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Code No. D-MBA-201

BRILLIANT’S®

Bilingual (English & Hindi)

www.thebrilliants.in

A§J«oOr Ed§ {hÝXr ^mfm ‘|

OperationsResearch

MBASemester-2nd

According to New SyllabusDAVV, INDORE

Dr. Nirmal Jain

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Operations ResearchExamination Scheme: Student shall be evaluated on two components: 20 internaland 80 end semester examination.There will be 20 marks for internal evaluation, three internal evaluations will be con-ducted out of which two will be written test and third will be assignment/presentation/quiz/class participation. Best two out of 3 evaluations will be considered as internal marks.The semester examination carrying 80 marks will have two sections A and B. Section Aworth 20 marks will consist of four theory questions out of which students will be requiredto attempt any two questions. Section B worth 60 marks will have six numerical/practicalproblems out of which a student will be required to attempt any four questions.

Course ContentsUnit 1. Introduction to Operations Research: Meaning, Scope of Operations Research

in Management, Advantages and Limitations of Operations Research, ORModels.

Unit 2. Linear Programming: Meaning of Linear Programming, General Mathemati-cal Formulation of LPP, Graphical Analysis, Simplex Method, Two-phaseMethod, Big M-Method Duality and Post Optimality Analysis, Advantage andLimitation of LPP.

Unit 3. Transportation Model: Mathematical Formulation, Initial Basic Feasible Solu-tion, Vogel's Approximation Method, Optimization (Minimization and Maximi-zation) Using Modified Distribution Method and Stepping Stone Method.

Unit 4. Assignment Model as a Particular Case of Transportation Model, Formulationof Assignment Problems, Solution of Assignment Problems using HungarianMethod (Minimization and Maximization), Route Allocation, Travelling Sales-man Problem.

Unit 5. Introduction, Scope in Management Decisions, Queuing Models M/M/1 (Infi-nite and Finite Population), Probability Calculations and Application of M/M/C(Infinite Population).

Unit 6. Introduction, Scope in Management, Single Equipment Replacement Modeland Group Replacement.

Unit 7. Introduction to Games, Maximin and Minimax Principles, Pure and MixedStrategies, Solutions of Games using- Algebraic and Graphical Methods.

Unit 8. Introduction to Simulation, Monte Carlo Technique and its Applications.Unit 9. Computation of Sequential Probability of States for Different Periods, Steady

State Probability of States and Application of Markov Chain.

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BRILLIANT'S Operations Research 4

1. Introduction to Operations Research

CONCEPT AND CHARACTERISTICS OF OPERATIONS RESEARCHAm°naoeÝg [agM© H$s AdYmaUm Ed§ {deofVmE±

Q.1. Define Operations Research. / Am°naoeÝg [agM© H$mo n[a^m{fV H$s{OE&[2019, 2017, 2013, 2011, 2009, 2008]

ORWhat are the essential characteristics of Operations Research?Am°naoeÝg [agM© H$s Amdí¶H$ {deofVmE§ ³¶m h¢? [2018, 2003]

OROperations Research is "An art of winning war without actually fighting them."Justify.Am°naoeÝg [agM© ''b‹S>mB© {H$E {~Zm ¶wÕ OrVZo H$s H$bm h¡&'' à‘m{UV H$s{OE& [2016, 2012]

METHODOLOGY OF OPERATIONS RESEARCH / Am°naoeÝg [agM© H$s ‘oWS>mobm°OrQ.2. Explain how and why Operations Research Methods have been valuable in aiding

executive decisions. / ì¶m»¶m H$s{OE {H$ Am°naoeÝg [agM© ‘oWS²>g, Ep³O³¶y{Q>d H$mo {S>{gOÝgboZo ‘| {H$g àH$ma go Am¡a ³¶m| ‘hÎdnyU© h¡? [2016]

SCOPE, APPLICATIONS AND IMPORTANCE OF OR / OR Ho$ ñH$mon, Cn¶moJ Ed§ ‘hÎdQ.3. Explain in detail the Scope of Operations Research.

Am°naoeÝg [agM© Ho$ ñH$mon H$mo {dñV¥V ‘| g‘PmBE& [2017]OR

With suitable examples from the industry, describe the scope of an OperationsResearch. / B§S>ñQ´>r go g§~§{YV Cn¶w³V CXmhaU Ho$ gmW Am°naoeÝg [agM© Ho$ ñH$mon H$s ì¶m»¶mH$s{OE& [2015]

OR MODELS/TOOLS AND TECHNIQUES / OR ‘m°S>ëg/Qy>ëg Ed§ Q>op³Z³gQ.4. "Operations Research (OR) is an aid for the executive in making his decisions by

providing him with the needed quantitative information, based on the scientificmethod analysis." Discuss this statement in detail, illustrating it with models ofOR that you know.''Am°naoeÝg [aMg© (OR) Ep³O³¶y{Q>d H$mo gmB§{Q>{’$H$ ‘oWS> EZm{b{gg Ho$ AmYma na Amdí¶H$³dm§{Q>Q>o{Q>d BÝ’$m°‘}eZ àXmZ H$a CZHo$ {S>{gOZ ‘oqH$J ‘| ghm¶H$ hmoVm h¡&'' AmnH$mo OR Ho${Og ‘m°S>b H$s OmZH$mar h¡, CgHo$ CXmhaU Ho$ gmW Bg H$WZ H$s ì¶m»¶m H$s{OE& [2017]

