OR Final Project Back Work

8/9/2019 OR Final Project Back Work

1/24

THE MCS CORPORATION PROJECTAMEYA SAMPAT & HUY NGUYEN

Operation Research Methods

Professor Sharkey

1!"#!"1

Introduction/Problem BackgroundThe M$S $orporation% prodcers of the toy '(ino)a**%+ is interested in ,a-i,i.in/ pro0ts

hi*e ,ini,i.in/ prodction cost2 Actin/ as ad3isors to the co,pany% or /rop as char/ed to


2/24

0nd the ansers to three 4estions to he*pM$S reach the ,ost cost5e6cient prodction ,ethod2

The 0rst 4estion as 'Sho*d they re,o3e the )a*anced po*icy that re4ires each of M$S

prodction faci*ities to prodce the sa,e n,)er of toys7+ The second 4estion as% 'Sho*d

M$S $orporation insta** 8astProd% a syste, that o*d a**o for faster and cheaper prodction of

(ino)a**s7+ The third 4estion in3o*3es a /reen initiati3e that the M$S $orporation is prsin/2

9n order to *oer the car)on e,ission to )e*o the per,itted *i,it of 1" ,etric ton% the co,pany

has an option to insta** a certain n,)er of so*ar pane*s per faci*ities2 The insta**ation o*d he*p

redce a cost that certain faci*ities o*d incr that o*d dri3e o3era** cost2

To anser the 4estions% an ana*ysis as done in e-ce* sin/ Operations Research

Methods hich co*d )e app*ied to de3e*op a decision choice2 The fo**oin/ report detai*s the

0ndin/s of the report and i** a*k thro/h the steps sed to co,e to that decision2


3/24

Remoal o! t"e Polic#$e%ning t"e Problem

$rrent*y% M$S operates nder the po*icy that each faci*ity i** prodce the sa,e n,)er of

(ino:a** toys each ,onth2 9n other ords% the faci*ities are +)a*anced+ in that each i** prodces

e-act*y 1!; of M$S


4/24

Operation ith :a*ance Po*icy

Or /rop sed E-ce* So*3er to ca*c*ate ,onth*y prodction cost and shippin/ cost2 :e*o is an

e-a,p*e of the cost ca*c*ation >for (ece,)er? and an e-p*anation for ho e for,*ated the

cost2

Troy% NY'nit&/"

our

Energ#()*+/"

our

Energ#

Co&t/Hr

$eci&ion

,ariable&

(Hr&+

Time-imit(Hr&+ Co&t

No. o!Product

&

Prodine 1 # "" "21B

DB21DB1DB 1#"

BBB2BBBBB#

B112111111

Prodine BB

;BD2;;;;;;

1C"2;C";C

Prod

ine ; 1 CB

;B1;2DD

DDDF

DB21DB1D

B

(e,a

nd

Tota* No2 of

Prodcts@C##2####

#CC##2#

##CNeark%NProdine 1 B 1" "21D

FB2D;;;;; 1#" ;#2B

=CF21####C

Prodine BB

=;FD2CB1F12####

#CProdine ; 1 CB =C=;2CB

FB2D;;;;;;

(e,and

Tota* No2 of

Prodcts@

C##2####

#C

C##2#

##CHarris)r/% PA

Prodine 1 = " "2"F

1"2 1#" "=

="D2DDDDDF

Prodine ; ;B

1#;"#2####

#CProdine ; "2B ;"" C#"

B121111111

(e,and

Tota* No2 of

Prodcts@C##2####

#CC##2#

##C

Tota*cost

0123.4443

Tota* Spp*y ;""

Tota* (e,and ;""

Table 5b6 Sam7le o! Production Co&t Calculation !or Balance Polic# O7eration

Para,eter e-p*anation@

(ecision 3aria)*es@ the ti,e each prodction *ine in a partic*ar factory operates2 They are

deter,ined )y E-ce* So*3er as an opti,a* so*tion to ,ini,i.e prodction cost2 Since M$S


5/24

ses the e4a* 'ear and tear+ po*icy% a** three prodction *ines in each factory i** ha3e

the sa,e operatin/ ti,e2 Each of the decision 3aria)*es has to )e s,a**er than the 1#"

hor ti,e *i,it% the ,a-i,, a,ont of ti,e a ,achine can operate e3ery ,onth2

$ostEnergy

Hour

EnergyCost

Hour DecisionVariable.

