m and s.docxqestion bank10mt62

7/26/2019 m and s.docxQestion Bank10mt62

1/12

MODELLING AND SIMULATION

Unit1

1. A) With an example, define model of a !tem. Gi"e the #laifi#ation of diffe$ent t!pe

of model of a !tem%) With ne#ea$! example, tate an! & it'ation (he$e im'lation i not app$op$iate tool

to 'e.

#) With a neat flo( #ha$t, %$iefl! explain the diffe$ent tep in"ol"ed in im'lation t'd!.

&. a) What i a !tem, im'lation and !tem en"i$onment Lit the ad"anta*e and

diad"anta*e of im'lation

%) With the help of an example, explain the #omponent of a !tem#) Diffe$entiate %et(een+

i) Di#$ete -ontin'o' !tem

ii) Stati# d!nami# tool

iii) Dete$miniti# Sto#hati# im'lation

i") Endo*eno' exo*eno' e"ent") a) Explain in detail the im'lation of 'en#hin* model.

/. %) A %a0e$ / do2en of %$ead loaf ea#h da!, p$o%a%ilit! dit$i%'tion of #'tome$ i in

ta%le 1. -'tome$ 1,&, / o$ 3 do2en of %$ead loaf a##o$din* to the dit$i%'tion *i"en

in ta%le &. A'me that on ea#h da! all the #'tome$4 o$de$ ome do2en of %$ead loaf.

The ellin* p$i#e i 5 6738do2en and ,alon* #pt o /.98do2en. The left o"e$ %$ead loaf

(ill %e old fo$ half p$i#e at the end of da!. :aed on 6 da! im'lation #al#'late the

p$ofit of the %a0e$ intead of / do2en a$e %alan#ed pe$ da! (ill it %e mo$e p$ofita%le.

Ta%le 1+ ;$o%a%ilit! dit$i%'tion of #'tome$ of #'tome$ da!.

N'm%e$ 9 1 1& 13

;$o%a%ilit! ./6 ./ .&6 .1

Ta%le &+ ;$o%a%ilit! dit$i%'tion of do2en o$de$ed

N'm%e$ 1 & / 3

;$o%a%ilit! .3 ./ .& .1

5andom di*it fo$ #'tome$ < 6 =1 >/ &3 ?=5andom di*it fo$ do2en 7 6 / > 9

3. a) With an aid of flo( dia*$am, explain "a$io' tep in a im'lation t'd!.

6. a) 5epeat

=. %) A ne(pape$ elle$ %'! ne( pape$ fo$ 5. // ea#h and ell them fo$ 5 6 ea#h

pape$ not old at the end of the da! a$e old a #$ap fo$ 5 .6 ea#h. ;ape$ #an %e

p'$#hae in %'ndle of onl! 1. The$e a$e / t!pe of ne( da! "i2@ GoodB, Cai$B,


2/12

;oo$B (ith p$o%a%ilitie ./6, .36, .& $epe#ti"el!. Dete$mine the optimal n'm%e$

of pape$ %! imila$l! demand fo$ & da!

>. a) What i !tem !tem en"i$onment Explain the #omponent of a !tem (ith

example.

%) (hat a$e the ad"anta*e of im'lation

#) Di#' the t!pe of model of a !tem.9. a) Explain the #allin* pop'lation, e$"i#e time e$"i#e me#hanim of a 'e'in* !tem

%) 5epeat &=) 'l! &1&

? a) Explain in %$ief a imple 'e'in* model $ep$eent it 'in* 'e'in* notation.

%) Lit de#$i%e in %$ief in fi"e element8#ha$a#te$iti# of the 'e'in* !tem.#) A *$o#e$! ha one #he#0o't #o'nte$. -'tome$ a$$i"e at thi #he#0 o't #o'nte$ at

$andom f$om 1 to 9 min'te apa$t ea#h inte$ a$$i"al time ha the ame p$o%a%ilit! of

o##'$$en#e. The e$"i#e time "a$! f$om 1 to = min'te (ith p$o%a%ilitie a *i"en %elo(.

Se$"i#e min'te) 1 & / 3 6 =

;$o%a%ilit! .1 .& ./ .&6 .1 .6

Sim'late the a$$i"al of 6 #'tome$ #al'#'late

i) a"e$a*e (aitin* time fo$ a #'tome$

ii) p$o%a%ilit! that a #'tome$ ha to (aitiii) p$o%a%ilit! of a e$"e$ %ein* idle

i") a"e$a*e e$"i#e time

") A"e$a*e time %8( a$$i"al, 'e the follo(in* e'en#e of $andom n'm%e$

5andom di*it fo$ a$$i"al ?1/ >&> 16 ?39 /? ?&&

5andom di*it fo$ '$"i"al time 93 1 >3 6/ 1> >?

