Production Planning 2010

7/26/2019 Production Planning 2010

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PRODUCTION PLANNING

PROF.A.K.CHATTERJEE


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PRODUCTION PLANNING

Planning implies looking ahea in!o !he "#!#$e.%ase on ho& "a$ ahea in!o !he "#!#$e one is

looking a!' &e ha(e !he "ollo&ing )lassi"i)a!ion

CLA**IFICATION OF PLANNING

Long Range Planning: Planning Horizon 5-10years.

+ei#m Range Planning: Planning Horizon 1year.

*ho$! Range Planning: Planning Horizon lessthan 1yr.


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PRODUCTION PLANNINGPRODUCTION PLANNINGby definition would constitute

planning for production /operations for the upcoing year

!ediu and short range". #he ediu range planning ay

be further classified based on the deand.

#he ediu range planning proble is tered as $ggregate

Production Planning in the literature. %n such cases the

deand%s assued to be &ynaic and &eterinistic in nature.


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AGGREGATE PRODUCTION

PLANNING PRO%LE+

E,A+PLE -&eterine the iniu cost

production plan. 'e(d. data is gi)en below:

*an +eb ,ar

&eand 100 5 15

'# ap 100 100 100

# ap 5 5 5

'ele)ant cost: '# cost/unit 's.100

# cost/unit 's.15

%/unit/period 's. 5


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PLANNING PRO%LE+ )on!.

PLAN -

*an +eb ,ar

'# 100 100 100

# 0 0 0PLAN /

*an +eb ,ar

'# 100 5 100

# 0 0 5#radeoff: Produce an unit in '# and carry it o)er as

in)entory for # periods as against producing the

sae unit in #


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FOR+ULATION

&ecision )ariables:

12 no. of units to be produced in *an '#

31 2 no. of units to be produced in *an #2 no. of units to be produced in +eb '#

3 2 no. of units to be produced in +eb #

42 no. of units to be produced in ,ar '#

34 2 no. of units to be produced in ,ar #%1 2 in)entory at the end of *an

% 2 in)entory at the end of +eb

%4 2 in)entory at the end of ,ar


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FOR+ULATION )on!.,iniise 100!16.64"6 15 !3163. 634"

6 5!%16%.6%4"7

8ub9ect to 1631 - %1 2 100%16.63. - %.2 5

%.64 634 -%4 2 15

1 . 4; 10031 3. 34; 5

1 . 4 31 3. 34 %1 %. %4< 0


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PRODUCTION PLANNING

*TRATEGIE*

+a!)hing Deman Plan: Production(uantity in any onth is e(ual to the deand

for the corresponding onth. !as can be seen

in Plan "

Le(el *!$a!eg0: %plying that the production

(uantity reains constant fro onth toonth. !as can be seen in Plan 1"


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DETER+ININGPRODUCTION

PLANNING *TRATEGIE*

#ransportation ,ethod

*an +eb ,ar ap

*an '# 100 # 5

+eb '# 100

# 5

,ar '# 100# 5

&eand 100 5 15


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DETER+ININGPRODUCTION

PLANNING *TRATEGIE*

E1ample /: &eand forecast for the onths *an to

$pr are 5 4= units. #he rele)ant

costs are!a"Production ost 2 c!>" 2 146 > if > ? 0

2 0 otherwise

!b" %n)entory ost 2 's.1/unit le)ied on the end ofonth in)entory.

&eterine the iniu cost production plan.


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CONCEPT OF DO+INANT *E2UENCE

%n any plan the total production is e(ual to the total deand Hence the #otal

)ariable cost for any plan will be sae here 's.@.

#he trade-off is thus between the fi>ed cost of 's.14 and % of 's.1.#o gain

further insight to the proble consider the deand of an ite in the upcoing

two onths as 100 A 50 units. #he proble is to find the iniu cost

production plan. #he rele)ant costs are the fi>ed cost $ !14 here" and in)entorycarrying cost H. !1 here"

#he alternati)e plans can be written as:

1. Produce 100 in first onth and 50 in the second

. Produce 101 in first onth and =B in the second4. Produce 10 in first onth and =@ in the second

n. Produce 150 in first onth and 0 in the second


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CONCEPT OF DO+INANT *E2UENCE )on!.'

