Operations Research Course File

Sree Vidyanikethan Engineering College

VARDHAMAN COLLEGE OF ENGINEERING

Shamshabad 501218, Hyderabad, AP

www.vardhaman.org

VARDHAMAN COLLEGE OF ENGINEERING

Shamshabad 501218, Hyderabad, AP

www.vardhaman.org

Department of

Mechanical EngineeringCOURSE FILEAcademic Year:2010 -11

Semester : Odd / Even

Faculty Details

Name of the Faculty:N. Srinivasa ReddyDesignation

:Assistant Professor

Department :M.ECourse Details

Name of the Course: B.Tech / M.Tech

Batch

:2007Branch/Specialization: M.E

Regulations:R07Class

: I / II / III / IVSize:56Semester: I / II

Title of the Subject: OPERATIONS RESEARCHSubject Code

:07A7EC03

Nature of the Subject: Core / Elective / Basic / AdvancedNo. of Weeks

: _15_

No. of periods/week: _05_ ( 04 Lectures +_01 Tutorials)

Note:

1. The question papers in respect of Objective Tests (OT I and OT II) and Descriptive Tests (DT I and DT II) of this subject should be included in the course file.

2. Time Table and syllabus copy provided to you must also be filed in it.

3. Attach marks statement of the students in respect of OT I, OT II DT I and DT II for this subject in your course file.

4. Photocopy of the best and the worst answer sheets for OT I, OT II, DT I and DT II, be included in the course file.

5. List of Assignments / Seminar topics you have given to the students should also be included in the course file.6. The J. N. T. University End Examination Question Paper for this subject must be included in the course file.

7. A record of the best and worst marks achieved by the students in every quiz tests must be maintained properly.

8. Additional resources like OHP transparences, handouts, course material, lecture notes used may also be filed in it.

Department of

Mechanical EngineeringSTATUS PAPERAcademic Year: 2010 -11


Name of the Faculty

:N.SRINIVASA REDDYSubject

: OPERATION RESEARCH

Subject Code: 07A7EC03Class & Branch / Specialization: IV B.TECH I SEM / MECHANICAL1.TARGET:1.1. Percentage Pass: ___100____

1.2. Percentage above 60% of Marks: ____80__

2.COURSE PLAN:(Please write how you intend to cover the contents: i.e., coverage of units by lectures, guest lectures, design exercises, solving numerical problems, demonstration of models, model preparation, or by assignments etc.)

1. Coverage of Subject, unit-wise by teaching in the class 2. Student interaction with the subject, by applications in daily life examples

3. Solving numerical problems related to topic and additional problem to solve on their own in the class.

4. Assignments from previous question papers

5. Handouts for both theory and problem for self practicing the subject other than class hours

6. Quiz and brain storming etc. techniques to learn the subject fast & applications

7. Latest updates from internet and videos related to concept provided to the student

8. Uploading Previous Year Papers & Their solutions for future reference for Regular External Exams.3.Method of Evaluation:

3.1 Continuous Assessment Examinations

: Yes / No3.2 Assignments / Seminars

: Yes / No

3.3 Mini Projects

: Yes / No

3.4 Subjective and Objective as per University Norms: Yes / No3.5Others: (Please Specify)

4.List out any Additional / New topics / Topics-Beyond-Syllabus or any innovation you would like to introduce in teaching the subject in this semester:

1. Seminars by students by browsing the subject related Websites & Journal, to get depth of knowledge beyond the class work2. Making students to join Technical Societies or Associations which organizing the subject research works, job opportunities, advance. topics info.3. Encourage the students to participate in conference papers (or) workshops conducted by technical institutions / organizations.Signature of HOD Signature of Faculty

Date: Date:

Department of

Mechanical EngineeringGUIDELINES TO STUDY THE SUBJECTAcademic Year: 2010 -11


Name of the Faculty


:OPERATIONS RESEARCH

Subject Code: 07A7EC03Class & Branch/Specialization: IV B.TECH I SEM / MECHANICAL1. Guidelines to Study the Subject:

1. Make the environment that creates interest to study the subject & regular to the class work in the process of

Teaching learning methodology

2. Seminars on any topic from the concern subject, which students likes to present more effectively, modifications (or) corrections by the concern faculty to learn the subject perfect.3. Tutorials for the weak students, to do more number of problems and explain the subject.4. Make class into groups and making group competitions like quizzes, Group Discussions etc..5. Problems practice from different text books and reference books and external exam papers.

