DOC/LP/01/28.02.02
LP- ME 1018
LESSON PLAN
LP Rev. No: 01
Date: 07.12.09
Sub Code & Name : ME 1018 – OPERATIONS RESEARCH
Unit:
I
Branch:
ME
Semester :
VIII
Page 1 of 4
Unit syllabus: LINEAR MODEL : The phases of OR study – formation of an L.P model- graphical
solution – simplex algorithm – artificial variables technique– Big M method, two phase method.
Objective: At the end of the Unit the students will be able to Formulate LPP from the given statements and
solve them both graphically and by Simplex methods.
Session
No
1
2
3
4
5
6
7
8
Topics to be covered
Introduction, Phases of OR study, Types of Data, Optimisation Techniques
for various types of data: OR- Definition, Applications, Various OR
techniques.
Mathematical Formulation of Decision Problems – Steps – a discussion and
it’s importance
Problems on Mathematical Formulation
Problems on Mathematical Formulation
Problems on Mathematical Formulation
Problems on Mathematical Formulation
Graphical method solution to LPP (with illustration)
All possible forms of solution to LPP - discussion & illustrations
Additional problems on graphical solution
Simplex method solution to LPP –ordinary form, std and canonical form of
LPP , Principle behind Simplex method– initial ,basic, feasible and basic
feasible solution to LPP – a discussion.
Simplex Procedure– Steps – optimal solution to LPP (with illustration )
Time
(mins)
20
50
50
50
50
20
30
50
25
1,2,3,
4,5
1,2
25
Problems on Simplex Method – different types with illustrations
10
Problems on LPP ( at least 2 problems ) for various types of solution to
LPP ( Unique, alternate, unbounded and infeasible solution to LPP.
Tutorials on Graphical and Simplex method
50
Big M Method and Two phase method solution to LPP procedure. – a discussion.
Problem solving by Big M Method and Two phase method
20
13
Solving additional problems on Big M and Two Phased methods
50
14
Tutorials on Big M method and Two Phased Simplex Method
50
15
Revision – Unit 1
50
12
Teaching
Aids
30
9
11
Ref
1,2
50
50
30
1,2,3,
4,5
1,2,4,
5
1,2,4,
5
1,2,3,
4
3,4,5,
BB
DOC/LP/01/28.02.02
LP- ME 1018
LESSON PLAN
LP Rev. No: 01
Date: 07.12.09
Sub Code & Name : ME 1018 – OPERATIONS RESEARCH
Unit:
I I and III
Branch:
ME
Semester :
VIII Page 2 of 4
Unit syllabus:
2. TRANSPORTATION PROBLEM : Optimal solution by north west corner method- least cost method
– Vogel’s approximation method – optimality test – MODI method. Assignment problem – formulation –
Hungarian method -unbalanced assignment problem.
3. NETWORK MODELS: Shortest route – minimal spanning tree - maximum flow models – project
network- CPM and PERT network-critical path scheduling.
Objective: At the end of these unit the students will be able to formulate Transportation problems and
solve it by various methods to find initial solution and later find optimal solutions. They would be able to
solve assignment problems. Understand project management through drawing precedence diagrams,
calculating project completion times and identifying critical paths.
Session
No
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Topics to be covered
Introduction to Transportation models: Formulation.
Balanced and unbalanced transportation models.
Initial solution to transportation problems. – North West Corner method, Least
Cost method and VAM method of getting solutions.
Solving additional problems on initial basic feasible solution
Solving problems on Transportation models - Unbalanced type.
Solving problems on Transportation models – Degeneracy, Finding Optimal
Solution by Stepping stone and MODI method.
Solving problems on transportation models
Tutorials on Transportation problems
CAT 1
Introduction to Assignment problems-Formulation, Illustration, problems.
Solving additional problems on Assignment
Tutorials on Assignment Problems and Revision –Unit 2
Network Analysis – Network Diagrams –AOA and AON Diagrams - Dummy
Activities – Numbering of nodes using Fulkerson’s rule.
CPM & PERT techniques – an introduction. CPM -Time Computations.
Slacks and Floats – an introduction about forward and backward recursive
algorithms for time computations (CPM)
Problems on CPM
Probable time estimates – optimistic, pessimistic and most probable time
estimates – PERT/Time calculations. Computation of probability of
completing the project
Problems on PERT & CPM
Network Models: Introduction to Shortest Path Method, Minimum Spanning
Tree and Maximum Flow method, Shortest path: Systematic method problems
Shortest Path: Dijkstra’s Algorithm and problems, Flyod’s Algorithm and
problems.