#he costs of the alternati)e plans can be seen as $$ 6 H $6HCC$ 6 50H. $s H is positi)e one

needs to consider only the first and the last option

alternati)e. #hus if the re(uireent for the twoonths are &1and &. respecti)ely it is

sufficient to consider the following two plans for

optiality: 1. &16 &. 0 and . &1 &.#hese are called the doinant se(uences.


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CONCEPT OF DO+INANT *E2UENCE )on!.'

#he nuber of doinant se(uences for a # period

proble 2 #-1 thus for a 4 period proble with

re(uireents &1& &4 #he iniu cost plan

will be one aong the following eight plans:

1. &16 & 6 &4 00

. &16 & 0 &4

4. &1 & 6 &4 0

=. &1 & &4


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THE T3RE CO+PAN3 PRO%LE+

$priori $nalysis:

*!ep -%dentify deand and supply gap

+on!h N4F Deman 54R Ho#$s %alan)e O#!p#! Rema$k

*une + 1000 D 10 5@0 1000

E =000 D 5@0 0 4@F D o)er

E ' 1=@ 144

*uly + 5000 D 400 0 500 D o)er

+ ' 450 11@ 500 6 400 '

E @000 ' 1@0 1=@ @000 61=@ '

$ugust + 5000 D F00 =00 5000

E 4000 D =00 0 FF D o)er

E ' 54 = 444 6 = '


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+ro 8tep 1 its clear that enough supply is there to eet all deands.

*!ep /alculate the contribution per unit for each of the product G

achine cobinations. 1 unit of + produced by D /c will gi)e a

contribution 2 's. !B G 4.B0 G 0.4 G 0.F0" 2 's. =. !neglecting the% which is a relati)ely sall aount". #hus for +D cobination

there is a positi)e contribution. $ (uic chec re)eals that all other

cobinations +' ED E' yield a positi)e contribution iplying it

is worthwhile producing (uantity e(ual to the total deand of both

types of tyres i.e. 15000 of E and 11000 of +


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#HI #3'I ,P$E3 P'JKI,

*!ep 6$s total production 2 total deand the

re)enue is a constant 2 's.!15000 > 6 11000 > B"

2 's. 0=000. 8iilarly the total aterial cost as

well as the shipping cost are also constant.*!ep 7ne ay infer fro the analysis that:

!1"%n this case profit a>iization and cost

iniization are e(ui)alent.

!" #he trade-off is essentially between operating cost

and %


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Eotethat the proble can be forulated A sol)ed

using KP. 3ou ay reinforce your learning fro '

by defining the decision )ariables ob9ecti)e and the

constraints. +or e.g.De)ision (a$ia8les

Iach of the two tyres can be produced by two

different achines in any of the 4 onths gi)ing rise

to a total of 1 )ariables. +or e.g. ne ay denoteED1 as the no. of units of nylon !E" tyres to be

produced by wheeling !D" achine in *une !say".

$re there any other type of &ecision )ariablesL


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THE T3RE PRO%LE+ )on!.

Cons!$ain!sA(aila8ili!0 o" ma)hine ho#$s in an0 pe$io.

%n *une the wheeling achine is a)ailable for only 00 hrs.

Iach E A + tyre re(uires 0.15 and 0.1 hrs of wheeling

achine respecti)ely. %f ED1 A +D1 denote the productionin *une of E and + using D then 0.15ED1 6 0.1 +D1 ;

00

+a!e$ial %alan)e E9#a!ion.

+or e)ery period and e)ery product one needs to ensure

that beginning in)entory 6 aount produced - aount

deanded 2 ending in)entory. +or *une for Eylon tyre

Jeg. %n)entory 2 0 if *une end %n)entory 2 %E1 then

ED16E'1-%E12=000


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,$88 P'&M#%E PK$EE%EN

$E& P'*I# PK$EE%EN

,ass Production represents high )olue

ProductionO Pro9ect is a one shot affair. #he

data for these are siilar looing but the(ueries and hence the planning techni(ues

are different. +or e>aple gi)en the data on

an assebly the (uery ay be to deterine

how the acti)ities are to be planned to get

a defined continuous output per hour.


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A**E+%L3 DATA

A)!i(i!0 Time;mins.< Imm.P$e.A. / =

%. - A

C. / AD. - %'C

E. 6 D

uestion: How any persons to eploy andacti)ities to be assigned to eachL

&esired output rate 2 0 units/hour.