6. Browse the internet and journals for advance topics of the subject and latest technology.

7. Making Prototype models or Analogy to deliver the subject more interactive.8. Assignments on each topic ,class tests to check the confidence level of the student on each topic

including theory and problematic2. On completion of this Subject / Course the Student shall be able to:

1. Students have an ability to apply knowledge of mathematics, science & engineering.2. Student have an ability to identify, illustrate, solve, formulate, distinguish & compare

different engineering problems.3. Students will able to demonstrate an ability to design and conduct experiments, analyze and interpret data

4. Student will show the understanding of impact of engineering solutions on the society and also will

be aware of contemporary issues

5. Student will develop confidence for self education and ability for life-long learning.

6. Student can participate and succeed in competitive examinations, seminars & conferences.

7. Students has the ability to use modern engineering tools, software and equipment to analyze problems.Signature of HOD Signature of Faculty

Date: Date:

Department of

Mechanical EngineeringCOURSE OBJECTIVESAcademic Year: 2010 -11


Name of the Faculty


: OPERATIONS REASEARCHSubject Code: 07A7EC03Class & Branch/Specialization: IV B.TECH I SEM / MECHANICALS. NoObjectivesOutcomes

1. Define &Formulate the Linear Programming Problem, utilization of Simplex method, Big M method, Two phase method to Maximize the profit & Minimize the lossA,B,E,F,G

2. Identify the Transportation problem to compile for least transportation cost, Select the Sequencing Problem to manipulate & modify the man hours to reduce the idle time. Solve & design the Assignment problem to assign the jobs to the workers on individual basis to complete the job in required time.B,E

3. Reproduce the items that deteriorate with time using replacement policy, predict the age of the item which requires replacement either with value of money counted or not. Justify &resolve the items that fail suddenly using individual or group replacement techniquesA,B,F

4. Design different optimal strategies to win the game, justify the games using minimax or maximini principle to compute the value of the game using saddle point or dominance rule or graphical methodA,B,C

5. List out different waiting lines & describe the trade off between cost of service and cost of waiting time, compute the performance using probability distribution.A,B,C

6. Define inventory model and different stocks & their computationsDistinguish between deterministic & probabilistic inventory models .how the price breaks influence the inventory controlA,C,F

7. Distinguish between Linear programming problem & Dynamic programming problem for solving a problem. Develop recursive function based on Bellmans principle of optimality to get an optimal solution. Select various dynamic programming models to strengthen a decision problem. A,E

8. Differentiate between analytical and simulation models , using Monte Carlo simulation technique for solving various types of problems. Develop random numbers ,design best solutions using computer languages for simulationD,E

Note: For each of the objective indicate the appropriate Outcomes to be achieved. Kindly refer to page number-6, to know the illustrative verbs that can be used to state the objectives.

Signature of HOD Signature of Faculty

Date: Date:

Department of

Mechanical EngineeringCOURSE OUTCOMESAcademic Year: 2010 -11


Name of the Faculty


: OPERATIONS REASEARCHSubject Code: 07A7EC03Class & Branch/Specialization: IV B.TECH I SEM / MECHANICAL1. The expected outcomes of the course / subject are:S. NoGeneral Categories of outcomesSpecific outcomes of the course

AAn ability to apply knowledge of mathematics, science and engineering

BAn ability to identify, formulate and solve engineering problems.

CAn ability to design and conduct experiments, analyze and interpret data.

DThe ability to use modern engineering tools, software and equipment to analyze problems.

EA knowledge of impact of engineering solutions on the society and also on contemporary issues.

FA recognition of the need for, and an ability to engage in self education and life-long learning.

GAn ability to use the techniques, skills and modern engineering tools necessary to face competitive examinations and engineering practices.

2. Objectives Outcomes Relationship Matrix (Indicate the relationship by X mark)Programme objectivesABCDEFG

1

2

3

4

5

6

7

8

Department of

Mechanical EngineeringCOURSE OBJECTIVES

VERBSAcademic Year: 2010 -11


These verbs can also be used while framing questions for Mid Term Examinations.

