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Figure 8.4 Economic order quantity (EOQ) model.
(Note that this model has been modified)
Example 9.1 - An EOQ Model for Bedrock' !ro"lem
100
Annual Demand 12,000
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Figure 8. 8roduction order quantity (8OQ) model.
Example 9.( - )#e !*OQ Model and +olu%ion %o ,imo' !ro"lem.
Input Annual Demand 2,100
=etup %o&t '30.00
*nit %o&t '0.00
Annual production rate 2,00
*nit oldin$ co&t per year (to option&)
(i) in '& per year
(ii) a& o unit co&t 20.0
Annual unit oldin$ co&t '/.00
Output 8OQ 130.12
2>.14
3.3
?a@imum inentory leel 223.
Annual oldin$ co&t '/
Annual &etup co&t '/
!otal co&t '/3,3
Cell Formula Copied to
E10 ;9(E>BB,E4,ECE>)
E11 ;9(E100,Boldin$ co&t cannot "e +eroB,BB)E12 =Q!(2CECE36E10)C=Q!(E/6(E/ - E))
E1 2CE126E/
E13 2CE126E
E1 E12C(E/ - E)6E/
E1/ 0.CE10CE1
E1 ECE36E12
E14 E1/ E1 ECE
8roduction run time, o (in eeF&)
Optimal cycle time, !o (in eeF&)
A B C D E F
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Figure 8. 8roduction order quantity (8OQ) model.
G H I J K L M N O P
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Figure 8. 8roduction order quantity (8OQ) model.
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Q
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Figure 8. Quantity di&count model or te eelie %ompany.
Example 9./ - A Quan%i%& 0icoun% Model for %#e #eelie 2ompan&
Input Annual Demand 1,00 User input cellsOrderin$ %o&t '40.00 are shaded
*nit oldin$ co&t per year (to option&)
(i) in '& per year
(ii) a& o unit co&t 0.0
DISCOUNT TABLE *nit %o&t £10.00 £8.00 £.00
0 1000 !000
Annual unit oldin$ co&t '.00 '2.30 '1.40
Output 242.4 1/.2 /.1AdHu&ted order quantitie& 242.4 1000.0 2000.0
!otal co&t& '1,43> '1,20 '10,4/0
?inimum total co&t i& £10"80 2
Optimal order quantity i& !000.0
%ycle time i& #.$ eeF&
Cell Formula Copied to
911 ;9(IG/BB,IGC9>,IG/) G11:11912 ;9(9110,Boldin$ co&t cannot "e +eroB,BB)
91 =Q!(2CIGCIG36911) G1:1
913 ;9(91#910,91,910) G13:13
91 IGCIG36913 0.C913C911 IGC9> G1:1
91 ?;5(91:1)
1 ?A!%(91,91:1,0) - 1
914 O99=E!(914,-3,1)
91> 2C9146G
?inimum di&count quantity, ?ini
Qi
A B C D E F G H I
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Figure 8.3 Deliery car$e model or te armer&J co-operatie.
Example 9.4 - A 0elier& 2#arge Model for %#e Farmer' 2o-opera%ie
Input Daily Demand (in tonne&) .0 User input cells*nit %o&t '100.00 are shaded
*nit oldin$ co&t per day (to option&)
(i) in '& per day '1.0
(ii) a& o unit co&t
DELI%E&' TABLE eorder %o&t £80.00 £1$0.00 £180.00
10 !0 $0
Daily unit oldin$ co&t '1.0 '1.0 '1.0
Output 1.> 22.4 2/.4AdHu&ted order quantitie& 10.0 20.0 2/.4
!otal co&t& '2 ' '30
?inimum total co&t i& £$$! 0
Optimal order quantity i& 10.0
%ycle time i& $.$ day&
Cell Formula Copied to
91 =Q!(2CIGC9>6911) G1:1
913 ;9(916913 0.C913C911 IGCIG3 G13:1
91> 9146G
?a@imum deliery quantity, ?a@i
Qi
A B C D E F G H I
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Figure 8.8 Determini&tic model it planned &tora$e&.
Example 9. - An 5nen%or& Model 6i%# +#or%age Allo6ed
Input Annual Demand 12,000=etup6Orderin$ %o&t '0.00 User input cells
*nit %o&t '2.00 are shaded
oldin$ co&t (to option&)
(i) in '& per year
(ii) a& o unit co&t 0.0
=orta$e co&t per unit per year '3.00
*nit oldin$ co&t per year '.0
Output /4.2?a@imum &tocF leel 2.>
KacF-order &i+e 332.