OR

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BRILLIANT'S Operations Research 5

Explain the analogue models and symbolic models giving one example for each.EZmbm°J ‘m°S>ëg VWm {gå~m°{bH$ ‘m°S>ëg H$s ì¶m»¶m, à˶oH$ Ho$ {bE EH$ CXmhaU Xr{OE&

[2017]

ADVANTAGES OF OR / OR Ho$ bm^

Q.5. Discuss the advantages of OR. / OR Ho$ bm^m| H$s MMm© H$s{OE& [2019]OR

Write the advantages of Operations Research.Am°naoeÝg [agM© Ho$ bm^ {b{IE& [2017, 2014, 2013]

LIMITATIONS OF OR / OR H$s gr_mE±Q.6. Discuss the limitations of Operations Research.

Am°naoeÝg [agM© H$s gr_mAm| H$s ì`m»`m H$s{OE& [2019, 2014]OR

Write the disadvantages of Operations Research.Am°naoeÝg [agM© H$s hm{Z`m± {b{IE& [2017, 2014, 2013]

APPLICATION OF OR IN BUSINESS DECISION MAKING PROCESS{~OZog {S>grOZ _oqH$J àmogog _| OR H$m Cn`moJ

Q.7. Explain the applications of different OR used in business decision making process.{~OZog {S>grOZ _oqH$J àmogog _| {d{^Þ OR Ho$ Cn`moJ H$mo g_PmBEŸ& [2016]

ORDiscuss the utility of OR Techniques for taking business decisions of quality.Šdm{cQ>r g§~§Yr {~OZog {S>grOZ coZo _| OR Q>opŠZŠg H$s Cn`mo{JVm g_PmBEŸ&

Review Questions ..................................................................... 55

2. Linear ProgrammingMEANING AND FORMULATION OF LPP / LPP H$m AW© Ed§ ’$m°‘y©boeZ

Q.8. What are the assumptions of LPP? / LPP H$s ‘mݶVmE± ³¶m h¢? [2018, 2016, 2012]OR

What is Linear Programming? / {b{Z¶a àmoJ«mq‘J ³¶m hmoVm h¡? [2018, 2016]

APPLICATIONS OF LINEAR PROGRAMMING/ {c{Z`a àmoJ«mq_J H$s Cn`mo{JVmE±Q.9. Discuss the applications of Linear Programming.

{b{Z¶a àmoJ«mq‘J Ho$ Cn¶moJ H$s MMm© H$s[OE& [2017]OR

Write a short note on application of linear programming.{b{Z¶a àmoJ«mq‘J Ho$ Cn¶moJ na g§{jßV {Q>ßnUr {b{IE& [2006]

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TERMINOLOGIES IN LPP / LPP Ho$ Q>{‘©Zmobm°OrQ.10. What is meant by a feasible solution of an LPP?

{H$gr LPP Ho$ ’$s{O~b gm°ë¶yeZ go ³¶m VmËn¶© h¡? [2014]OR

Explain the significance of the following variables with examples: (i) Surplusvariables (ii) Slack variables (iii) Artificial variables.{ZåZ{b{IV d¡[aE~ëg Ho$ {deofVmAm| H$s ì¶m»¶m CXmhaU Ho$ gmW H$s{OE… (i) gaßbg d¡[aE~ëg(ii) ñboH$ d¡[aE~ëg (iii) Am{Q>©{’${e¶b d¡[aE~ëg& [2008]

GRAPHICAL ANALYSIS / GRAPHICAL METHOD FOR SOLVING LPPLPP H$mo hb H$aZo Ho$ {bE J«m{’$H$b EZm{b{gg/J«m{’$H$b ‘oWS>

Q.11. Explain the graphical method of solving an LPP involving two variables.Xmo d¡[aE~b dmbo LPP H$mo gm°ëd H$aZo H$s J«m{’$H$b ‘oWS> H$s ì¶m»¶m H$s{OE& [2017]

ORWrite a short note on 'LPP solution by Graphical Method'.'J«m{’$H$b ‘oWS> Ûmam LPP H$m gm°ë¶yeZ' na g§{jßV {Q>ßnUr {b{IE& [2013]

SIMPLEX METHOD FOR SOLVING LPP/ LPP H$mo hb H$aZo Ho$ {bE {gåßboŠg _oWS>Q.12. Write the algorithm of simplex method for solving linear programming problem.

