Advanced Operations Research-II

Paper Code: 
MAT 423A
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 (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

MAT 423A

 

 

Advanced Operations Research-II

 (Theory)

 

 

 

The students will be able to –

 

CO152: Solve simple problems of replacement and implement

practical cases of decision making under different business

environments like staff recruitment problems.

CO153: To derive the necessary conditions (KT conditions) for constrained nonlinear optimization problems and able to solve quadratic programming problems.

CO154: Apply knowledge to solve separable, geometric programming problems.

CO155: Discuss various methods to solve linear fractional programming problems and dynamic programming problems.

CO156: Define the dynamic programming technique concepts and demonstrate its applicability in decision making situations, which require to make a sequence of interrelated decisions.

CO157: Determining 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.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

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

 

 

 

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 minima Lagrangian 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 optimality model –I, II and III, Solution of LPP by 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. 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. 

 

References: 
  • 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.

 

Academic Year: 
2023-2024
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