5o. o order&6year 1.
%ycle time 2.> eeF&
Annual %o&t&LL..LL
=etup6orderin$ co&t '443./
oldin$ co&t '0.0
=orta$e co&t '/.>
8urca&e co&t '00,000
!otal co&t '01,/>
Cell Formula Copied to
E10 ;9(E4BB,E,E4CE)
E11 ;9(E100, BEnter a alue in eiter cell E or E4B,BB)
E1 =Q!(2CECE3C(E> E10)6(E>CE10))
E13 E>CE16(E> E10)
E1 E1 - E13
E1/ E6E1
E1 26E1/
E1> ECE36E1
E20 0.CE10CE13CE136E1
E21 E>C(E1 - E13)M26(2CE1)
E22 ECE
E2 =*?(E1>:E22)
Optimal order &i+e, Qo
A B C D E F G H
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Figure 8.8 Determini&tic model it planned &tora$e&.
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I J K L M N O P Q
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Figure 8.9 ?ultiple-product model it &tora$e &pace con&traint.
Example 9. - An 5nen%or& Model 6i%# +%orage +pace 2on%rain%
=etup co&t '1,00.0 User input cells
oldin$ co&t (a& o unit co&t) 0.0 are shaded
8roduct Demand *nit =pace EOQ Aera$e Naria"le
co&t (per unit) &pace co&t&
id$et 10,000 '14.00 0. 2.0 ./ '12,24
Gad$et 4,000 '1.00 0.2 20>.3 20.> '10,>2
8 ,000 '10.00 0.1 12.1 12>.> ',1>/
!otal& 13.3 '24,1/
8roduct Demand *nit =pace EOQ Aera$e Naria"le
co&t (per unit) &pace co&t&
id$et 03 '14.00 0. 1>>./ 2>/.> '12,>22
Gad$et /3 '1.00 0.2 1>>./ 1>3.0 '10,1
8 211/ '10.00 0.1 133. 10>.1 ',2
!otal& 00.0 '24,3>
8ercenta$e increa&e in aria"le co&t& 1.($)
S*alin+ Fa*tor , 7.37 (;nitially, &et =calin$ 9actor 1)
Sol-er arameter/
Set Tar+et Cell E2
Eual to ?a@
B2 C3an+in+ Cell/ E2
Su45e*t to Con/traint/ 14
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Figure 8.9 ?ultiple-product model it &tora$e &pace con&traint.
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K L M
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Figure 8.17 !e 5e&"oy pro"lem - a pro"a"ili&tic model it di&crete demand.
Example 9.3 - )#e e6"o& !ro"lem A !ro"a"ili%ic Model 6i%# 0icre%e 0emand
Input *nit %o&t, % '.00
=ellin$ 8rice, = '.00 User input cells are shaded
=crap alue, N '0.
Output
0 0.2 0. 30 '4
/ /0 0.1 0. 3 '34
0 0.1 0.1 33. '2
4 40 0.0 0.0 3 '11 3
60 7aimum pro9it , £(#
Cell Formula Copied to
E11 =*?(D11:DI14) E12:E14
911 =*?8OD*%!(%I11:%11,DI11:D11) %11CE12 912:91
914 =*?8OD*%!(%I11:%14,DI11:D14)
G11 EI3C911 - EIC%11 EIC(%11 - 911) G12:G14
;14 ?A!%(20,G11:G14,0)
D20 O99=E!(%10,;14,0)
20 ?A(G11:G14)
proit, E8i
Demand, Di
8i
%*?i
Optimal demand" :o ,
A B C D E F G H I J
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Figure 8.11 8ro"a"ili&tic model it &orta$e&.
Example 9.8 - A !ro"a"ili%ic Model 6i%# +#or%age
Input oldin$ co&t, '30.00 All user input cells
=orta$e co&t, K '00.00 are shaded
K6(K ) 0.>
Output
0.0 0.>3 Optimal amount
/ 4 0.03 0.>4
> 0.01 0.>>
4 10 0.01 1
Cell Formula Copied to
E E36(E3 E)
E11 =*?(DI11:D11) E12:E14911 ;9(E11#I),B Optimal amountB,BB)
912 ;9(A5D(E11
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Figure 8.1( =erice-leel model it aria"le demand6i@ed lead-time.