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Eetwor representation of the $ssebly

A

B

D

C

E

2

1

2

1 3

$88I,JK3 PK$EE%EN


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K%EI J$K$E%EN

Ni)en the data on an $ssebly consisting of

!a"the acti)ities coprising the $ssebly

!b" the tie re(uired to perfor each acti)ity and

! c" the precedence relationship go)erning the acti)ities

!suarized in ters of iediate predecessor"

the ob9ecti)e of Kine Jalancing proble is to decide on the

allocation of the acti)ities to )arious Dor stations so as

to achie)e a desired out put rate to a>iize the Kine

efficiency without )iolating the precedence constraints.


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8#IP8 +' K%EI J$K$E%EN

1. +ind the desired cycle tie fro the desired output

rate. 0units/hour would iply a cycle tie 2 4 in.

. +ind the re(uired nuber of wor stations. %f total

assebly tie 2 # then no. of worers to who the

whole assebly can be allocated has to be < #/2B/424 wor stations.

4. Prepare a list of all the acti)ities in specific order for

the purpose of allocation. Jasis of the ordering ay be

any heuristic e.g. 'an Positional Deight !'PD"heuristic would order the acti)ities based on PD !the

tie re(uired to perfor the acti)ity 6 tie re(uired to

perfor all its successors.


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8#IP8 +' K%EI J$K$E%EN

=. reate 8tations and start assigning acti)ities. #he acti)ity with the

highest PD is assigned to 8tation 1. hec the order obtainedfro 8tep 4 is $ J & I. #hus acti)ity $ stands assigned to

8tation 1.

5. +or subse(uent assignents calculate the reaining tie that can

still be assigned without )iolating the ycle #ie constraint. $s $taes in. 24 in its still possible to assign 1 in to 8tation

1. No down the order list to find the acti)ity taing 1 in. Jefore

assigning any acti)ity to a 8tation a)oid !a" ycle #ie and !b"

precedence )iolation.

F. %f none of the reaining acti)ities satisfy the abo)e condition

create a new 8tation and repeat the process till all acti)ities ha)e

been assigned


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PK$EE%EN +' *J 8HP 838#I,8

+or *ob 8hop 8ystes where each product ay be

re(uired to be processed on different achines in

different se(uences the identification of bottlenec

is not straightforward. Here the concept and

approaches of *ob 8hop 8cheduling assue

iportance.


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8HI&MK%EN: 8%ENKI ,$H%EI

P'JKI,P'JKI, 1 onsider 4 *obs each taing 1 4 hours respecti)ely to be

scheduled on a achine to iniize the a)erage waiting tie of the 9obs.

*OLUTION*ob 1 with iniu processing tie to be scheduled first *ob

with ne>t iniu tie second and so on.

P'JKI, onsider the abo)e proble with ore inforation. #he

waiting cost per hour for each *ob are 's. 0 =5 and F4. 3ou ha)e to decide on

the schedule that iniizes the total waiting cost.

*OLUTION#he p/w ratio !p 2 processing tie w2 waiting cost per hour" canbe calculated for each *ob. *ob with the iniu p/w is to be ordered first

followed by the *ob with the ne>t iniu and so on.


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*CHEDULING *INGLE +ACHINE

PRO%LE+

S

S1

i j

j i

T

T

Waiting cost under schedule S or S1 = waiting cost (WC) o !o"s other than #

and j$ % WC o !o" i and j& #t 'a "e noted that the WC o !o"s other than #

and j$ is sa'e in S and S1 and the dierence in WC is "ecause # and j&


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#D ,/ +KD 8HP

P'JKI, 4 #hree boos are to be printed and bound. #here is oneof each ind of /c. Processing tie data are gi)en below:

b9ecti)e is to order the boos so that iniu tie is taen to

coplete all the boos.

%ook N#m8e$ P$in!ing Time ;Ho#$s< %ining Time ;Ho#$s where the

iniu P occurs. %f P occurs on the 1st/c put that 9ob first. %f P

occurs on the nd/c put that 9ob last. hec P2 1 occurs on /c 1.

Hence 9ob will coe first.*!ep / 'eo)e the 9ob fro the list and repeat till all 9obs are

scheduled. #hus 9ob 1 will be ordered last. #hus the schedule 4 1

will iniize the a>iu flow tie which is the tie by which

all 9obs are copleted !tie by which 9ob 1 coes out fro thesecond /c"

No!e +low tie is the tie the 9ob spends in the 8hop.

,a>iu +low tie 2 +,$1 2+low tie of the 9ob which coes last.

Production Planning 2010

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