Unit2

1 A) Explain an! fo'$ #ha$a#te$iti# of a 'e'in* !tem

:) A mall *$o#e$! to$e ha onl! one #he#0o't #o'nte$. -'tome$ a$$i"e at thi

#o'nte$ at $andom f$om 1 to 1 min'te apa$t. Ea#h poi%le "al'e of inte$a$$i"al time

ha the ame p$o%a%ilit! of o##'$$en#e e'al to .1. the e$"i#e time "a$! f$om 1 to

= min'te apa$t (ith p$o%a%ilitie ho(n %elo(.

Se$"i#e time 1 & / 3 6 =

;$o%a%ilit! .1 .& ./ .3 .1 .6


3/12

De"elop im'lation ta%le fo$ 1 #'tome$ and find the follo(in*+

a) The a"e$a*e time %et(een a$$i"al.

%) The p$o%a%ilit! that a #'tome$ ha to (ait in the 'e'e.

#) The a"e$a*e e$"i#e time 5andom di*it fo$ a$$i"al+ ?1, >&. 16, ?3, /, ?&, >6, &/, /5andom di*it fo$ e$"i#e time+ 93, 1, >3, 6/, 1>, >?, ?1, =>, 9?, /9.

& a) :$iefl! explain man'al im'lation 'in* e"ent #hed'lin* fo$ in*le #hannel 'e'e/ a) Diffe$entiate %et(een #hi7'a$ F7S tet.

3 a) Six t$'#0 a$e 'ed to ha"e #oal f$om mine to the $ail the $oad. The$e a$e & loade$ and

one (ei*hin* #ale. Afte$ loadin*, a t$'#0 immediatel! mo"e to the #ale fo$ (ei*hin*

and e$"i#in* i a pe$ CICS. Afte$ (ei*hin* a t$'#0, %e*in a f$a'd time and then

afte$(a$d $et'$n to the loade$ 'e'e (ith the dit$i%'tion of t$a"el time a.

Inte$"al time in min'te mt) 3 = 9 1

;$o%a%ilit! .3 ./ .& .1

C'$the$ the dit$i%'tion of loadin* time (ei*htin* time a$e a+

Inte$"al time in min'te mt) 6 1 16

;$o%a%ilit! .../6&

Wei*hin* time in mt 1& 1=

;$o%a%ilit! .> ./

Sim'late the !tem to etimate the loade$ #ale 'tili2ation

6 a) Di#' in %$ief the "a$io' p$o%lem o$ e$$o$ (hi#h o##'$ (hile *ene$atin* pe'do

$andom n'm%e$.

%) Explain the t(o Goodne of fitB tet %! 'in* an app$op$iate example= a) ;$epa$e a ta%le 'in* e"ent #hed'lin* time ad"an#e al*o$ithm fo$ a #he#0 o't #o'nte$

top the im'lation (hen fifth #'tome$ depa$t. Etimate mean $epone time and

p$opotion of #'tome$ (ho pent o$ mo$e min'te in the !tem. E"ent noti#e m't

ha"e e"ent t!pe, time #'tome$ n'm%e$.

Inte$"al a$$i"al time 9 = 1 9 / 9 . . . . .


4/12


5/12

.31 .=9 .9? .?? .>3 .?1 .66 .=& ./= .&>

.1? .>& .>6 .9 .63 .& .1 ./= .1= .&9

.19 .1 .?6 .=? .19 .3> .&/ ./& .9& .6/

./1 .3& .3 .3 .9/ .36 .1/ .6> .=/ .&?

1/ a) When to 'e $andom "a$iate *ene$ation What i the diffe$en#e %8( $andom n'm%e$

*ene$ation and $andom "a$iate *ene$ation Explain (ith example.

%) Explain the in"e$e t$anfo$mation te#hni'e of p$od'#in* $andom "a$iate fo$

exponential dit$i%'tion. Gene$ate exponential "a$iate xi, (ith mean I. *i"e $andom

n'm%e$ 5i.1/=, .3&&, .=6?>, .>?=6, .>=?=.

Unit 4&5

13 a) Explain in detail the in"e$e t$anfo$mation te#hni'e fo$ exponential dit$i%'tion.

%) Explain #hi7'a$e *oodne of fit tet to a##ept o$ $eKe#t a #andidate dit$i%'tion.