$ost is the prodction cost for each

prodction *ine2 Tota* cost is the s, of a** costs fro, a** prodction *ines2

No2 of Prodcts Unit aria)*es I (ecision aria)*e2 The tota* n,)er prodcts of each

factory has to )e e4a* to e-act*y 1!; of the ,onth*y de,and de to )a*ance po*icy Tota* cost is hat E-ce* So*3er tries to ,ini,i.e2 9t is the prodction cost for that ,onth >in

this case (ece,)er?2


J Units shipped@ the a,ont of prodcts shipped fro, a partic*ar factory to a partic*ar

destination2 These are deter,ined )y E-ce* So*3er to ,ini,i.e the tota* shippin/ cost2 The

tota* a,ont of nits shipped fro, each factory has to )e e4a* to the spp*y of that

factory >i2e2 Tota* No2 of prodcts in Ta)*e 1)?2 The tota* a,ont of nits shipped to each

retai*er has to )e e4a* to the de,and of that retai*er2 J of Trips@ the n,)er of trips it takes to ship the a,ont of prodcts fro, one partic*ar

factory to partic*ar retai*er2 E-a,p*e@ it takes trips to ship ;"" prodcts fro, Harris)r/

to Pitts)r/h2 Each trip can on*y carry a ,a-i,, of B" prodcts2 These are a*so

deter,ine )y E-ce* So*3er2

Tota* $apacity J of Trips I B"2 The J of Units shipped a*ays has to )e s,a**er than

this n,)er2

Tota* Unit Shippin/ cost S, >J Units shipped I Shippin/ $osts Per Unit?2 The shippin/

cost per nit is pro3ided )y M$S in proKect data2


6/24

Tota* Trip cost S, J of Trips I Shippin/ $osts Per Trip?2 The shippin/ cost per trips

pro3ided )y M$S in proKect data2

Tota* $ost Tota* Unit Shippin/ cost L Tota* Trip cost2 This is the shippin/ cost and the

o)Kecti3e fnction that E-ce* So*3er tries to ,ini,i.e2


7/24

8or each ,onth% ta)*es *ike a)o3e are created to ca*c*ate the operation cost2 The operation cost

is the s, of shippin/ cost and prodction cost2 The res*ts are recorded in the Ta)*e 1d )e*o2

Tota*(e,and

Prodction$ost> ith:a*ance?

Shippin/cost>ith:a*ance?

Operationcost ith:a*anceMonth

anary 1=B 1CFF12= 11D2B# 1F"F2FD

8e)rary 1=CB1D#2#F 1;"B21# 1FFC2DB

March 1BB 1FB;2FC 1;F2# "BD;2;

Apri* 1BCB 1FDDB2B 1;D=2F# 1C"21

May 1=B" 1D;"C2"# 1;==2" 1F#B12B

ne 1=D" 1D#DB2D 1;=C21 "";2F=

*y 1=;" 1D"B=2B= 1;B#2D; 1F=112;C

A/st 1B"" 1DF;D2;; 1;;2=D "C"2D1

Septe,)er 1;"" 1#=1;2 1CC2;C 1C#F"2BF

Octo)er 1=CB 1D#2#F 1;""2CD 1FF;2=D

No3e,)er 1DCB ;#C2F 1B"D2D" B1D12C

(ece,)er ;"" F";D2CD 1DB;2"; ;"DF12D1

Tota*

;C=D#2C" 1#BBD2BB B="=B2B

Table 5d6 Mont"l# O7eration co&t 8it" Balance Polic#


8/24

Operation ithot :a*ance Po*icy

Usin/ the si,i*ar techni4e as descri)ed a)o3e ith operation ith )a*ance po*icy% ith the

e-ception of the de,and constraint >the tota* n,)er prodcts of each factory has to )e e4a* to

e-act*y 1!; of the ,onth*y de,and de to )a*ance po*icy5Ta)*e 1) para,eter e-p*anation?% e

o)tained the operation cost ithot the )a*ance po*icy2 9n addition% the prodction cost and

shippin/ are done si,*taneos*y2 The e-a,p*e of an inte/rated ,ode* >for *y? is shon )e*o2