ILLUSTRATIVE VERBS FOR STATING GENERAL OBJECTIVES

Know

ComprehendUnderstand

ApplyAnalyze

DesignGenerate Evaluate

ILLUSTRATIVE VERBS FOR STATING SPECIFIC OBJECTIVES:

A. Cognitive Domain

123456

KnowledgeComprehension UnderstandingApplication

of Knowledge & ComprehensionAnalysisof Whole w.r.t its constituentsSynthesis

combination of ideas/constituentsEvaluationjudgment

Define

Identify

Label

List

Match

Reproduce

Select

State Convert

Defend

Describe (a Procedure)

Distinguish

Estimate

Explain why/how

Extend

Generalize

Give examples

Illustrate

Infer

SummarizeChange

Compute

Demonstrate

Deduce

Manipulate

Modify

Predict

Prepare

Relate

Show

SolveBreakdown

Differentiate

Discriminate

Distinguish

Separate

SubdivideCategorize

Combine

Compile

Compose

Create

Devise

Design

Generate

Organize

Plan

Rearrange

Reconstruct

Reorganize

ReviseAppraise

Compare

Conclude

Contrast

Criticize

Justify

Interpret

Support

B. Affective Domain C. Psychomotor Domain (skill development)

Adhere

Assist

Attend

Change

Develop

Help

Influence

InitiateResolve

Select

Serve

ShareBend

Calibrate

Compress

Conduct

Connect

Convert

Decrease

DemonstrateDissect

Draw

Extend

Feed

File

Grow

Handle

IncreaseInsert

Keep

Elongate

Limit

Manipulate

Move precisely

Operate

PaintPerform

Prepare

Remove

Replace

Report

Reset

Run

SetStraighten

Strengthen

Time

Transfer

Type

Weigh

Department of

Mechanical EngineeringCOURSE SCHEDULE

(Expected)Academic Year: 2010 -11

Semester : Odd/ Even

Expected date of completion of the whole Subject / Course and remarks, if any:

S.NoUnit NoDescriptionDuration (Dates)Total

No. Periods

FromTo

1. ILinear Programming Problems19th Aug2k1031st Aug2k10

11

2. IITransportation problemsSequencing problems

Assignment problems26th July2k1009th Aug2k10

16th Aug2k1030th Aug2k1011th Aug2k10

18th Aug2k1015

3. IIIReplacement of Items13th Aug 2k1014th Aug2k1005

4. IVTheory of Games12th July2k1024th July2k1009

5. VWaiting Lines (or) Queuing Theory27th Sept2k1014th Oct2k1010

6. VIInventory Models14th Sept2k1025th Sept2k1010

7. VIIDynamic Programming18th Oct2k1030th Oct2k1010

8. VIIISimulation01stSept2k10

04th Sept2k1005

Remarks (if any):

Signature of HODSignature of Faculty

Date:Date:

Department of

Mechanical EngineeringSCHEDULE OF INSTRUCTIONS



UNIT NO: I Expected date of completion: 01st Sept2k10

S. NoDateNo. of PeriodsSubject

Topics / Sub-TopicsObjectives &

Outcome Nos.References

Text Books

Journals

Websites

1.20 Aug101OR Introduction

Types of Models} A,B,E,F,GO.R J.K.Sharma

O.R S.D.Sharma

2.21Aug102Formulation of LPP Problem

Graphical MethodO.R J.K.Sharma

O.R S.Kalavathy O.R Iyer

3.23Aug101Maximize Z or Minimize Z

DualityO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.26Aug102Simplex method

Slack, Surplus & Artificial VariablesO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

5.27Aug102Big M method

O.R Iyer

O.R S.Kalavathy O.R J.K.Sharma

6.30Aug102Two Phase Method O.R J.K.Sharma

O.R S.D.Sharma

7.31Aug101Degeneracy & Duality PrincipleO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

Total No. of Periods

11Objectives and Outcomes achievedOBJECTIVE: Define &Formulate the Linear Programming Problem, utilization of Simplex method, Big M method, Two phase method to Maximize the profit & Minimize the lossOUTCOMES: An ability to apply knowledge of mathematics, science and engineering, An ability to Identify, formulate and solve engineering problems., A knowledge of impact of engineering solutions on the society and also on contemporary issues., A recognition of the need for, and an ability to engage in self education and life-long learning., An ability to use the techniques, skills and modern engineering tools necessary to face competitive examinations and engineering practices.