{b{Z¶a n«moJ«mq‘J àm°ãb‘ H$mo gm°ëd H$aZo Ho$ {bE {gåßbo³g ‘oWS> H$s EëJmo[aX‘ {b{IE&[2015]

ORWrite a short note on 'LPP solution by simplex method'.'{gåßbo³g ‘oWS> Ûmam LPP H$m gm°ë¶yeZ' na g§{já {Q>ßnUr H$s{OE& [2013]

ORList out the application of simplex method.{gåßbo³g ‘oWS> Ho$ Cn¶moJ {b{IE& [2009]

DEGENERACY IN LPP / LPP ‘| {S>OZaogrQ.13. What do you mean by degeneracy problem in simplex method? How can it be

solved? / {gåßbo³g ‘oWS> ‘| {S>OZaogr àm°ãb‘ go Amn ³¶m g‘PVo h¢? Bgo {H$g àH$ma gm°ëd{H$¶m Om gH$Vm h¡? [2015]

ORExplain the concept of degeneracy in simplex method.{gåßbo³g ‘oWS> ‘| {S>OZaogr H$s H$ÝgoßQ> H$s ì¶m»¶m H$s{OE& [2008]

TWO PHASE METHOD / Xmo ’o$g ‘oWS>Q.14. Write a short note on Two Phase Method.

Xmo ’o$g ‘oWS> na g§{já {Q>ßnUr {b{IE& [2013]

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BIG-M METHOD OR METHOD OF PENALTIES{~J-M ‘oWS> ¶m noZëQ>rO H$s ‘oWS>

Q.15. Write a short note on Big-M Method.{~J-M ‘oWS> na g§{já {Q>ßnUr {b{IE& [2013]

DUALITY IN LINEAR PROGRAMMING/ {b{Z`a àmoJ«mq_J _| S²> yE{bQ>r

Q.16. Explain the concept of Duality./ S²>`yE{cQ>r H$s AdYmaUm H$mo ñnï> H$s{OEŸ& [2009]OR

Write a short note on Concept of Duality in Linear Programming.{b{Z¶a àmoJ«mq‘J ‘| S²>¶yE{bQ>r H$s AdYmaUm na g§{já {Q>ßnUr H$s{OE& [2007]

POST-OPTIMALITY ANALYSIS / nmoñQ>-Am°pßQ>‘o{bQ>r EZm{b{ggQ.17. Write a short note on: post-optimality analysis in LPP.

g§{jßV {Q>ßnUr {b{IE… LPP ‘| nmoñQ>-Am°pßQ>‘o{bQ>r EZm{b{gg& [2011]

ADVANTAGES & LIMITATIONS OF LINEAR PROGRAMMING TECHNIQUES{c[Z`a àmoJ«mq_J Q>opŠZŠg Ho$ bm^ Ed§ gr_mE±

Q.18. What are the major limitations of LPP? / LPP H$s ‘w»¶ gr‘mE± ³¶m h¢? [2018]OR

Discuss the advantages and limitations of Linear Programming.{b{Z¶a àmoJ«mq‘J Ho$ bm^ d gr‘mAm| H$s MMm© H$s{OE& [2017]

Solved Practical Questions ....................................................... 74

Review Questions ..................................................................... 136

3. Transportation ModelMEANING AND MATHEMATICAL FORMULATION OF TRANSPORTATION MODEL

Q´>m§gnmoQ>}eZ _m°S>b H$m AW© d _¡Wo_o{Q>H$b \$m°_y©boeZQ.19. With reference to transportation problem, explain the following terms:

Q´>m§gnmoQ>}eZ àm°ãb_ Ho$ g§X^© _|, {ZåZ{b{IV Q>åg© H$s ì`m»`m H$s{OE…(a) Feasible solution / \$s{O~b gm°ë`yeZ(b) Basic feasible solution / ~o{gH$ \$s{O~b gm°ë`yeZ(c) Optimal solution / Am°pßQ>_b gm°ë`yeZ(d) Non-degenerate basic feasible solution / Zm°Z-{S>OZaoQ> ~o{gH$ \$s{O~b gm°ë`yeZ

[2018]OR

Distinguish between Balanced and Unbalanced Transportation Problems.~¡b|ñS> VWm AZ~¡b|ñS> Q´>m§gnmoQ>}eZ àm°ãb_ Ho$ ~rM A§Va ~VmBE& [2013]

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METHODS FOR FINDING INITIAL SOLUTIONB{Z{e¶b gm°ë¶yeZ kmV H$aZo H$s ‘oWS>²g

Q.20. List various methods of solving a transportation problem. Which is the bestmethod of solving Transportation problem and why? / Q´>m§gnmoQ>}eZ àm°ãb‘ H$mo gm°ëdH$aZo H$s {d{^ÝZ ‘oWS> ~VmBE& Q´>m§gnmoQ>}eZ àm°ãb‘ gm°ëd H$aZo H$s ~oñQ> ‘oWS> H$m¡Z-gr VWm³¶m| h¡? [2012]

ORWrite a short note on North-West Corner Rule for solving Transportation Problem.Q´>m§gnmoQ>}eZ àm°ãb‘ H$mo gm°ëd H$aZo H$s Zm°W©-doñQ> H$m°Z©a ê$b na g§{jßV {Q>ßnUr {b{IE&