9/24

The )a*ance po*icy is re,o3ed so each factory is free to prodce as ,any prodcts as they can

ithot de,and constraints as *on/ as their tota* prodction e4a*s the tota* de,and2 The

spp*y constraints >the tota* a,ont of nits shipped fro, each factory has to )e e4a* to the

spp*y of that factory% i2e2 tota* no2 of prodcts? sti** re,ain2 8or e-a,p*e% Troy prodces ;"

prodcts% hich ,eans on*y a ,a-i,, of ;" nits can )e shipped fro, Troy2 Since the ,ode*

is no inte/rated% the o)Kecti3e fnction is no to ,ini,i.e the Tota* $ost > Unit shippin/ cost

L Tota* Trip $ost L Tota* Prodction $ost? instead of to separate o)Kecti3e fnction as in )a*ance

po*icy operation2 This Tota* $ost is ca*c*ated for each ,onth and recorded in the ta)*e )e*o2

Tota* (e,and

Operation cost ithot

:a*ance Po*icyMonth

anary 1=B 1B;BC2FB

8e)rary 1=CB 1BDD2F"

March 1BB 1#=C;21B

Apri* 1BCB 1C=D21;

May 1=B" 1B#C#2;F

ne 1=D" 1BFD121B

*y 1=;" 1B="#2

A/st 1B"" 1#1F2"D

Septe,)er 1;"" 1;CD12B

Octo)er 1=CB 1BF;F2CC

No3e,)er 1DCB 1""F2=1

(ece,)er ;"" #;12D;

Tota* 1DD1" "B#12

Table 5!6 Mont"l# O7eration co&t 8it"out

Balance Polic#


10/24

Com7ari&on

8ro, Ta)*e 1d and 1f% the ta)*e )e*o is created in order to co,pare the cost re/ardin/ )a*ance

po*icy2

Tota*(e,a

nd

Operationcost ith:a*ancePo*i3icy

Operation costithot :a*ance

Po*icy

Percentof

sa3in/sMonth

anary 1=B 1F"F2FC#C 1B;BC2FB;; "21

8e)rary 1=CB 1FFC2DB 1BDD2F "2;

March 1BB "BD;2;== 1#=C;21B;; "2"

Apri* 1BCB 1C"21 1C=D21; 1D2F

May 1=B" 1F#B12B11 1B#C#2;D#C "2

ne 1=D" "";2F== 1BFD121=C; "2

*y 1=;" 1F=112;CF 1B="#21# "2#

A/st 1B"" "C"2D1;; 1#1F2"D "21

Septe,)er 1;"" 1C#F"2BF11 1;CD12B;; 21

Octo)er 1=CB 1FF;2=C#C 1BF;F2C##C "2"

No3e,)er 1DCB B1D12C1#C 1""F2="#C 1#2#

(ece,)er ;"" ;"DF12D"DF #;12D#C 1=2D

Tota* B="=B2=# "B#12 1F2

Tota* Sa3in/s 93439.1:3 50.;Table 5g Total O7eration Co&t& Com7ari&on regarding

Balance Polic#

Conclu&ion

After re3iein/ ta)*e 1/% it as deter,ined that the ,ost cost eecti3e choice o*d )e to

operate the faci*ities ithot )a*ance2 here )a*ance is de0ned as 'prodction *e3e*s are thesa,e2+ The 0ndin/s indicate that the tota* cost of operatin/ ith )a*ance is B=%"=B2= and the

tota* ithot )a*ance )ein/ "B%#122 This o*d ,ean a sa3in/s of =D%CD=2"2 Ths% a

choice to choosin/ a prodction syste, ithot )a*ance po*icy o*d )e the )est ay of

reachin/ M$S $orporation


11/24

In&tallation o! $e%ning T"e Problem

As ,entioned )efore% M$S $orporation as cha**en/ed ith the 4estion of hether or not

to insta** a ne syste, ca**ed '8astProd2+ This syste, as desi/ned not on*y to rep*ace the

e-istin/ prodction *ine% )t it as desi/ned to trn ot (ino:a**s at a faster rate and conser3e

,ore ener/y2 A*tho/h the choice to insta** this ne syste, see,s tri3ia*% the decision asco,p*icated )y the re4ire,ent that M$S $orporation had to prchase a ne syste, for each of

their factories in order for any dea* to occr2

9n order to ,ake any decisions and ha3e ,ore *e3era/e drin/ a ne/otiation% M$S

$orporation re4ested that their 'reser3e price+ )e ca*c*ated2 The 'reser3e price+ as the

