Operations Research I

Goal: This course is designed to provide the students with the knowledge of the techniques of operations research and their applications.

General Objectives: On completion of this course, the diplomat should be able to:

1. Understand the nature of operations research.

2. Understand the definition and scope of linear programming.

3. Understand the graphical method of solving linear programming problems (involving only two variables).

4. Understand the simplex method of solving linear programming problems.

5. Understand sensitivity analysis.

6. Understand the principle of duality and its application.

7. Understand transportation and assignment problems

8. Understand network analysis.

1 1.1 Define operations research.

1.2 Outline the history of operations research.

1.3 Explain the concept of model building in operations research.

1.4 State the principles of modeling.

1.5 State the advantages and disadvantages of models in operations research.

Explain and discuss the concepts covered

2  2.1 Define linear programming.

2.2 Define a linear programme.

2.3 State the scope of linear programming.

2.4 Explain linear megnalities, their graphs and solutions.

2.5 State the two methods of solving linear Programming problems e.g. graphical and Explain and discuss the concepts covered

3 3.1 Draw graphs for the constraints of a linear programming problem

3.2 Identify the feasibility region in 3.1 above.

3.3 Identify the vertex of the feasibility region in 3.2 above.

Explain and discuss the concepts covered

4 3.4 Identify feasibility solution area (convex region).

3.5 Locate the vertices for the solution using the objective function.

3.6 Solve problems in two variables

Explain and discuss the concepts covered

5 4.1 Develop the simplex algorithm.

Explain and discussthe concepts covered

6 4.2 Identify basic variables, non-basic variables shadow prices (cost, evaluations etc).

4.3 Develop the simplex method with equalities as constraints.

7 4.4 Apply the simplex method to problems involving few variables.

4.5 Make use of a computer package for the simplex method

8 5.1 Explain sensitivity analysis techniques.

5.2 Apply the techniques of sensitivity analysis to some practical problems.

9 6.1 Derive dual linear program from primal program.

6.2 Solve optimization problems graphically using dual linear program.

10 6.3 Solve optimization problems by the dual simplex method.

6.4 Obtain the solution of the dual program from the primal program

11 7.1 Define transportation problems.

7.2 Explain northwest corner methods for starting a transportation problem.

7.3 Solve simple transportation problems using the simplex method.

7.4 Explain least-last rule as an alternative method of solving transportation problems.

7.5 Use a computer package to solve a

12 7.6 Solve an assignment problem as a special transportation problem.

7.7 Explain the row/column methods for solving assignments problems.

7.8 Use a computer package to solve an assignment problem

13 8.1 Define network analysis.

8.2 List some examples of network flow problems.

8.3 State and explain the origin of PERT and CPM techniques as aids to efficient project management.

8.4 List some applications of PERT and CPM in project managements.

8.5 Explain and evaluate the earliest and latest event times, float times and project completion time.

14 8.6 Estimate optimistic, pessimistic, most likely times.

8.7 Construct dependency tables and PERT networks

15 8.8 Explain a critical path and methods of identifying.

8.9 Evaluate project completion times; least cost

8.10 Use a computer package to solve a PERT network