[2007]

OPTIMALITY TEST IN TRANSPORTATION PROBLEMQ´>m§gnm}Q>oeZ àm°ãc_ _| Am°pßQ>_o{cQ>r Q>oñQ>

Q.21. Describe the computational procedure of Optimality Test in a TransportationProblem. / Q´>m§gnmoQ>o©eZ àm°ãb_ _| Am°{ßQ>_o{bQ>r Q>oñQ> Ho$ JUZm H$s à{H«$`m H$s ì`m»`m H$s{OE &

ORDiscuss the rational of MODI model with suitable example.MODI _m°S>c H$s Vm{H©$H$Vm H$mo Cn`wº$ CXmhaU XoH$a g_PmBE&

STEPPING STONE METHOD FOR OPTIMALITYAm°pßQ>‘o{bQ>r Ho$ {bE ñQ>oqnJ ñQ>moZ ‘oWS>

Q.22. Discuss stepping stone method to check optimality of initial solution.B{Z{e¶b gm°ë¶weZ H$s Am°pßQ>‘o{bQ>r MoH$ H$aZo Ho$ {bE ñQ>oqnJ ñQ>moZ ‘oWS> na MMm© H$s{OE&

DEGENERACY IN TRANSPORTATION PROBLEM/ Q´>m§gnm}Q>oeZ àm°ãc_ _| S>rOZaogrQ.23. How does the problem of degeneracy arise in a transportation problem? Explain

how to overcome it? / Q´>m§gnmoQ>}eZ àm°ãb‘ ‘| S>rOZaogr H$m àm°ãb‘ H¡$go CËnÝZ hmoVm h¡?ì¶m»¶m H$s{OE {H$ Bgo H¡$go g‘mßV {H$¶m OmE? [2017]

ORWhat do you understand by degeneracy in transportation model?Q´>m§gnmoQ>}eZ ‘m°S>b ‘| S>rOZaogr go Amn ³¶m g‘PVo h¢? [2016]

ORWhat is degeneracy in transportation problem? How is it removed?Q´>m§gnmoQ>}eZ àm°ãb‘ ‘| S>rOZaogr ³¶m hmoVr h¡? ¶h {H$g àH$ma hQ>m¶m OmVm h¡? [2011]

MAXIMIZATION IN TRANSPORTATION PROBLEMQ´>m±gnmoQ>©oeZ àm°ãc_ _| _¡pŠO_mBOoeZ

Q.24. Write a short note on: Maximization in Transportation Problem.g§{jßV {Q>ßnUr {b{IE… Q´>m±gnmoQ>©oeZ àm°ãc_ _| _¡pŠO_mBµOoeZŸ&

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Q.25. Distinguish between: / A§Va ñnï> H$s{OE…(i) Balanced and Unbalanced Transportation Problems

~¡b|ñS> VWm AZ~¡b|ñS> Q´>m§gnmoQ>o}eZ àm°ãbåg(ii) Stepping Stone and MODI Method / ñQ>oqnJ ñQ>moZ VWm MODI ‘oWS> [2013]

Solved Practical Questions ....................................................... 151

Review Questions ..................................................................... 235

4. Assignment ModelMEANING, SCOPE AND FORMULATION OF ASSIGNMENT MODEL

AgmBZ‘|Q> ‘m°S>b H$m AW©, joÌ Ed§ ’$m°‘w©boeZQ.26. Write difference between Transportation and Assignment Model.

Q´>m§gnmoQ>}eZ VWm AgmBZ‘|Q> ‘m°S>b Ho$ ~rM A§Va {b{IE& [2018, 2013]OR

What is assignment problem? Give two areas of its application.AgmBZ‘|Q> àm°ãb‘ ³¶m h¡? BgHo$ Cn¶moJ Ho$ Xmo Ear¶mO ~VmBE& [2017]

METHODS FOR SOLVING ASSIGNMENT PROBLEMAgmBZ‘|Q> àm°ãb‘ H$mo gm°ëd H$aZo Ho$ {bE ‘oWS>

Q.27. Explain the following in the context of assignment problem:{ZåZ{b{IV H$s ì¶m»¶m AgmBZ‘|Q> àm°ãb‘ Ho$ g§X^© ‘| H$s{OE…(a) Balanced Assignment Problem / ~¡b|ñS> AgmBZ‘|Q> àm°ãb‘(b) The Hungarian Method / h§Jo[a¶Z ‘oWS>(c) An Infeasible Assignment / BÝ’$s{O~b AgmBZ‘|Q> [2015, 2012]

ORWhat is an unbalanced assignment problem? How is the Hungarian method ap-plied for obtaining a solution if the matrix is rectangular? / AZ~¡b|ñS> AgmBZ‘|Q> àm°ãb‘³¶m hmoVm h¡? ¶{X ‘¡{Q>³g ao³Q>|Jwba hmo Vmo gm°ë¶yeZ kmV H$aZo Ho$ {bE h§Jo[a¶Z ‘oWS> H$m Cn¶moJ H¡$go{H$¶m OmVm h¡& [2014]