,a-i,, a,ont that M$S $orporation as i**in/ to pay for a certain type of contract2 :e*o

are the series of steps sed to ca*c*ate and the reser3e prices of the to types of syste,s2

Anal#&i&

e took si,i*ar approach as e did ith the re,o3a* of po*icy pro)*e,2 The operation costs ereca*c*ated sin/ E-ce* So*3er2 A** the prodction characteristics ere chan/ed to 8astProd

characteristics2 An e-a,p*e of this is shon in the ta)*e )e*o2

Troy% NY'nit&/"

our

Energ#()*+/"

our

Energ#

Co&t/Hr

$eci&ion

,ariable&

(Hr&+

Time-imit(Hr&+ Co&t

No. o!Produc

t&

Prod ine1 D ;"" "21B

;12F===== 1#"

1;=12#####C

BB2BBBBB#

Prod ine

D ;""

1;=12###

##C

BB2BBB

BB#Prod ine; D ;""

1;=12#####C

BB2BBBBB#

(e,and

Tota* No2 of

Prodcts@C##2###

##CC##2#

##CNeark%NProd ine1 D ;"" "21D

;12F===== 1#"

1;=12#####C

BB2BBBBB#

Prod ine D ;""

1;=12#####C

BB2BBBBB#

Prod ine; D ;""

1;=12#####C

BB2BBBBB#

(e,and

Tota* No2 of

Prodcts@C##2###

##CC##2#

##CHarris)r/% PAProd ine1 D ;"" "2"F

;12F===== 1#"

1;=12#####C

BB2BBBBB#

Prod ine D ;""

1;=12#####C

BB2BBBBB#

Prod ine; D ;""

1;=12#####C

BB2BBBBB#

(e,and


12/24

Tota* No2 of

Prodcts@C##2###

##CC##2#

##C

Tota*cost 514:

Tota* Spp*y ;""

Tota* (e,and ;""Table a6 Sam7le o! =a&t Production Co&t Calculation !or Balance Polic#

O7eration !or $ecember


13/24

To /et an nderstandin/ of ho ,ch M$S $orporation as i**in/ to pay% the cost of operatin/

the pre3ios syste, for three years ith )a*ance and ithot )a*ance as ca*c*ated and

co,pared to the cost of operatin/ the 8astProd ith )a*ance and ithot )a*ance2 The ta)*e

)e*o shos or 0ndin/s2

NormalO7eration

co&t 8it"BalancePolic#

=a&tProdO7eration

co&t 8it"BalancePolic#

NormalO7eration

co&t 8it"outBalancePolic#

=a&tProd

O7erationco&t 8it"

Balance Polic#Month

anary 1F"F2FC##C D#FF2D1 1B;BC2FB;;; #CD2D"D;;;

8e)rary 1FFC2DB F"=D2F"BBB# 1BDD2F #FC12=B

March "BD;2;=== F;;B2B1 1#=C;21B;;; C1=2D1##C

Apri* 1C"21 F#B;2C1 1C=D21; C;#B2F1D;;;

May 1F#B12B111 DFB#2#FBBB# 1B#C#2;D##C #DD12B;###C

ne "";2F== F11C211CCD 1BFD121=C;; #FD=2=F

*y 1F=112;CDF DD#=2;D=== 1B="#21# #C1;21"D##C

A/st "C"2D1;;; F"C2=D 1#1F2"D C";12=###C

Septe,)er 1C#F"2BF111 D1"2;#DDDF 1;CD12B;;; #1B#2;;###C

Octo)er 1FF;2=C##C F"==2B; 1BF;F2C###C #FBF2FBD;;;

No3e,)er B1D12C1##C 11;B2BB 1""F2="##C DC"F2#F1##C

(ece,)er ;"DF12D"DDF 1;FD2";111 #;12D##C 1"B;B2F=

Tota* B="=B2=BD 11B;112"=BD "B#12 DD1D121"=

;5year Tota* 4?52:.4242 29:022.5242 ?5:432.?? ?9:92.25; Year(ierence =1#"2# ;B1="2;=D

Ta)*e Operation $ost $o,parison Ta)*e

9n order to deter,ine the reser3e price% the prodction costs >for nor,a* operation ith

)a*ancin/% 8astProd ith )a*ancin/% nor,a* operation ithot )a*ancin/ and 8astProd ithot