Example 9.9 - A +erice-:eel Model 6i%# ;aria"le 0emand< Fixed :ead-)ime
Input ; mu/t 4e in *on/i/tent time unit/
!ime (day, eeF, mont, year) eeF
Orderin$6=etup %o&t '100.00 ?ean 00
*nit %o&t '10.00 =tandard deiation /0
oldin$ co&t (to option&) >
(i) in '& per year eeF
(ii) a& o unit co&t 0.0
*nit oldin$ co&t per eeF '0.04 2
Output
eorder leel6point, 221.0 oldin$ co&t o &aety &tocF '1
Order quantity, Q 11/./ oldin$ co&t o normal &tocF '4
=aety &tocF 221.0 Orderin$6&etup co&t& '4)o%al co% per 6eek '4>
Cell Formula Copied to
D4 E3 D10, P4, 1/
E10 ;9(E>BB,E46G10,E>CE/6G10)
G10 ;9(E3BdayB,/,;9(E3BeeFB,2,;9(E3BmontB,12,1)))
E11 ;9(E100,BEnter a alue in eiter cell E4 or E>B,BB)
D1 C4 D1
D13 =Q!(2CCE6E10)
D1 O*5D*8(5O?=;5N()C/C=Q!(4),0)
1 D1CE10
13 D13CE1062
1 ;9(D130,BB,EC6D13)
1/ =*?(1:1)
Demand i/ normall2;di/tri4uted
=erice Reel , =R
Read !ime, Rt
A B C D E F G H I J K
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Figure 8.1/ =erice-leel model it aria"le demand6aria"le lead-time.
Example 9.17 - A +erice-:eel Model 6i%# Fixed 0emand< ;aria"le :ead-)ime
Input ; mu/t 4e in *on/i/tent time unit/!ime (day, eeF, mont, year) eeF
Demand 00 ?ean
Orderin$6=etup %o&t '100.00 =tandard deiation 1
*nit %o&t '10.00 >
oldin$ co&t (to option&)
(i) in '& per year User input cells are shaded
(ii) a& o unit co&t 0.0
*nit oldin$ co&t per eeF '0.04 2
Output Read time /./ eeF oldin$ co&t o normal &tocF '4
eorder leel6point, 22.3 Orderin$6&etup co&t& '4
Order quantity, Q 11/./ )o%al co% per 6eek '/
Cell Formula Copied to
D13 5O?=;5N()C/
E13 E3
D1 ECD13
D1/ =Q!(2CECE/6E11)
13 D1/CE11621 E/CE6D1/
1/ =*?(13:1)
Lead;time i/ normall2;di/tri4uted
=erice Reel , =R
A B C D E F G H I J
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Figure 8.1/ =erice-leel model it aria"le demand6aria"le lead-time.
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Figure 8.14 8eriodic reie (i@ed-period) model.
Example 9. 11 - A !eriodic *eie6 =i.e. Fixed-!eriod> Model
Input ; mu/t 4e in *on/i/tent time unit/
!ime (day, eeF, mont, year) day ?ean 30Orderin$6=etup %o&t '0.00 =tandard deiation 1
*nit %o&t '10.00 >
oldin$ co&t (to option&) 4 day
(i) in '& per year '20.00 1/ day
(ii) a& o unit co&t /0
*nit oldin$ co&t per day '0.0 /
Output
eorder leel6point, 1041.0 oldin$ co&t o &aety &tocF '/./
Order quantity, Q 1021.0 oldin$ co&t o normal &tocF '2.>
=aety &tocF 121.0 Orderin$6&etup co&t& '1.>/
)o%al co% per da& '/./
Cell Formula Copied to
D1 3C( 4) D1
D13 D1 - >
D1 O*5D*8(5O?=;5N(/)CC=Q!(4),0)
Demand i/ normall2;di/tri4uted
=erice Reel , =R
Read !ime, Rt
eie 8eriod
=tocF On-and
A B C D E F G H I J K
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Figure 8.1 ?ulti-period model it &eeral con&traint&.
Example 9.1( - A Mul%i-!eriod Model 6i%# +eeral 2on%rain%
Input All user input cells are shaded
Annual Demand ,/00
Orderin$ %o&t '.00 Output
*nit %o&t '2.00 EOQ 00.00
*nit oldin$ co&t per year (to option&) %ycle time
(i) in '& per year (in mont&) 1.0
(ii) a& o unit co&t 20.0 !otal co&t ',20
*nit oldin$ co&t per year '0.30
?ontly Order Endin$ %o&t per
?ont Demand Quantity ;nentory 8eriod1 230 ! 230 !
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Figure 8.1 ?ulti-period model it &eeral con&traint&.
