## OPERATION RESEARCH (CCE)

 SHE Level 4 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code MHH324729 Module Leader Martin MacDonald School School of Computing, Engineering and Built Environment Subject SCEBE - School Office Trimesters A (September start) B (January start)

### Summary of Content

The aim of the course is to introduce students to use quantitive methods and techniques for effective decisions-making; model formulation and applications that are used in solving engineering decision problems.

### Syllabus

History and development of OR, Applications, modelling in operation research, O.R. models and their applications. Formulation of Linear Programming Problem, Graphical solution, Simplex procedure for maximization and minimization, Duality concept, Sensitivity analysis under different situations. Mathematical formation of Assignment problem, methods to solve balanced and unbalanced assignment problems, Maximization problems, Assignment with restrictions, Travelling salesman problem. Mathematical formulation of Transportation problem, methods to obtain initial basic feasible solution (IBFS), NWCR and VAM, conditions for testing optimality, MODI method for testing optimality solution of balanced and unbalanced problems, Degeneracy and its resolution. Introduction to Game Theory, Minimax and maximin principle, Solution of zero sum two persons games - Saddle point algebraic method, Dominance properties, Graphical method and solutions of games by LPP. Introduction to Queuing Model, Queuing system, Transient and steady states, Terminology, Probability distributions in queuing models, Kendall's notation classification of queuing models, Model I (M/ M/ I) : (00/fcfs) birth and death model, General Erlang queuing model, Model II - Simulation of Queuing model. Network diagram representation, Critical Path Method (CPM) and PERT method, time estimates, crashing, time charts, PERT and CPM for project scheduling, resource planning, case studies.

### Learning Outcomes

On completion of this module the student should be able to:1. Formulate LP problems (AM1). 2. Describe the logic underlining the steps in solving LP problems by the Simplex method (AM1). 3. Formulate the dual problem; use the Dual Simplex method to find the optimal solution of an LP (AM1, AM5). 4. Conduct sensitivity analysis (AM5). 5. Formulate and solve the transportation and assignment problems (AM1). 6. Describe and solve Game Theory problems (AM1). 7. Describe the elements of a queuing model and the role of the exponential distribution in queuing models (AM1, AM5). 8. Use CPM and PERT to find the critical path and time schedule of project (AM1, AM5).

### Teaching / Learning Strategy

The main teaching method will be based on lectures. Tutorials will be used to reinforce the module material and to discuss the issues raised by the directed reading.

-360 1. Hamdy A Taha, (2006) Operations Research, 8 th Edition, Pearson Prentice Hall, NJ 07458. 2. S. D. Sharma.(2009) Operation Research, Kedarnath and Rannalt Publications, 3. Hiller F.S, and Liberman G.J. (2001) Introduction to Operation Research, 7 th Edition, McGraw Hill. Ronald. L. Rardin, (2002) Optimization in Operation Research, Pearson Education, Asia.

### Transferrable Skills

Lectures, Tutorial Questions, further development of skills problem solving, numerical analysis, Implement Practical cases.

### Module Structure

Activity Total Hours
Tutorials (FT) 28.00
Assessment (FT) 16.00
Lectures (FT) 56.00
Independent Learning (FT) 100.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 3.00 50.00 45% Final Examination - Unseen written examination-3 Hours
Exam (School) 1.50 20.00 n/a Mid-Term Test - Unseen written examination-1½ Hours
Coursework 1 n/a 30.00 n/a Open-ended industry related case Study report of 2000 words