)a*ancin/? ere ca*c*ated )y s,,in/ the ,onth*y rate for a 1 ,onth period% ith n,)ers at

the top of the co*,n representin/ anary and the )otto, )ein/ (ece,)er2 This then as

,*tip*ied )y three as the co,pany re4ested a three year period to )e ana*y.ed2 Then the

dierence as taken of the respecti3e syste,s and their ne conterparts to deter,ine the

reser3e price of a syste, )a*anced and n)a*anced2

Conclu&ion

9n this speci0c sitation% M$S $orporation did not re4est a speci0c decision to )e ,ade2

9nstead% they asked to 0nd the 'reser3e price+ that represents the ,a-i,, price they ere

i**in/ to pay for a certain type of contract2 The reser3e price for a syste, that ses )a*ancin/

as =1#%"2#" and the reser3e price for a syste, ithot )a*ancin/ a,onted to

;B1%="2;B2 :ased so*e*y o these n,)ers% M$S $orporation o*d ha3e to pay ,ore ,oney

for a syste, that ses )a*ancin/ than a syste, that doesn


14/24

Im7lementing t"e @reen Initiatie$e%ning t"e Problem

8o**oin/ the e3er /roin/ trend of /oin/ /reen and the desire to )e in co,p*iance ith ftre/o3ern,ent restrictions% M$S $orporation desired to 'redce their ,onth*y co,)stion

e,issions to *ess than or e4a* to 1" ,etric tons across its faci*ities2+ To do this% they are *ookin/

into prchasin/ so*ar pane*s that o*d ha3e a *ife cyc*e of 03e years and a**o the co,pany to

recei3e a credit of 2 ,etric tons of e,issions ,onth*y for e3ery pane* insta**ed2 The pane*s

o*d )e ot0tted at certain *ocations and o*d prodce ener/y for 1""" Q hors2 Each pane*

cost 1D"""2 9n addition% M$S $orporation can prchase car)on credits to oset e,issions o3er

their thresho*d2 So ith that infor,ation% M$S $orporation o*d *ike to kno ho ,any so*ar

pane*s to prchase and ho ,any car)on credits they sho*d prchase at a speci0c price for

car)on credit2

Anal#&i&

The ana*ysis i** )e done separate*y for the to cases@ )a*ance sp*ittin/ po*icy and opti,a*

sp*ittin/

:a*ance Sp*ittin/ Po*icy

8irst% e ca*c*ated the tota* a,ont of car)on credit needed for each ,onth and the n,)er of

so*ar pane*s and their opti,a* *ocations2 At this sta/e% the price of a car)on credit is nknon so

e te,porari*y ass,ed car)on credit prchase does not e-ist for ca*c*ation prposes2

e se the sa,e ta)*e that e sed for pro)*e, 1>re,o3a* of po*icy?2 To this ta)*e% e added

to 3aria)*e co*,ns@ e,issions per prodcts and tota* e,issions2 A so*ar pane* ta)*e is a*so

added to ca*c*ate the cost of so*ar pane*s and ho to *ocate so*ar pane* p*ace,ent so that the

cost is ,ini,a*2 An e-a,p*e of or ca*c*ation >for No3e,)er? is in ta)*e ;a on the fo**oin/

pa/e2


Tota* E,ission e,ission per prodct I J prodcts2 This /i3es the a,ont of e,ission of

each prodction *ine2 The tota* e,ission of the ho*e co,pany as a*so ca*c*ated as the

s, of a** e,ission2

J so*ar pane*s@ the n,)er of so*ar pane*s are p*aced at a partic*ar factory deter,ined

)y E-ce* So*3er

$ost!,onth@ $ost of ha3in/ an e-tra so*ar pane*2 Each so*ar pane* cost 1D%""" o3er 03e

years hich is an e4i3a*ent of ;""!,onth

Qh!Unit@ each so*ar pane* pro3ides its factory 1""" kh of free ener/y2 The tota* Qh is

the tota* a,ont of free ener/y each factory /ets2

Tota* $ credits@ 2 I J so*ar pane*s2 Tota* car)on credit that a factory /ets for insta**in/

so*ar pane*s2

Ener/y cost sa3e tota* Qh I ener/y cost >Q? per hor2 The a,ont of ,oney each

factory sa3es de to free ener/y pro3ided )y so*ar pane*s2 This has to )e s,a**er than the

s, of prodction cost of that factory2


15/24

E,ission 5 so*ar car)on credits tota* e,ission 5 tota* $ credit2 This n,)er has to )e