MAXIMIZATION PROBLEM IN ASSIGNMENT MODELAgmBZ‘|Q> ‘m°S>b ‘| ‘¡p³O‘mBOoeZ àm°ãb‘

Q.28. Explain how will you solve maximization problems by assignment method.Amn ‘¡p³O‘mBOoeZ H$s àm°ãb‘ H$mo AgmBZ‘|Q> ‘oWS> Ûmam H¡$go gm°ëd H$a|Jo, ì¶m»¶m H$s{OE&

ORDiscuss how to solve assignment problem for maximization.‘¡p³O‘mBOoeZ Ho$ {bE AgmBZ‘|Q> àm°ãb‘ H$mo H¡$go gm°ëd H$a|Jo, ì¶m»¶m H$s{OE&

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MULTIPLE SOLUTIONS / ‘pëQ>nb gm°ë¶yeZQ.29. What do you understand by Multiple Solutions in Assignment Problem?

AgmBZ‘|Q> àm°ãb‘ ‘| ‘pëQ>nb gm°ë¶yeZ go Amn ³¶m g‘PVo h¢?

THE TRAVELLING SALESMAN (ROUTING) PROBLEMQ´>odqbJ goëg‘¡Z (ê$qQ>J) àm°ãb‘

Q.30. Write a short note on 'Travelling salesman Problem and its solution'."Q´>odqbJ goëg‘¡Z àm°ãb‘ VWm BgHo$ gm°ë¶yeZ' na g§{jßV {Q>ßnUr {b{IE& [2013]

ORExplain the 'Travelling salesman problem'.'Q´>odqbJ goëg‘¡Z àm°ãb‘" H$s ì¶m»¶m H$s{OE& [2009]

RESTRICTIONS ON ASSIGNMENTS/ AgmBZ_|Q²>g na à{V~§YQ.31. How an assignment problem can be solved if a particular assignment is prohibited?

`{X {H$gr AgmBZ_|Q> àm°ãc_ _| {H$gr {d{eï> AgmBZ_|Q> na à{V~ÝY hmo Vmo Cgo {H$g àH$magm°ëd {H$`m Om gH$Vm h¡?

ORDiscuss the process to solve restricted assignment problem with an illustration.à{V~§{YV AgmBZ‘|Q> àm°ãb‘ H$mo gm°ëd H$aZo H$s àmogog H$s CXmhaU g{hV ì¶m»¶m H$s{OE&

Solved Practical Questions ....................................................... 250

Review Questions ..................................................................... 280

5. Waiting Line ModelsINTRODUCTION, ASSUMPTIONS, SCOPE AND CHARACTERISTICS OF QUEUING

SYSTEM / ³¶yBªJ {gñQ>‘ H$m n[aM¶, ‘mݶVmE±, joÌ Ed§ {deofVmE±Q.32. Write a short note on Waiting Line Models.

doqQ>J bmBZ ‘m°S>b na g§{jßV {Q>ßnUr {b{IE& [2013, 2009]OR

Write a short note on Queuing Theory.³¶yBªJ ϶moar na g§{jßV {Q>ßnUr {b{IE& [2012]

ORAnalyze the following queuing systems by describing their various systemproperties: (a) Hospital Emergency Room (b) Traffic Light (c) Computer Systemat a University / {ZåZ{b{IV ³¶yBªJ {gñQ>‘ H$s {d{^ÝZ {gñQ>‘ àm°nQ>uO H$s ì¶m»¶m H$a CÝh|EZmbmBO H$s{OE… (a) hm°pñnQ>b B‘aO|gr ê$‘ (b) Q´>¡{’$H$ bmBQ> (c) {H$gr ¶y{Zd{g©Q>r ‘| H$å߶yQ>a{gñQ>‘ [2010]

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QUEUING MODEL I (M/M/1): (FIFO/∞) (SINGLE SERVER, UNLIMITED QUEUEMODEL) AND PROBABILITY CALCULATIONS / Š`yBªJ _m°S>b I (M/M/1): (FIFO/∞)

(qgJb gd©a/AZ{b{_Q>oS> Š`y _m°S>b) VWm àmo~o{~{bQ>r H¡$볶yboeZQ.33. Explain the different classification of queuing models. Describe both single server

and multi server queuing models./ Š`yBªJ ‘m°S>ëg Ho$ {d{^Þ dJuH$aU H$mo g‘PmBE&EH$b gd©a Am¡a ~hþ gd©a Š`yBªJ _m°S>b XmoZm| H$m dU©Z H$s{OE& [2015]

ORExplain different types of waiting line models in queuing theory.Š`yBªJ {gÕm§V ‘| {d{^Þ àH$ma H$s àVrjm aoIm ‘m°S>b H$mo g‘PmBE& [2014]

ORExplain M/M/1 Waiting Line Model./ M/M/1 doqQ>J bmBZ _m°S>b H$mo g_PmBEŸ& [2005]

