Advanced Operations Research-II

Paper Code: 
24MAT423(A)
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Understand the basic concepts of non-linear programming problems.
  2. Understand the quadratic programming problems, Geometric programming problems,   Replacement problems, Dynamic programming problems, network analysis problems.

 

Course Outcomes: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

 

24MAT

423(A)

 

 

Advanced Operations Research-II

 (Theory)

 

 

 

CO154: Solve simple problems of replacement and implement practical cases of decision making under different business environments, like staff recruitment problems.

CO155: Derive the necessary conditions (KT conditions) for constrained nonlinear optimization problems and be able to solve quadratic programming problems.

CO156: Apply knowledge to solve separable, geometric programming problems.

CO157: Explain the dynamic programming techniques and demonstrate its applicability in decision making situations that require making a sequence of interrelated decisions.

CO158: Determine the optimal allocation of jobs to machines by minimizing total elapsed time in sequencing and to find solutions to network scheduling problems using s PERT-CPM.

CO159: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions,  Topic  presentation, Assigned tasks

 

 

Quiz, Class Test, Individual projects,

Open Book Test, Continuous Assessment, Semester End Examination

 

 

(Note: Non-Programmable scientific calculator up to 100 MS is permitted)

 

Unit I: 
Replacement models:
15.00

Gradual failure, Sudden failure, Replacement due to efficiency deteriorate with time, Staffing problems, Equipment renewal problems.

 

Unit II: 
Nonlinear Programming:
15.00

Formulation and graphical method for unconstrained problem of maxima and minima, constrained problem of maxima and minima Lagrangian method, Khun-Tucker condition. Quadratic programming: Wolf and Beals method.

 

Unit III: 
Separable programming and Geometric programming:
15.00

Definition, Reduction to separable programming problem to LPP, Separable programming algorithm. Geometric programming: Formulation and solution of GPP (Unconstraint type and with quality constraint).

 

Unit IV: 
Linear fractional programming:
15.00

 Definition, Linear fractional algorithm, Computational procedure of fractional algorithm. Dynamic programming: Introduction, Bellman principle of optimality model –I, II and III, Solution of LPP by dynamic programming.

 

Unit V: 
Sequencing and Network Scheduling:
15.00

Network Scheduling by PERT-CPM, Network logical sequencing, Concurrent activities, Critical path analysis, Probability consideration in PERT, Distinction between PERT and CPM.

 

Essential Readings: 
  • S. D. Sharma, Operations Research, Kedar Nath Ram Nath and Co. 2002.
  • Kanti Swarup, P.K.Gupta and Manmohan, Operations Research, S. Chand and Company Ltd, New Delhi, 2007.
  • Hamady A. Taha, Operations Research an Introduction, Prentice Hall.2007.
  • B.S. Goel and S.K. Mittal, Operation Research, Pragati Prakashan, 2014. 

SUGGESTED READING

  • S. I. Gass, Linear Programming, McGraw Hill Book Co.1965.
  • F.S. Hiller and G.J. Lieberman, Introduction to Operations Research, Addison Wesley, 2011.
  • R.S. Garfinkel and G.L. Nemhauser, Integer Programming, Wiley, New York, 1972.
  • G. Hadley, Linear programming, Oxford and IBH Publishing, New Delhi, 1962.
  • P.K. Gupta and D.S. Hira, Problem in Operation Research, S. Chand and Co. New Delhi, 2010.

e- RESOURCES

JOURNALS

 

Academic Year: 
2024-2025
  • Printer-friendly version
  • PDF version