*oer than 1" >,etric tons? in order to ,eet the Green 9nitiati3e re4ire,ent2

So*ar $ost J so*ar pane*s I cost!,onth2 The tota* cost of insta**in/ a** so*ar pane*s in

that ,onth2

Tota* cost s, >cost? L so*ar cost 5 s, >ener/y cost sa3e?2 The tota* cost of prodction2

A** other para,eters are e-p*ained pre3ios*y in re,o3a* of po*icy pro)*e,2

E-ce* So*3er is set to ,ini,i.e to tota* tost and retrns tecision taria)*es of tors of each

factory rn and a,ont of so*ar pane*s each factory insta**ed2

The res*ts of this ca*c*ation are s,,ari.ed in the ta)*e )e*o2

J so*ar

pane*s

an 8e) Mar Apr May n * A/ Sep Oct No3 (

Troy% NY " " " " " " " " " " " "

Neark% N = # D ; = ; B " = 1F ;


16/24

Harris)r/%

PA

" " " " " " " " " " " "

$ost so*ar 1D;

1

1F1"

;

1FFC

=

"D=

B

1D##

C

1F1#

#

1D=1

B

1FB;

D

1#=

1;

1F1"

;

BFB

;

;

F$ credit

needed

"2;C

=B

"2C;

DB

121"

#

12=#

##

"2BB

#B

"2CC

=F

"2=1

"F

"2F

"#

" "2C;

DB

;2#B

"C

#

=Ta)*e ;) So*ar pane*s ana*ysis

e rea*i.e that no ,atter ho ,any so*ar pane*s M$S $orporation need% they i** *ocate the, atNeark% N for opti,a* cost2 Hence% e kno that the e-tra cost that each so*ar pane* )rin/s is

;""5 1""">21D? 1"!,onth or 1=="!year >)ecase each so*ar pane*s cost ;"" )t sa3e

1""" Qh at the ener/y cost of 21D!Qh in Neark?2

Ne-t% e do the ana*ysis to he*p M$S decide the n,)er of pane*s to )y dependin/ on price2

The a*/orith,@ e increase price of car)on credit fro, "!car)on credit nti* the e-tra cost of

)yin/ a** car)on credit is e4a* or hi/her than the e-tra cost of )yin/ a** car)on credit and one

so*ar pane*2 e keep repeatin/ the process for n a,ont of so*ar pane*s >i2e2 e increase price of

car)on credit nti* the e-tra cost of )yin/ a** car)on credit and n so*ar pane*s is e4a* or hi/her

than the e-tra cost of )yin/ a** car)on credit and nL1 so*ar pane*s?2 The reason that thisa*/orith, orks is that% as the price of car)on credit increases% or de,and for car)on credit

prchase decreases and or de,and for so*ar pane*s increases2 The ta)*e )e*o shos the

ca*c*ation2 $ase 1 represents the decision and cost hen M$S )ys n so*ar pane*s% case

represents the decision and cost hen M$S )ys nL1 so*ar pane*s2

The E-ce* So*3er i** try to ,a-i,i.e $ credit price fro, " nti* the tota* e-tra cost of case 1

e4a* or )are*y srpasses the cost of case 2 The res*ts )e*o can )e interpreted as if a car)on

credit price is #B=2BB or )e*o it is opti,a* for M$S to )y " so*ar pane*s and on*y prchase

$ar)on credit to ,eet their /reen initiati3e2

Para,eter E-p*anation@

$ credit price@ the price for one car)on credit2 This is the sa,e for )oth cases2 This 3a*e is

increased fro, " nti* the tota* e-tra cost 1 tota* e-tra cost 2

J so*ar pane*s@ the n,)er of so*ar pane*s prchased for each case2

So*ar pane*s e-tra cost J so*ar pane*s I 1==" )ecase each so*ar pane*s cost e-tra