WAITING LINE MODEL II (M/M/1): (FIFO/N/∞) AND PROBABILITY CALCULATIONdoqQ>J cmBZ _m°S>c II (M/M/1): (FIFO/N/∞) VWm àmo~o{~{bQ>r H¡$볶yboeZ

Q.34. Explain different classification of queuing models. Describe both single serverand multi server queuing models./ ³¶yBªJ ‘m°S>b Ho$ {d{^ÝZ àH$mam| H$mo g‘PmBE& qgJbgd©a VWm ‘ëQ>r gd©a XmoZm| ³¶yBªJ ‘m°S>b H$s ì¶m»¶m H$s{OE& [2015]

ORExplain different types of waiting line models in Queuing Theory.³¶yBªJ ϶moar ‘| doqQ>J bmBZ ‘m°S>ëg Ho$ {d{^ÝZ àH$mam| H$mo g‘PmBE& [2014]

WAITING LINE MODEL III (M/M/C): (FCFS/∞) AND PROBABILITYCALCULATIONS

(Multiple Servers, Unlimited Queue Model)doqQ>J bmBZ ‘m°S>b III (M/M/C): (FCFS/∞) VWm àmo~o{~{bQ>r H¡$볶yboeZ

(‘ëQ>rnb gd©g©, AZ{b{‘Q>oS> ³¶y ‘m°S>b)

Q.35. Explain the different classification of queuing models. Describe both single serverand multi server queuing models.³¶yBªJ ‘m°S>b Ho$ {d{^ÝZ àH$mam| H$mo g‘PmBE& qgJb gd©a VWm ‘ëQ>r gd©a XmoZm| ³¶yBªJ ‘m°S>b H$sì¶m»¶m H$s{OE& [2015]

ORExplain different types of waiting line Models in Queuing Theory.³¶yBªJ ϶moar ‘| doqQ>J bmBZ ‘m°S>ëg Ho$ {d{^ÝZ àH$mam| H$mo g‘PmBE& [2014]

ORWrite difference between various Queuing Models.{d{^ÝZ ³¶yBªJ ‘m°S>b ‘| A§Va {b{IE& [2013]

Solved Practical Questions ....................................................... 300

Review Questions ..................................................................... 312

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6. Replacement ModelsINTRODUCTION AND OBJECTIVE OF REPLACEMENT MODEL

[aßbog‘|Q> ‘m°S>b H$m n[aM¶ Ed§ CÔoí¶Q.36. What is replacement? Describe some important replacement situations.

[aßbog‘|Q> ³¶m h¡? [aßbog‘|Q> H$s Hw$N> ‘hÎdnyU© n[apñW{V¶m| H$s ì¶m»¶m H$s{OE& [2014]OR

Write a critical essay on replacement problem.[aßbog‘|Q> àm°ãb‘ na EH$ AmbmoMZmË‘H$ {Z~§Y {b{IE& [2011]

ORWhat is replacement model? Describe some important replacement situationsand policies for the hospital in which you are working.[aßbog‘|Q> ‘m°S>b ³¶m h¡? Amn {Og hm°pñnQ>b ‘| H$m¶© H$a aho h¢ CgHo$ {bE [aßbog‘|Q> H$s Hw$N>‘hÎdnyU© n[apñW{V¶m| Ed§ nm°{bgrO H$s ì¶m»¶m H$s{OE&

TYPES OF FAILURE OF ITEMS/ AmBQ>åg Ho$ Iam~ hmoZo Ho$ àH$maQ.37. Explain the Types of Failure of Items with suitable example.

AmBQ>åg Ho$ Iam~ hmoZo Ho$ àH$mam| H$s ì`m»`m Cn`wº$ CXmhaU Ho$ gmW H$s{OEŸ&OR

Explain the following: (i) Sudden failure (ii) Gradual failure.{ZåZ{c{IV H$s ì`m»`m H$s{OEŸ: (i) AMmZH$ Iam~ hmoZm (ii) Yrao-Yrao Iam~ hmoZmŸ&

REPLACEMENT OF ITEMS THAT DETERIORATE WITH TIMEg‘¶ Ho$ gmW Iam~ hmoZo dmbo AmBQ>åg H$m [aßbog‘|Q>

Q.38. Discuss the replacement policy of items whose maintenance costs increase withtime and the value of money remains same during the period. / CZ AmBQ>åg H$s[aßbog‘|Q> nm°{bgr H$s ì¶m»¶m H$s{OE {OZH$s ‘oÝQ>oZ|g H$m°ñQ> g‘¶ Ho$ gmW ~‹T>Vr h¡ VWm BgAd{Y ‘| ‘Zr H$s d¡ë¶y pñWa ahVr h¡& [2017, 2009]

ORDiscuss the replacement policy for equipments that deteriorate with time.g‘¶ Ho$ gmW Iam~ hmoZo dmbr Bp³dn‘|Q> H$s [aßbog‘|Q> nm°{bgr H$s ì¶m»¶m H$s{OE&