+oler !arame%er Set Tar+et Cell 92
Eual to ?in
B2 C3an+in+ Cell/ E13:E2
Su45e*t to Con/traint/ E13:E2 # 20 Quantity di&count con&traint
E13:E2
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Figure 8.1 ?ulti-period model it &eeral con&traint&.
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Figure 8.1 ?ulti-period model it &eeral con&traint&.
K
30
3132
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Example 9.1/ - A +imula%ion Model for 5nen%or& 2on%rol
0emand %a"le :ead-%ime %a"le
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Figure 8.(7 ?8 model or te Fitcen ta"le e@ample.
2ae +%ud& 9.1 - A Ma%erial *e$uiremen% !lanning =M*!> Model
T3e BO7 Ta4le
art Num4er De/*ription BO7 Id. No. o9 Lead On lanned
Le-el Code Unit/ Time ?and Order User input
!a"le 0 1 1 1 0 &el. &o@ cells are
!op A&&em"ly 1 1001 1 2 0 2 shaded
!a"le !op 2 2001 1 1 140
Draer 2 2002 1 1 200
Re$ A&&em"ly 1 1002 1 1 100 2
Re$& 2 200 3 1 20 /
=ide un$ 2 2003 2 1 0 /
%onnectin$ un$ 2 200 1 1 110 /
T3e 7& Output Ta4le
1
Ta4le Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Ma%er !roduc%ion +c#edule 7 7 187 187 177 7 7 7
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 0 0 0 0 0 0 0 0
5et equirement& 0 0 10 140 100 0 0 0
8lanned Order eceipt& 0 0 10 140 100 0 0 0
8lanned Order elea&e& 0 0 10 140 100 0 0 0 0
2
Top A//em4l2 Lead Time , !
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 0 10 140 100 0 0 0 0
=ceduled eceipt& 0 177 0 0 0 0 0 0
On and 0 0 20 0 0 0 0 0
5et equirement& 0 0 1/0 100 0 0 0 0
8lanned Order eceipt& 0 0 1/0 100 0 0 0 0
8lanned Order elea&e& 0 1/0 100 0 0 0 0 0 0
Ta4le Top Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 1/0 100 0 0 0 0 0 0
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 140 20 0 0 0 0 0 0
5et equirement& 0 40 0 0 0 0 0 0
8lanned Order eceipt& 0 40 0 0 0 0 0 0
8lanned Order elea&e& 0 40 0 0 0 0 0 0 0
A B C D E F G H I J K L
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Figure 8.(7 ?8 model or te Fitcen ta"le e@ample.
3
Dra@er Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 1/0 100 0 0 0 0 0 0=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 200 30 0 0 0 0 0 0
5et equirement& 0 /0 0 0 0 0 0 0
8lanned Order eceipt& 0 /0 0 0 0 0 0 0
8lanned Order elea&e& 0 /0 0 0 0 0 0 0 0
Le+ A//em4l2 Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 0 10 140 100 0 0 0 0
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 100 100 0 0 0 0 0 0
5et equirement& 0 0 140 100 0 0 0 0
8lanned Order eceipt& 0 0 140 100 0 0 0 0
8lanned Order elea&e& 0 0 140 100 0 0 0 0 0
/
Le+/ Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 120 20 300 0 0 0 0 0
=ceduled eceipt& 0 177 0 0 0 0 0 0On and 20 10 0 0 0 0 0 0
5et equirement& 0 3>0 300 0 0 0 0 0
8lanned Order eceipt& 0 3>0 300 0 0 0 0 0
8lanned Order elea&e& 0 3>0 300 0 0 0 0 0 0
Side &un+ Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& /0 /0 200 0 0 0 0 0
=ceduled eceipt& 10 0 0 0 0 0 0 0 0
On and 0 0 0 0 0 0 0 0 5et equirement& 10 /0 200 0 0 0 0 0
8lanned Order eceipt& 10 /0 200 0 0 0 0 0
8lanned Order elea&e& 10 /0 200 0 0 0 0 0 0
4
Conne*tin+ &un+ Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 0 140 100 0 0 0 0 0
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 110 40 0 0 0 0 0 0
5et equirement& 0 100 100 0 0 0 0 08lanned Order eceipt& 0 100 100 0 0 0 0 0
A B C D E F G H I J K L
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7172
73
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8283
84
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Figure 8.(7 ?8 model or te Fitcen ta"le e@ample.
8lanned Order elea&e& 0 100 100 0 0 0 0 0 0A B C D E F G H I J K L
95
96
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Figure 8.(7 ?8 model or te Fitcen ta"le e@ample.
M N
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Figure 8.(7 ?8 model or te Fitcen ta"le e@ample.