Additional Problems on Floyd’s algorithm. Minimum Spanning Tree:
Kruskal’s algorithm and problems. PRIM method and problems.
Maximum Flow method: problems, Labelling method- applications and
problems
Revision –Unit 3
CAT 2
Time
(mins)
Ref
Teachin
g Aids
30
20
50
50
50
50
50
BB
3,4,5
50
50
50
50
50
50
3,4,5
BB
50
50
50
50
50
50
DOC/LP/01/28.02.02
LP- ME 1018
LESSON PLAN
LP Rev. No: 01
Sub Code & Name : ME 1018 – OPERATIONS RESEARCH
Unit:
IV
Branch:
ME
Semester :
VIII
Date:07.12.09
Page 3 of 4
Unit syllabus :
4. REPLACEMENT MODELS: Replacement of items that deteriorate with time – value of money
changing with time –not charging with time – optimum replacement policy – individual and group
replacement. Sequencing problem: models with n jobs with 2 machines – problem with n jobs with 3
machines.
5. QUEUING THEORY: Queuing models – queuing systems and structures – notation –parameter –
single server and multi server models – Poisson input – exponential service – constant rate service – infinite
population.
Objective: At the end of these units the students would be able to understand the issues behind replacement
of equipment that deteriorate with time, and those that deteriorate suddenly. They would understand the
procedure of processing n jobs through w machines and 3 machines respectively. The students would be
able to understand the concept of queues with single and multi servers.
Session
Time
Teaching
(mins)
No
Topics to be covered
Ref
Aids
Replacement models- Introduction, Replacement of items that deteriorate
35
with time. Case 1- Value of money does not change with time50
Illustration.
Solving problems on Case 1
50
36
Solving problems on Case 1
50
37
Case 2 Value of money changes with time
50
38
Solving problems on Case 2
50
39
Replacement of items that fail suddenly-individual and group
40
50
3,4,5
replacements.
BB
Additional problems on group replacements.
50
41
Sequencing-Introduction, Terminology, assumptions, and notations,
42
50
Problems on processing n jobs on 2 machines
Solving additional problems on processing n jobs on 2 machines
50
43
Introduction and illustration processing n jobs on 3 machines
50
44
Problems on processing n jobs on 3 machines
50
45
Revision Unit 4
50
46
Queuing theory : Queuing models : Assumptions : Queuing Costs :
47
50
Queuing Terminology
Elements of Queues – Kendell – Lee Notation A discussion.
48
50
Probability Distribution in Queuing models : Poisson
49
1,2,3,
and Exponential Distribution in arrival and service time – Service Rules
50
4
– Limited and unlimited queues and system – Characteristics of Queuing
BB
models
Single server and Multi sever Queues – Probability and performance
50
50
measures – a discussion.
Single server queuing models – performance measures – discussion with
51
50
problems.
Multi- server queuing models – performance measures – discussion with
52
50
problems.
Tutorials and Revision - unit 5
53
50
Introduction to additional topics - Inventory Management.
50
54
55
Introduction to additional topics – Game Theory
CAT 3
50
75 minutes
DOC/LP/01/28.02.02
LP- ME 1018
LESSON PLAN
LP Rev. No: 01
Date: 07.12.09
Sub Code & Name : ME 1018 – OPERATIONS RESEARCH
Unit:
Branch:
Semester :
ME
VIII
Page 4 of 4
Course Delivery Plan:
Week
Units
1
2
3
4
5
6
7
8
9
10
11
12
13
I II I II I II I II I II I II I II I II I II I II I II I II I II
1
2
3
4
5
References:
1.
2.
3.
4.
5.
Operations Research –An introduction - HAMDY .A.TAHA. Prentice Hall of India
Private Limited, New Delhi, 2006.
Operations Research – Principles and Practice – Ravindran , A., Phillips, D.T. and
Solberg, J.J., John Wiley Sons Singapore, 2001.
Operations Research Dr. S.D. Sharma, Kedamath Ram Natha & Co 2002.
Introduction to Operations Research – Prem Kumar Gupta and Hira, S.Chand & Co.
New Delhi- 2002.
Problems in Operations Research – Prem Kumar Gupta and Hira, S.Chand & Co.
New Delhi- 2002
Prepared by
Signature
Name
Designation
Date
Mrs. N.Rajeswari
Asst. Professor, Dept. of Mech. Engg.
07.12.09
Approved by
Dr.N.Nallusamy
Prof and HOD-ME
07.12.09