SINGLE EQUIPMENT REPLACEMENT MODELS AND GROUP REPLACEMENT MODELSqgJb Bp³dn‘|Q> [aßbog‘|Q> ‘m°S>ëg Ed§ J«wn [aßbog‘|Q> ‘m°S>ëg

Q.39. What is the difference between group replacement and individual replacement?Under which circumstances group replacement may become profitable?J«wn [aßbog‘|Q> VWm B§{S>{dOwAb [aßbog‘|Q> ‘| ³¶m A§Va h¡? {H$Z n[apñW{V¶m| Ho$ AÝVJ©V J«wn[aßbog‘|Q> bm^H$mar hmo gH$Vm h¡? [2016]

OR

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Explain different replacement models for machines and equipments. Which modelis better and why? / ‘erÝg VWm Bp³dn‘|Q²>g Ho$ {bE {d{^ÝZ [aßbog‘|Q> ‘m°S>ëg H$mo g‘PmBE&H$m¡Z-gm ‘m°S>b ~ohVa h¡ VWm ³¶m|? [2014]

ORWrite difference between preventive and breakdown maintenance.{àdopÝQ>d VWm ~«oH$S>mCZ ‘oÝQ>oZoÝg Ho$ ~rM A§Va {b{IE& [2013]

REPLACEMENT OF STAFF / ñQ>m’$ H$m [aßbog‘|Q>Q.40. Discuss the process to solve staffing problem by replacement model.

ñQ>mq’$J àm°ãb‘ H$mo [aßbog‘|Q> ‘m°S>b Ho$ Ûmam gm°ëd H$aZo H$s àmogog H$s MMm© H$s{OE&OR

What do you understand by staffing problem? How this can be solved? Discussin detail. / ñQ>mq’$J àm°ãb‘ go Amn ³¶m g‘PVo h¢? Bgo {H$g àH$ma gm°ëd {H$¶m Om gH$Vmh¡? {dñVma go MMm© H$s{OE&

Solved Practical Questions ....................................................... 321

Review Questions ..................................................................... 351

7. Game TheoryINTRODUCTION TO GAMES AND PURE AND MIXED STRATEGIES

Iob VWm ߶moa Am¡a {‘³ñS> ñQ´>oQ>oOr H$m n[aM¶

Q.41. What is a game in game theory? What are the properties of a game?Jo‘ ϶moar ‘| Jo‘ ³¶m h¡? EH$ Iob Ho$ JwU ³¶m h¢? [2019]

ORWhat are the assumptions mode in game theory? / Jo‘ ϶moar ‘| ³¶m YmaUmE± h¢? [2018]

ORDescribe: Pure and Mixed Strategies.dU©Z H$s{OE… ߶moa EÊS> {‘³ñS> ñQ´>oQ>oOr& [2015]

TWO-PERSONS ZERO SUM GAMES AND MAXIMIN & MINIMAX PRINCIPLESQy>-ng©Ýg Oramo g‘ Joåg VWm ‘¡p³g{‘Z Ed§ {‘Zr‘¡³g {àpÝgnëg

Q.42. Explain the 'best strategy' on the basis of minimax criterion of optimality.{‘{Z‘¡³g H«$mBQ>o[a¶Z Am°’$ Am°pßQ>‘o{bQ>r Ho$ AmYma na '~oñQ> ñQ´>oQ>oOr' H$s ì¶m»¶m H$s{OE&

[2019]OR

Explain two person zero sum game by giving suitable example.Cn¶wº$ CXmhaU XoH$a Qy>-ng©Ýg Oramo g‘ Jo‘ H$s ì¶m»¶m H$s{OE& [2018]

OR

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BRILLIANT'S Operations Research 14

Describe: (a) Maximin and Minimax Principles (b) Zero Sum Game and SaddlePoints. / dU©Z H$s{OE… (a) ‘¡p³g[‘Z VWm {‘[Z‘¡³g {gÕmÝV (b) Oramo g‘ Jo‘ VWm g¡S>bnm°B§Q>²g& [2015]

DOMINANCE PRINCIPLE IN GAME THEORY / Jo‘ ϶moar ‘| S>mo{‘Zo§g qà{gnb

Q.43. Explain the concept of Dominance in game theory.Jo‘ ϶moar ‘| S>mo{‘Zo§g H$s AdYmaUm H$mo g‘PmBE& [2010]

ORWrite the dominance rule. / S>mo{‘Z|g ê$b {b{IE& [2005]

ORDiscuss the dominance property in game theory.Jo‘ ϶moar ‘| S>mo{‘Z|g àm°nQ>u na MMm© H$s{OE&

TWO PERSON ZERO SUM GAME WITHOUT SADDLE POINT(ARITHMETIC METHOD)

{~Zm g¡S>b nm°B§Q> Ho$ Qy>-ng©Z Oramo g‘ Jo‘ (A§H$J{UV {d{Y)

Q.44. What is the process to determine optimal strategies if saddle point does not exist?¶{X g¡S>b nm°B§Q> CnpñWV Zht h¡, Vmo Am°pßQ>‘b ñQ>oQ>oOr H$mo {ZYm©[aV H$aZo H$s ³¶m à{H«$¶m h¡?

