations Research.
  • Developing the ability to formulate models for practical decision making situations in different functional areas of business.
  • Becoming familiar with the techniques available to structure mathematical models.
  • Solving the resulting models.
  • Developing an ability to interpret the solutions to these problems.

Upon completion of this course, the students will be able to:

  • Formulate mathematical models of practical problems in Marketing, Production / Operations Management, Finance, Accounting, Human Resources and other areas of business, then to solve them and finally to interpret the results as they might have to do, as managers of large enterprises making decision.

1. Introduction to Operations Research
1.1 Introduction
1.2 Historical Development
1.3 Definitions of Operations Research
1.4 Models in Operations Research
1.5 Elements of Model Construction..
1.6 Scientific Method in OR/ Phases of OR Study
1.7 Operations Research Techniques.

2. Linear Programming : Model Formulation and Applications
2.1 Introduction
2.2 Structure of Linear Programming Model
2.3 General Mathematical model of Linear Programming Model.
2.4 Model Formulation
2.5 Examples of LP Model Formulation (LP Applications)

3. Linear Programming : The Graphical Method
3.1 Introduction
3.2 Graphical Solution Method.
3.3 Extreme Point Enumeration Approach
3.4 Iso- profit (Cost) Function Approach
3.5 Special Cases
3.6 Alternative (or Multiple) Optimal Solutions, Unbounded solution, Infeasible Solution, Redundancy.

4. Linear Programming : The Simplex Method
4.1 Introduction
4.2 Standard Form of the LP Model
4.3 Setting up the Initial Simplex Tableau
4.4 Improving the Solution
4.5 Stopping Criterion
4.6 Solving a Minimization Problem Using the Simplex Method
4.7 Special Cases
4.8 Infeasibility, Unbounded ness, Alternative (Multiple) Optimal Solutions, Degeneracy
5. Transportation Problem
5.1 Introduction
5.2 A Network Model and LP Formulation for a Transportation Problem
5.3 Transportation Tableau
5.4 The Balanced Transportation Problem
5.5 Methods for Finding Initial solution
5.6 North – West Corner Method
5.7 Least Cost Method
5.8 Vogel’s Approximation Method (VAM)
5.9 Determining an Optimal Solution
5.10 The Stepping-Stone Method
5.11 Modified Distribution (MODI) Method
5.12 Variations in Transportation Problem
5.13 Unbalanced Supply and Demand
5.14 Degeneracy
5.15 Alternative / Multiple Optimal Solutions
5.16 Prohibited Routes
5.17 Maximization Transportation Problem

6. Assignment Problem
6.1 Introduction
6.2 LP Formulation of the Assignment Problem
6.3 Difference Between Transportation Problem and Assignment Problem
6.4 The Hungarian Method for Solving an Assignment Problem
6.5 Variations of the Assignment Problem
6.6 Multiple Optimal Solutions
6.7 Maximization Case in Assignment Problem
6.8 Unbalanced Assignment Problem
6.9 Restrictions on Assignments

7. Network Flow Models
7.1 Network Components
7.2 The Shortest Route Problem
7.3 The Shortest Route Solution Approach
7.4 The Minimal Spanning Tree Problem
7.5 The Minimal Spanning Tree Solution Approach
7.6 The Maximal Flow Problem
7.7 The Maximal Flow Solution Approach

8. Project Scheduling : PERT/CPM Network
8.1 Introduction
8.2 Preparation of (Network) Arrow Diagram
8.3 Activity Time Estimates
8.4 Computations for Critical Path
8.5 Determination of the Critical Path
8.6 Probability Considerations in Project Scheduling
8.7 Cost Considerations in Project Scheduling (Time-Cost Trade – Offs)

9. Decision Analysis
9.1 Structuring the Decision Situation : Payoff Tables
9.2 Decision Making without Probabilities
9.3 The Criterion of Optimism (Maximax or Minimin)
9.4 The Criterion of Pessimism (Maximin or Minimax)
9.5 The Minimax Regret Criterion (Savage Criterion)
9.6 The Hurwicz Criterion (The Criterion of Realism.)
9.7 The Equal Likelihood Criterion (Laplace Criterion.)
9.8 Decision Making with Probabilities
9.9 Expected Monetary Value (EMV)
9.10 Expected Opportunity Loss (EOL)
9.11 Expected Value of Perfect Information (EVPI)
9.12 Decision Trees. (Graphical Diagram of the Decision making Process).

10. Dynamic (Multistage) Programming
10.1 Introduction
10.2 Fundamental Concepts of Dynamic Programming
10.3 Applications of Dynamic Programming (Students ate expected to develop the Network models associated with simple problems and find the optimal solutions.)

Lectures, seminars, course manuals, workshops, assignments, self study

  • සරත් එස්. නාඔටුන්න, (2008), සංකාර්ය පර්යේෂණ/කළමනාකරණ විද්‍යාව : සිද්ධාන්ත සහ භාවිතය, තරංජි පි‍්‍රන්ට්ස්.
  • David R. Anderson, Dennis J. Sweeney, and Thomas A. Williams (2007). An Introduction to Management Science : Quantitative Approaches to Decision Making, 11th Edition, Thomson South – Western .
  • Frederick S. Hillier and Gerald J. Lieberman, (2005) Introduction to Operations Research, 8th Edition, McGraw Hill, New York.
  • Hamdy A. T. (2008), Operations Research : An Introduction, 8th Edition, Prentice Hall: New Delhi.
  1. Sang M. L, Laurence J. M., and Taylor, B.W (1981), Management Science, Wm.C. Brown Company Publishers.