Date: Date:

Department of


(Expected)Academic Year:2010 -11


UNIT NO: II Expected date of completion: 20th Aug2k10




Text Books

Journals

Websites

1.26Jul102Transportation problem Introduction & Basic feasible solution by

NWCM method} B,EO.R J.K.Sharma

O.R S.D.Sharma

2.28Jul101Basic feasible solution by

LCM methodO.R J.K.Sharma

O.R S.Kalavathy

3.29Jul101Basic feasible solution by

VAM methodO.R S.D.Sharma

O.R Iyer

4.30Jul102Optimality test by MODI method & problemsO.R Iyer

O.R V.K.Kapoor

5.09Aug102Sequencing Introduction

Sequence of 2 machines & idle timeO.R S.Kalavathy O.R J.K.Sharma

6.11Aug101Sequence of 3 machines & idle time O.R J.K.Sharma

O.R S.D.Sharma

7.11Aug101Sequence of n machines & idle timeO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

8.11Aug101Problems on different machines &

their sequenceO.R S.D.Sharma

O.R Iyer

O.R Natarajan

9.16Aug102Assignment Problem introduction &

Hungarian methodO.R S.Kalavathy O.R Hiller O.R S.D.Sharma

10.18Aug102Traveling Sales man problem &

Maximum Profit & Unbalanced ProblemO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor


15Objectives and Outcomes achievedObjectives: compile for least transportation cost, Select the Sequencing Problem to manipulate & modify to reduce the idle time. Solve & design the Assignment problem to assign the jobs to the workers Outcomes :A knowledge of impact of engineering solutions on the society and also on contemporary issues. An ability to identify, formulate and solve engineering problems


Date: Date:

Department of




UNIT NO: III Expected date of completion: 16th Aug 2k10




Text Books

Journals

Websites

1.13Aug101Replacement introduction} A,B,FO.R J.K.Sharma

O.R S.D.Sharma

2.13Aug101Replacement of items that deteriorate with time when money value is not countedO.R J.K.Sharma


3.13Aug101Replacement of items that deteriorate with time when money value is countedO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.14Aug101Replacement of items that fail completelyO.R S.Kalavathy O.R Iyer

O.R Wagner

5.14Aug101Individual replacement &

group replacementO.R Iyer

O.R Wagner


05Objectives and Outcomes achievedObjectives: Reproduce the items that deteriorate with time using replacement policy, predict the age of the item which requires replacement either with value of money counted or not. Justify &resolve the items that fail suddenly using individual or group replacement techniques

Outcomes :An ability to apply knowledge of mathematics, science and engineering, An ability to identify, formulate and solve engineering problems. A recognition of the need for, and an ability to engage in self education and life-long learning


Date: Date:

Department of




UNIT NO: IV Expected date of completion: 25th Jul2k10




Text Books

Journals

Websites

1.12Jul101Theory of games introduction}A,B,CO.R J.K.Sharma

O.R S.D.Sharma

2.12Jul101Saddle point & theoryO.R J.K.Sharma


3.14Jul101Pure , mixed strategies & dominanceO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.16Jul101Problems on different StrategiesO.R Iyer

O.R V.K.Kapoor

5.16Jul101Value of the gameO.R Iyer

O.R S.Kalavathy

6.23Jul101Dominance property O.R J.K.Sharma

O.R S.D.Sharma

7.23Jul101Problems on dominanceO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

8.24Jul101Graphical method for mx2 gameO.R S.D.Sharma

O.R Natarajan

9.24Jul101Graphical method for 2xn gameO.R S.Kalavathy O.R Hiller


09Objectives and Outcomes achievedOBJECTIVE: Design different optimal strategies to win the game, justify the games using minimax or maximini principle to compute the value of the game using saddle point or dominance rule or graphical methodOUTCOMES: An ability to apply knowledge of mathematics, science and engineering. An ability to identify, formulate and solve engineering problems.An ability to design and conduct experiments, analyze and interpret data