ORDiscuss mixed strategy to determine value of the game.d¡ë¶y Am°’$ Jo‘ H$mo {ZYm©[aV H$aZo Ho$ {bE {‘³ñS> ñQ´>oQ>oOr na MMm© H$s{OE&

ORExplain Arithmetic method of game theory. / Jo‘ ϶moar H$s A§H$J{UV {d{Y g‘PmBE&

SOLUTION OF GAMES USING GRAPHICAL METHODSJ«m{’$H$b {d{Y go Joåg H$m hb

Q.45. Write a short note on 'Graphical Method' which used in solving games problem.‘J«m{’$H$b {d{Y’ na EH$ g§{já {Q>ßnUr> {b{IE Omo Joåg H$s g‘ñ¶m H$mo hb H$aZo ‘| Cn¶moJH$s OmVr h¡&

ORExplain the graphical method of solving (2 × n) and (m × 2) games.(2 × n) VWm (m × 2) Iobm| H$mo hb H$aZo H$s J«m{’$H$b {d{Y H$r ì¶m»¶m H$s{OE&

MATRICES METHOD / ‘¡{Q´>³g ‘oWS>Q.46. Explain the Arithmetic method for n × n games.

n × n Iobm| Ho$ {bE AarW‘o{Q>H$ ‘oWS> H$s ì¶m»¶m H$s{OE&OR

Explain method of matrices. / ‘¡{Q>gog H$s {d{Y g‘PmBE&

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SOLUTION OF GAMES USING ALGEBRAIC METHODSEëOo{~«H$ {d{Y go Joåg H$m hb

Q.47. Write a short note on Algebraic Method for solving games problem.Jo‘ H$s g‘ñ¶m H$mo hb H$aZo Ho$ {bE EëOo{~«H$ ‘oWS> na EH$ g§{já {Q>ßnUr {b{IE&

ORExplain algebraic method for games without saddle point.g¡S>b nm°B§Q> Ho$ {~Zm Iob Ho$ {bE EbOo{~«H$ ‘oWS> H$s ì¶m»¶m H$s{OE&

ITERATIVE METHOD / BQ>ao{Q>d ‘oWS>Q.48. Explain iterative method of approximate solution.

Eàm°p³g‘oQ> gm°ë¶yeZ H$s BQ>ao{Q>d ‘oWS> H$mo g‘PmBE&

Solved Practical Questions ....................................................... 369

Review Questions ..................................................................... 391

8. SimulationNATURE AND SCOPE OF SIMULATION

{gå¶yboeZ H$m ZoMa Ed§ ñH$mon

Q.49. Write a short note on 'Simulation and its applications'.'{gå¶yboeZ Am¡a BgHo$ AZwà¶moJm|' na EH$ g§{jßV {Q>ßnUr {b{IE& [2014, 2013, 2012]

ORWrite a short note on: Simulation.EH$ g§{jßV {Q>ßnUr {b{IE: {gå¶yboeZ& [2008, 2007, 2006, 2004]

MONTE-CARLO TECHNIQUE OF SIMULATION AND ITS APPLICATIONS{gå¶yboeZ H$s ‘m|Q>o-H$mbm} Q>op³ZH$ Am¡a BgHo$ AZwà¶moJ

Q.50. Discuss the Monte Carlo Method of solving problem, illustrating it by outlining aprocedure to solve a specified problem of your choice.àm°ãb‘ H$mo hb H$aZo H$s ‘m|Q>o-H$mbm} {d{Y na MMm© H$s{OE, AnZr ng§X H$s EH$ ñno{g’$mBS>àm°ãb‘ H$mo hb H$aZo Ho$ {bE EH$ à{H«$¶m H$s ê$naoIm V¡¶ma H$aHo$ Bgo Xem©BE& [2016]

ORWrite a short note on 'Monte-Carlo Techniques with applications'.'AZwà¶moJm| Ho$ gmW ‘m|Q>o-H$mbm} Q>op³Z³g' na EH$ g§{jßV {Q>ßnUr {b{IE& [2015]

Solved Practical Questions ....................................................... 408

Review Questions ..................................................................... 419

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9. Markov Chain AnalysisQ.51. Write a detailed note on: Markov Chain Analysis.

EH$ {dñV¥V {Q>ßnUr {b{IE… ‘mH$m}d MoZ EZm{b[gg&[2015, 2014, 2012, 2011, 2009, 2008, 2007, 2006, 2004, 2002]

ORWrite a short note on: Assumptions of Markov Analysis.EH$ g§{já {Q>ßnUr {b{IE… ‘mH$m}d EZm{b{gg H$s YmaUmE±& [2007]

ORWhat do you understand by Markov process? In what areas of management canthey be applied? /‘mH$m}d àmogog go Amn ³¶m g‘PVo h¢? ‘¡ZoO‘oÝQ> Ho$ {H$Z joÌm| ‘| CÝh| bmJy{H$¶m Om gH$Vm h¡? [2003]

Solved Practical Questions ....................................................... 431

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