16 a) 5epeat of 6 &?)'l! < &6

1= a) With ill't$ati"e example, de#$i%e the o8p anal!i fo$ tead! tate im'lation1> a) Example the #on#ept of !tem (ith an! me li"e example

%)Di#' the "a$io' (a! of modelin* of a 8m#) $epeat

19 a) What i a##eptan#e < $eKe#tion te#hni'e Gene$ate th$ee poion "a$iate (ith mean

J .&

1? a) Di#' in detail a%o't the "a$io' element of an! *ene$al 'e'in* 8m. f'$the$

explain the need fo$ im'lation in thi en"i$onment the "a$io' mea'$e 'ed to

e"al'ate the 8m& Explain ho( (hat fo$ the in"e$e t$anfo$m te#hni'e i 'ed to ample f$om t(o

di#$ete dit$i%'tion.

%) Di#' ho( the ample mean i etimated 'nde$ no$mal poion dit$i%'tion&1 a) Explain the a##eptan#e < $eKe#tion te#hni'e. Gene$ate 6 poion "a$iate (ith mean

J .&6

%) Explain #hi'a$e *oodne of fit tet. Appl! it to poion a'mption (ith J /7=3

data i2e 1 and o%e$"ed f$e'en#! Oi 1& 1 1? 1> 1 9 > 6 6 / / 1&& a) What i in"e$e t$anfo$m te#hni'e De$i"e an exp$eion fo$ exponential

dit$i%'tion.


6/12

Unit 6& 7

&/ a) Explain ho( the method of hito*$am #an %e 'ed to identif! the hape of a

dit$i%'tion.

d) Explain (ith a neat dia*$am, the model %'ildin* "e$ifi#ation and "alidation.

%) Uin* H&tet, tet fo$ h!pothei that the data *i"en follo( 'nifo$m dit$i%'tion at J

.6.

The #$iti#al "al'e i 1=.?

i 9 9 1 ? 1& 9 1 13 1 18

%) ;$epa$e a ta%le e"ent #hed'lin* time ad"an#e al*o$ithm m, 'ntil the #lo#0 $ea#he

time 16, 'in* the inte$a$$i"al and e$"i#e time *i"en %elo( in the o$de$ ho(n. The

hoppin* e"ent (ill %e at time /.

Inte$"al time 3 6 & 9 / >

Se$"i#e time 6 / 3 = & >

%) De#$i%e ho( the method of hito*$am #an %e 'ed to identif! the hape of a

dit$i%'tion.

&3 a) Explain the #hi7'a$e *oodne of fit tet to a##ept o$ $eKe#t a #andidate dit$i%'tion

%) :$iefl! explain the th$ee < tep app$oa#h that aid in the "alidation p$o#e

&6 a) Explain in detail a%o't the model %'ildin*, "e$if!in* "alidation in the model

%'ildin* p$o#e th$o'*h a dia*$am.

%) Co$ the follo(in* e'en#e #an the h!pothei that the n'm%e$ a$e independent #an %e

$eKe#ted on the %ai of len*th of $an 'p do(n (hen J .6


7/12

./3 .? .&6 .9? .33 .1& .&1

.3= .=> .9/ .>? .=3 .>= .91

.?3 .>3 .&& .?= .?? .>> .=>

.6= .31 .6& .?? .& .3> ./

.1> .9& .6= .?? .& .3> ./

.1> .9& .6= .36 ./1 .>9 .6

.>? .>1 .&/ .9& .?/ .=6 ./>

./? .3&

&= a) A e'en#e of 1 fo'$ di*it n'm%e$ ha %een *ene$ated anal!i indi#ate thefollo(in* #om%ination f$e'en#ie

-om%ination O%e$"ed f$e'en#!

Oi

Co'$ diffe$ent 6=6

Di*it

One pai$ /?&

T(o pai$ 1>

Th$ee li0e di*it &3

Co'$ li0e di*it &

:aed on po0e$ tet #he#0 (hethe$ the n'm%e$ a$e independent, ele J.6%) Explain in"e$e t$anfo$m te#hni'e fo$ exponential dit$i%'tion. Sho(n the

#o$$epondin* *$aphi#al inte$p$etation.

&> a) Explain (ith a neat dia*$am model %'ildin* "e$ifi#ation and "alidation&9 a) Define im'lation, im'lation model, entitie, mea'$e of pe$fo$man#e and a#ti"itie.

%) Lit / #i$#'mtan#e 'nde$ (hi#h im'lation i the app$op$iate tool and t(o

#i$#'mtan#e 'nde$ (hi#h im'lation i not the app$op$iate tool.