1=="!year2


17/24

$ credit needed@ the tota* a,ont of car)on credit that /oes o3er 1" ,etric ton *i,it and

need to )e co,pensated )y either so*ar pane*s or $ar)on credit prchase

$ credit 5 so*ar credit $ credit needed 5 "2 I J so*ar pane*s2 The a,ont of $ar)on

credits *eft after sin/ so*ar pane*s car)on credit aka the car)on credit needed to )e

prchase

$ credit prchase cost $ credit price I >$ credit 5 so*ar credit?2 The cost each ,onth to

prchase car)on credit2 This cost is not app*ied for ,onths that ha3e their >$ credit 5 so*ar

credit? 3a*e s,a**er or e4a* to "% sch as Septe,)er in this e-a,p*e2

Tota* e-tra cost So*ar pane*s e-tra cost L $ credit prchase cost2

8ro, the ana*ysis% the res*t ta)*e )e*o is created2 The ta)*e shos the ran/e of $ar)on credit

price and the opti,a*n,)er of so*ar pane*s sho*d )e prchased >e2/2 9f the price of car)on

credit is 1""">hich is )eteen FF12C1 and 1B#=2C% then it is opti,a* for M$S to )y e-act*y

for so*ar pane*s?2 hen the price is a)o3e FF=121F% it is si,p*y not )ene0cia* for M$S to )y

any $ar)on credits and they sho*d insta** a** ;= so*ar pane*s2 At prices sch as ;#"" or C""%

there are ,*tip*e opti,a* so*tions for ho ,any so*ar pane*s sho*d )e )o/ht2 9t depends on

the co,panycost of insta**ation% cost of ,aintenance? to

decide2


18/24

$ar)on creditPrice >per car)on

credit?

Opti,a*n,)erof so*arpane*s8ro, To

"#B=2B=B

=B "

#B=2B=B=B

##21C= 1

##21C=

D1=2CB=1

D1=2CB=1

FF12C"CC1 ;

FF12C"CC1

1B#=2CD =

1B#=2CD

"=F2#;; B

"=F2#;; ="" #

="";"D#2#

B= C;"D#2#

B= ;#"" D

;#"" F

;#"" 1"

;#"" 11

;#"" 1

;#"" 1;

;#"" 1=

;#"" 1B

;#"" 1#

;#"" 1C

;#""BC==2"=

=; 1DBC==2"=

=; C"" 1F

C"" "

C"" 1

C""

C"" ;

C"" =

C"" B

C"" #

C"" C

C"" D

C"" F

C"" ;"


19/24

C"" ;1

C"" ;

C""FF=121F

1B ;;

A)o3e FF=121F ;=Ta)*e ;d

Opti,a* Sp*ittin/

e app*y a si,i*ar ,ethod for opti,a* sp*ittin/2 8irst% e ca*c*ated the tota* a,ont of car)on

credit needed for each ,onth and the n,)er of so*ar pane*s and their opti,a* *ocations2 The

res*ts are shon )e*o2

J so*arpane*s

an 8e) Mar Apr May n * A/ Sep Oct No3 (ec

Troy% NY " " " " " " " " " " C

Neark% N " " " " " " " " " " " "

Harris)r/% PA " " " " " " " " " " " "$ar)on$redit " " " " " " " " " "

12;C#

=2;FD

$ost dierenceF#D2

FF ;;""

Ta)*e ;e

e noticed that No3e,)er and (ece,)er are the on*y to ,onths that e-ceed the $ar)on *i,it2

e a*so rea*i.ed that M$S $orporation i** need to *ocate so*ar pane*s at Troy% NY for opti,a*

cost2 Hence% e kno that the e-tra cost that each so*ar pane*s )rin/ is ;""5 1""">21B? 1B"!,onth or 1D""!year >)ecase each so*ar pane*s cost ;"" )t sa3e 1""" Qh at the

ener/y cost of 21B!Qh in Troy?2

Ne-t% e do the ana*ysis to he*p M$S decide on the n,)er of pane*s to )y dependin/ on price2

e app*y the sa,e a*/orith, that e sed for )a*ance sp*ittin/2 Hoe3er% for the opti,a*

sp*ittin/% e add a constraint that the a,ont of ener/y sa3es a*ays has to )e s,a**er than the

a,ont of ener/y sed at that factory2 This constraint did not appear on the ana*ysis for )a*ance

sp*ittin/ )ecase it is a*ays tre for that scenario2

An e-a,p*e of the e-a,p*e is shon on the ne-t pa/e2 The para,eter stays the sa,e e-cept@