Date: Date:

Department of




UNIT NO: V Expected date of completion: 14th Oct2k10




Text Books

Journals

Websites

1.Sept101Waiting lines introduction} A,B,CO.R J.K.Sharma

O.R S.D.Sharma

2.Sept101Single channelO.R J.K.Sharma


3.Sept101Poissons arrivalsO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.Oct101Exponential service times - finiteO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

5.Oct101Exponential service times - infiniteO.R Iyer


6.Oct103Multichannel

Exponential service times - finiteO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

7.Oct102Exponential service times - infiniteO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor


10Objectives and Outcomes achievedOBJECTIVE: List out different waiting lines & describe the trade off between cost of service and cost of waiting time, compute the performance using probability distribution OUTCOMES: An ability to apply knowledge of mathematics, science and engineering. An ability to identify, formulate and solve engineering problems. An ability to design and conduct experiments, analyze and interpret data


Date: Date:

Department of




UNIT NO: VI Expected date of completion: 26th Sep2K10




Text Books

Journals

Websites

1.Sept101Inventory introduction} A,C,FO.R J.K.Sharma

O.R S.D.Sharma

2.Sept101Single item deterministic modelO.R J.K.Sharma


3.Sept101Purchase inventory model with one price breakO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.Sept101Purchase inventory model with multi price breakO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

5.Sept101Shortages not allowedO.R Iyer


6.Sept103Stochastic modelsDemand may be discrete variable or continuous variableO.R J.K.Sharma

O.R S.D.Sharma

7.Sept102Instantaneous production and demand Continuous demand and no set up costO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor


10Objectives and Outcomes achievedObjective: Define inventory model and different stocks & their computations. Distinguish between deterministic & probabilistic inventory models .how the price breaks influence the inventory control

Outcomes: An ability to apply knowledge of mathematics, science and engineering. An ability to design and conduct experiments, analyze and interpret data. A recognition of the need for, and an ability to engage in self education and life-long learning


Date: Date:

Department of




UNIT NO: VII Expected date of completion: 30th Oct2K10




Text Books

Journals

Websites

1.Sept101Dynamic Programming introduction} A,EO.R J.K.Sharma

O.R S.D.Sharma

2.Sept102Bellmans Principle of optimalityO.R J.K.Sharma


3.Sept102Applications of dynamic programmingO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.Sept101Capital budgeting ProblemO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

5.Sept101Shortest path problemO.R Iyer


6.Sept101Linear Programming ProblemO.R J.K.Sharma

O.R S.D.Sharma

7.Sept102Problems related to Dynamic programmingO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor


10Objectives and Outcomes achievedObjective: Distinguish between Linear programming problem & Dynamic programming problem for solving a problem. Develop recursive function based on Bellmans principle of optimality to get an optimal solution. Select various dynamic programming models to strengthen a decision problem

Outcomes: An ability to apply knowledge of mathematics, science and engineering. A knowledge of impact of engineering solutions on the society and also on contemporary issues.


Date: Date:

Department of




UNIT NO: VIII Expected date of completion: 5th Sep2K10




Text Books

Journals

Websites

1.Sept101Simulation Definition} D,EO.R J.K.Sharma

O.R S.D.Sharma

2.Sept101Types of simulation modelsO.R J.K.Sharma


3.Sept101Phases of simulation & applicationsO.R S.D.Sharma

O.R Iyer

O.R Wagner

4.Sept101Advantages and disadvantagesO.R S.Kalavathy O.R Iyer

O.R V.K.Kapoor

5.Sept101Simulation LanguagesO.R Iyer



05Objectives and Outcomes achievedObjective: Differentiate between analytical and simulation models , using Monte Carlo simulation technique for solving various types of problems. Develop random numbers ,design best solutions using computer languages for simulation

Outcomes: The ability to use modern engineering tools, software and equipment to analyze problems. A knowledge of impact of engineering solutions on the society and also on contemporary issues


Date: Date:

