ADVANCED OPERATIONS RESEARCH-II (Optional Paper)

Paper Code: 
MAT423A
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.

Learning Outcomes

Learning and teaching strategies

Assessment

After the completion of the course the students will be able to:

CLO114- Understand and Solve Replacement problems.

CLO115- To derive the necessary conditions (KT conditions) for constrained nonlinear optimization problems and able to solve quadratic programming problems.

CLO116- Derive methods to solve separable, geometric programming problems.

CLO117- Discuss various methods to solve linear fractional programming problems and dynamic programming problems.

CLO118- Explain problems related to sequencing and PERT-CPM to solve network analysis problems.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical

 

 

 

 

Presentations by Individual Students

Class Tests at Periodic Intervals.

Written assignment(s)

Semester End Examination

 

Unit I: 
I
15.00

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

Unit II: 
II
15.00

Nonlinear Programming: Formulation and graphical method for unconstrained problem of maxima and minima,Constrained problem of maxima and minimaLagrangian method, Khun-Tucker condition.Quadratic programming: Wolf and Beals method.

Unit III: 
III
15.00

Separable programming: 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: 
IV
15.00

Linear fractional programming: Definition, Linear fractional algorithm, Computational procedure of fractional algorithm.Dynamic programming: Introduction, Bellman principle of optimalitymodel –I, II and III, Solution of LPPby dynamic programming.

 

Unit V: 
V
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. 1992.
  • Kanti Swarup, P.K.Gupta, Manmohan, Operations Research, S.Chand and Company Ltd, New Delhi, 2007.
  • Hamady A. Taha, Operations Research an Introduction, Prentice Hall.2007.
  •  B.S. Goel, S.K.Mittal, Operation Research, Pragati Prakashan, 2014. 

 

References: 

  • S. I. Gass, Linear Programming, McGraw Hill Book Co.1958.
  •  F.S.Hiller, 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, D.S.Hira, Problem in Operation Research, S.Chand and Co. New Delhi,2010.

 

 

Academic Year: 
2019-2020
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