#) Explain in %$ief (ith a neat fi*'$e the tep in"ol"ed in a im'lation t'd!&? a) :$iefl! define an! 6 #on#ept 'ed in di#$ete e"ent im'lation

%) Identif! the #on#ept in the follo(in* example i.e example of i /3) d$a(in* $ele"ant

fi*'$e)


8/12

#) Six d'mp t$'#0 a$e 'ed to ha'l #oal f$om the ent$an#e of a mine to $ail$oad. Ea#h

t$'#0 i loaded %! one of t(o loade$. Afte$ loadin*, t$'#0 immediatel! mo"e to the

#ale to %e (ei*hed a oon a poi%le. :oth the loade$ the #ale ha"e a fi$t #ome

fi$t e$"ed (aitin* line fo$ t$'#0 t$a"el time f$om a loade$ to #ale i #onide$ed

ne*li*i%le. Afte$ %ein* (ei*hed a t$'#0 %e*in t$a"el time d'$in* (hi#h time t$'#0

'nload) then afte$(a$d $et'$n to the loade$ 'e'e. The a#ti"itie of loadin* time

t$a"el time a$e *i"en in the follo(in* ta%le.

Loadin* time 1 6 6 1 16 1

Wei*hini time 1& 1& 1& 1= 1& 1=

T$a"el time = 1 3 3 9

End of im'lation i #ompletion of & (ei*hin* f$om the #ale. Depi#t the im'lationta%le etimate the loade$ #ale 'tili2ation. A'me that fi"e of the t$'#0 a$e at the

loade$ one i at the #ale t time .

/ a) Diffe$entiate %8( t$'l! $andom n'm%e$ pe'do $andom n'm%e$. Mention 3

p$ope$tie that $andom n'm%e$ ho'ld poe.%) Uin* m'ltipli#ati"e #om*$'ential method fo$ *ene$atin* $andom n'm%e$, lit the

$andom n'm%e$ find the pe$iod of *ene$ato$ fo$ a1/, m=3, Ho&

#) A e'en#e of 1 fo'$ di*it n'm%e$ ha %een *ene$ated an anal!i indi#ate the

follo(in* #om%ination f$e'en#ieCo'$ diffe$ent di*it 6=6, one pai$/?&, t(o pai$, th$ee li0e di*it &3

$emainin* a$e fo'$ li0e di*it. :aed on the po0e$ tet, tet (hethe$ thee n'm%e$ a$eindependent. Ue le"el of i*nifi#an#e .6

/1 a) Ela%o$ate the need fo$ *ene$atin* $andom "a$iate. Gi"en p$o%a%ilit! ma f'n#tion

pmt of $andom "a$ia%le a et of 'nifo$m $andom "a$ia%le o"e$ the $an*e ,1)

de#$i%e the method to *ene$ate $andom "a$ia%le.

%) Gi"en the 'nifo$m dit$i%'tion on 1, & (ith pmt p x) 180, x1,&, 0, *ene$ate

the $andom "a$iate fo$ the fi"e $andom n'm%e$ .91, .1&, ./3, .6= and .?/) De$i"e

the fo$m'la 'ed. Ue 01 fo$ *ene$atin* $andom "a$iate./& A) Explain the need fo$ inp't modelin* hito*$am method of identif!in* the inp't

dit$i%'tion.

%) The n'm%e$ of "ehi#le a$$i"in* at a f'n#tion in a fi"e min'te pe$iod (a o%e$"ed fo$1 da!. The $e'ltin* data i a follo( .

No of a$$i"al 1 & / 3 6 = > 9 ? 1 11

C$e'en#! 1& 1 1? 1> 1 9 > 6 6 / / 1


9/12

It i p$e'med that the a$$i"al follo( a poion dit$i%'tion (ith pa$amete$ J /.3

Uin* #hi7'a$e tet, dete$mine (hethe$ the a'mption that a$$i"al follo( poion

dit$i%'tion #an %e a##epted at a .6 le"el of i*nifi#an#e.

Note+ expe#ted "al'e 'ed %! , 6 fo$ #al#'lati"e p't the "al'e #al#'lated "al'e

in a ta%'la$ fo$m

// a) 5epeat%) De#$i%e the th$ee tep app$oa#h (hi#h ha %een 'ed a an aid in the "alidation

p$o#e/3 a) What i im'lation State an! t(o of it me$it t(o limitation. State an! t(o

it'ation (he$e im'lation #an %e 'ed.

%) Di#' the t!pe of model of a 8m#) Explain "a$io' tep in a im'lation t'd!.

W$ite the flo( #ha$t fo$ im'lation t'd!.

/6 a) De#$i%e a 'e'in* !tem (ith $epe#t to a$$i"al and e$"i#e me#hanim !tem

#apa#it!, 'e'e di#ipline, flo( dia*$am of a$$i"al and e$"i#e e"ent.