Department of

Mechanical EngineeringCOURSE COMPLETION STATUSAcademic Year: 2010 -11


Actual Date of Completion & Remarks, if any:

S.NoUnit NoActual date of completion with remarks, if any

No. of Objectives Achieved

1. I30th August 2K101

2. II19th August 2K102

3. III14th August 2K103

4. IV24th July 2K104

5. V

6. VI

7. VII

8. VIII


Date:Date:

Department of

Mechanical EngineeringTUTORIAL SHEET-1Academic Year: 2010 -11


This Tutorial is concerned to Unit Number/s:

(Please write the Questions/ Problems/ Exercises. Which you would like to give to the students)

Question NumberDate Tutorial Question

Objectives to which these questions are related

116th July2k10Solve the following game

4

2

3

4

5


Date:Date:

Department of

Mechanical EngineeringTUTORIAL SHEET - IIAcademic Year: 2010 -11




Question NumberDateTutorial Question


1

2

3

4

5


Date:Date:

Department of

Mechanical EngineeringTUTORIAL SHEET - III Academic Year: 2010 -11




Question NumberDateTutorial Question


1

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3

4

5


Date:Date:

Department of

Mechanical EngineeringLESSON PLAN

(UNIT-I)Academic Year: 2010 -11


Subject

:

Subject Code:

Branch/Specialization:

Start Date: Date of completion:

S. NoTopics and / Sub-Topics CoveredTotal No. of Periods

1. Teaching Aids Used:

2. Instructional Objectives: (On completion of this Unit the Student shall be able to)

1.

2.

3.

4.

3. Teaching Points:

4. Assignment question/s:


Question NumberDateAssignment Question


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Date: Date:

Department of


(UNIT-II)Academic Year: 2010 -11


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(UNIT-III)Academic Year: 2010 -11


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Date: Date:

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(UNIT-IV)Academic Year: 2010 -11


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Date: Date:

Department of


(UNIT-V)Academic Year: 2010 -11


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(UNIT-VI)Academic Year: 2010 -11


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(UNIT-VII)Academic Year: 2010 -11


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(UNIT-VIII)Academic Year: 2010 -11


Subject

: Operations Research

Subject Code:07A7EC03Branch/Specialization: IV B.TECH I SEM / MECHANICALStart Date: 01st Sept2k10 Date of completion: 04th Sept2k10


0102

03

04Definition of Simulation & Types of simulationPhases of Simulation, advantages & disadvantages of Simulation

Simulation Languages

Applications of Simulation Inventory & Queuing Problems0101

01

02

1. Teaching Aids Used: Class Room (Chalk Board)2. Instructional Objectives: (On completion of this Unit the Student shall be able to)

1. Distinction between analytical & simulation models2. Understanding the advantages and disadvantages of simulation3. Apply Monte Carlo simulation technique4. Develop random number generation, intervals & applications to different O.R. problems3. Teaching Points:

1. Definition of simulation & why it is used?2. Define random number

3. Define pseudo-random number

4. Explain Monte-Carlo Technique

5. Advantages of simulations

6. Limitations of simulation

7. Revising the concepts of Inventory & queuing problems

8. Applications of simulation related to inventory and queuing problems





1What is simulation? discuss about application of simulation

2Discuss the application of simulation technique to inventory problem

3Discuss the advantages and disadvantages of simulation

4Explain the phases of Simulation models

5Explain in brief the various types of simulation model


Date: Date:

Department of

Mechanical EngineeringINTERNAL ASSESSMENT MARKSAcademic Year: 2010 -11


Name of the Faculty:N.Srinivasa ReddySubject

: Operations Research

Subject Code:07A7EC03Branch/Specialization: IV B.TECH I SEM / MECHANICALBest and the worst Internal Marks Details:

S.No.Mid ExamsMaximum MarksBest MarksWorst MarksRemarks

1Objective Test 1

2Descriptive Test 1

3Objective Test 2

4Descriptive Test 2

5*Class Test 1

6*Class Test 2

7*Class Test 3

8*Class Test 4

* indicate if any remedial tests were conducted, if any.


Date: Date:

Rev: 03/ME/2010Cover Page

Rev: 03/ME/2010

Page 17

Documents

Operations Research Course File