8a$e-"reaF M N
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Figure 8.(7 ?8 model or te Fitcen ta"le e@ample.
M N
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Figure 8.(7 (cont.)
3
Dra@er Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 1/0 100 0 0 0 0 0 0
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 200 30 0 0 0 0 0 0 5et equirement& 0 /0 0 0 0 0 0 0
8lanned Order eceipt& 0 /0 0 0 0 0 0 0
8lanned Order elea&e& 0 /0 0 0 0 0 0 0 0
Le+ A//em4l2 Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 0 10 140 100 0 0 0 0
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 100 100 0 0 0 0 0 0
5et equirement& 0 0 140 100 0 0 0 0
8lanned Order eceipt& 0 0 140 100 0 0 0 0
8lanned Order elea&e& 0 0 140 100 0 0 0 0 0
/
Le+/ Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 120 20 300 0 0 0 0 0
=ceduled eceipt& 0 177 0 0 0 0 0 0
On and 20 10 0 0 0 0 0 0
5et equirement& 0 3>0 300 0 0 0 0 08lanned Order eceipt& 0 3>0 300 0 0 0 0 0
8lanned Order elea&e& 0 3>0 300 0 0 0 0 0 0
Side &un+ Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& /0 /0 200 0 0 0 0 0
=ceduled eceipt& 10 0 0 0 0 0 0 0 0
On and 0 0 0 0 0 0 0 0
5et equirement& 10 /0 200 0 0 0 0 0
8lanned Order eceipt& 10 /0 200 0 0 0 0 08lanned Order elea&e& 10 /0 200 0 0 0 0 0 0
4
Conne*tin+ &un+ Lead Time , 1
eeF 5um"er Oerdue 1 2 3 / 4
Gro&& equirement& 0 140 100 0 0 0 0 0
=ceduled eceipt& 0 0 0 0 0 0 0 0
On and 110 40 0 0 0 0 0 0
5et equirement& 0 100 100 0 0 0 0 0
8lanned Order eceipt& 0 100 100 0 0 0 0 0
8lanned Order elea&e& 0 100 100 0 0 0 0 0 0
A B C D E F G H I J K L
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Figure 8.(1 ?odel or te part-period "alancin$ (8KK) metod.
(Note that this model has been modified)
Example 9. 14 - A Model for %#e !ar% !eriod Balancing =!!B> Me%#od
5npu% Orderin$ (or =etup) %o&t '200 User input cells*nit oldin$ co&t '1.00 are shaded
Economic part period (E88) 200
10 100 10 0 0 100 2 20
eriod" 1 ! $ 6 ( < 8 #
0 100 00 0 200 /00 1 1/0
0 100 300 300 /00 > 1 10 1>10
-1.0 -0. 1.0 1.0 2.0 .> /.> .4 4./0. 1.0 0. 1.0 1.0 2.0 .> /.> .4 4./
Order 0a%a ? 10 100
0 An/@er la*e an order 9or !(0 unit/ in period 1
0 0 1 2 3 /
-10 -100 0 0 100 22 300 12 120
0 0 0 0 100 2 2 40 >0
-1.0 -1.0 -1.0 -1.0 -0. 0./ 2./ . .>
0. 1.0 1.0 1.0 1.0 0. 0./ 2./ . .>
Order 0a%a ? 10 0 02 An/@er la*e an order 9or !00 unit/ in period $
0 0 0 0 0 1 2 3
-10 -100 -10 -1 -0 0 100 0 /0
0 0 0 0 0 0 100 10 210
-1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -0. -0. 0.1
0.1 1.0 1.0 1.0 1.0 1.0 1.0 0. 0. 0.1
Order 0a%a ? 100 2 20
An/@er la*e an order 9or !!0 unit/ in period
0 0 0 0 0 0 0 0 0
%opy cell ran$e K11:R1 repeatedly don te &pread&eet, placin$ te cur&or in cell& K1>,
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Figure 8.(1 ?odel or te part-period "alancin$ (8KK) metod.
(Note that this model has been modified)
A B C D E F G H I J K L M
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8roduct 5o. in 8roduct 7ear %a&
name &tocF price lo
Gi+mo 10 '10.00 1 1
Gad$et 2 '12.0 2 3
id$et 4 '20.00 4
=procFet 30 '3.0 3 1/
Sample Fi+ure
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%olumn(K) 2 o(K)
%olumn(D:D>) 3 o(D:D>)
;5DE(K3:D,2,) '12.0 5O?=;5N(0.>)
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I
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1./33>
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