%) A ne(pape$ elle$ #laifie hi da! into *oodB and %adB one (ith p$o%a%ilit! .3

and .= $epe#ti"el!. The amo'nt of ne(pape$ old a$e *i"en %! the dit$i%'tion %elo(.

Good -opie old ;$o%a%ilit!

16 .6

& .1

&6 .&

/ ./6

/6 ./

:ad -opie old ;$o%a%ilit!

16 .1

& ./

&6 .3

/ .16

/6 .6


10/12

Pe #an %'! a #op! of the ne(pape$ himelf %! 1 e'$o and he ell it (ith the p$i"e of 1.9

e'$o. Unold #opie m't %e th$o(n a(a!. :aed on 6 da! of im'lation #al#'late the

p$ofit of the ne(pape$ elle$. Intead of &6 ne(pape$ pe$ da! if / ne(pape$ pe$

da! a$e p'$#haed (ill it %e mo$e p$ofita%le

5andom di*it fo$ t!pe of da! +/ 3 > 9

5andom di*it fo$ no of +> /> ?/ > 36

-opie old

/= a) 5epeat

%) S'ppoe the maxim'm in"ento$! le"el M, i 11 'nit the $e"ie( pe$iod N i 6 da!.

Etimate %! im'lation, the a"e$a*e endin* 'nit in in"ento$! n'm%e$ of da! (hen aho$ta*e #ondition o##'$.

The n'm%e$ of 'nit demanded pe$ da! i *i"en %! the follo(in* p$o%a%ilit!

dit$i%'tion a'me that o$de$ a$e pla#ed at the #loe of %'ine a$e $e#ei"ed fo$

in"ento$! at the %e*innin* of %'ine a dete$mined %! the lead7time. Initiall! im'lation

ha ta$ted (ith in"ento$! le"el of / 'nit on o$de$ of 9 'nit #hed'led to a$$i"e in t(o

da! time.

Demand 1 & / 3

;$o%a%ilit! .1 .&6 ./6 .&1 .?

Lead time i a $andom "a$ia%le, (ith the follo(in* p$o%a%ilit! dit$i%'tion

Lead time da!) 1 & /

;$o%a%ilit! .= ./ .1

Note+ The e'en#e of $andom di*it fo$ demanded $andom di*it fo$ lead7time ho'ld

%e #onide$ed in the *i"en o$de$.

5D fo$ demand &38/68=68918638/89>8&>8>/8>83>83683981>8?8

5D fo$ lead time 688//> a) What i the $ole of maxim'm denit! maxim'm pe$iod in *ene$ation of $andom

n'm%e$ With *i"en eed 36, #ontant m'ltiplie$ &1, in#$ement 3? mod'l' 3,

*ene$ate a e'en#e of fi"e $andom n'm%e$.


11/12

%) Co$ the follo(in* e'en#e #an the h!pothei that the n'm%e$ a$e independent #an %e

$eKe#ted on the %ai of len*th of $'n 'p do(n (hen J .6, 2e$o 61.?=

./3 .? .&6 .9? .9> .33 .1&

.9/ .>= .>? .=3 .> .91 .?3.?= .?? .>> .=> .6= .31 .6&

.3> ./ .1> .9&.6= .6 .36.?? .>1 .&/ .1? .9& .?/ .=6

.&1 .3= .=>

.>3 .&& .>3

.>/ .?? .&./1 .>9 .6

./> ./? .3&

%) A e'en#e of 1 fo'$ di*it n'm%e$ ha %een *ene$ated anal!i indi#ate the

follo(in* #om%ination f$e'en#ie. :aed on po0e$ tet #he#0 (hethe$ the n'm%e$

a$e independent. Ue J.6, H&.6,& 6.??.

%) The time $e'i$ed fo$ 6 diffe$ent emplo!ee to #omp'te and $e#o$d he n'm%e$ ofho'$ d'$in* the (ee0 (a mea'$ed (ith the follo(in* $e'lt in min'te. Ue #hi7

'a$e tet to tet the h!pothei that thee e$"i#e tie a$e exponentiall! dit$i%'ted. Ta0e

the n'm%e$ of #la inte$"al a 0=, J.6.

Emplo!ee Time Emplo!ee Time Emplo!ee Time

1 1.99 &1 1.3& 31 .9

&

/

36

=

>

#) What i a##eptan#e < $eKe#tion te#hni'e Gene$ate / poion "a$iate (ith mean J

.&. 'e the follo(in* $andom n'm%e$ .3/6>, .313=, .9/6/, .??6&, .9&3

/9 a) 5epeat


12/12

%) fo$ the *i"en e'en#e of 4 and

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