So*ar pane*s prchase cost ;#"" I so*ar pane*s2 The cost of prchasin/ so*ar pane*s is

sed instead of e-tra cost >prchase cost5ener/y sa3in/ cost?2

Tota* ener/y sed in Troy@ the ,a-i,, a,ont of ener/y that can )e sa3ed sin/ so*ar

pane*s2

Ener/y sa3in/ cost Min >tota* ener/y sed in Troy I 21B% J so*ar pane*s I 1B"?2

$onstraint that the a,ont of ener/y sa3es a*ays s,a**er than the a,ont of ener/y

sed at that factory2

Tota* cost so*ar pane*s prchase cost L $ credit prchase cost 5 ener/y sa3in/ cost


20/24

$ase 1

$ase

$credi

tprice

Jso*arpane

*s

$credi

tprice

Jso*arpane

*s

(ecision3aria)*e

552:5

1552:

5

So*arpane*s

prchase cost>1

yr?

CB#""

CF"

"Tota*

an 8e) Mar Apr May n * A/ Sep Oct No3 (ec

$ creditneeded

" " " " " " " " " "12;C

#=2;FD

$ credit5 so*ar

credit>case 1?

5=2 5=2 5=2 5=2 5=2 5=2 5=2 5=2 5=2 5=25

2D=

"21FD

$ credit5 so*ar

credit>case ?

5=2= 5=2= 5=2= 5=2= 5=2= 5=2= 5=2= 5=2= 5=2= 5=2=5

;2"=

5"2""

$ creditprchase cost 1

" " " " " " " " " " " B" B"

$ creditprchase cost

" " " " " " " " " " " " "

Tota*Ener/ysed in

Troy

;"#

;"#

#;#1

D;DF

"CD

;"#

1D#B#

=;;;

D11121

=;;;

B=CB"

DF

Ener/ysa3in/

cost>case 1?

;1B"

;1B";1B

";1B"

;"=12C

;1B"

CFD2;

;1B"11#

2C;1B"

;1B"

;1B";B="

C

Ener/ysa3in/

cost>case ?

;;""

;;"";;"

";;""

;"=12C

;;""

CFD2;

;;""11#

2C;;""

;;""

;;"";#CB

C

O)Kecti3e

fnction

552:5

Total co&t

5

Total co&t

===;2;;;;

===;2;;;;

Ta)*e ;f $ar)on Prchase Price 3s2 So*ar pane*s ana*ysis

8ro, the ana*ysis% the res*t ta)*e )e*o is created2 The ta)*e shos that the ran/e of $ar)on

credit price and the opti,a*n,)er of so*ar pane*s sho*d )e prchased2 hen the price is

a)o3e 11;B"2F% it is si,p*y not )ene0cia* for M$S to )y any $ar)on credits and they sho*d

insta** a** so*ar pane*s2 At prices sch as =B"" or FCB"% there are ,*tip*e opti,a* so*tions


21/24

for ho ,any so*ar pane*s sho*d )e )o/ht2 9t depends on the co,pany preferences and!or

n*isted costs >cost of insta**ation% cost of ,aintenance? to decide2


22/24

$ar)on creditPrice >per

car)on credit?

Opti,a*n,)erof so*arpane*s8ro, To

" =B"" "

=B"" 1

=B""

=B"" ;=B"" =

=B"" B

=B""=CDC2

;= #=CDC2

;= F""" C

F"""F###2#

#C DF###2#

#C FCB" F

FCB" 1"

FCB" 11

FCB" 1

FCB" 1;

FCB" 1=

FCB" 1B

FCB" 1#

FCB" 1C

FCB"

1"""D2

;; 1D1"""D2;; 1"B"" 1F

1"B""11"=12

#C "11"=12

#C11;B"2

F 1

A)o3e 11;B"2F


23/24

Conclu&ion

Balance S7litting O7timal S7litting

$ar)on creditPrice >per car)on

credit?

Opti,a*n,)erof so*arpane*s

$ar)on creditPrice >per

car)on credit?

Opti,a*n,)erof so*arpane*s

8ro, To 8ro, To

"#B=2B=B

=B " " =B"" "#B=2B=B

=B##21

C= 1 =B"" 1##21

C=

D1=2CB

=1 =B"" D1=2CB=1

FF12C"CC1 ; =B"" ;

FF12C"CC1

1B#=2CD = =B"" =

1B#=2CD

"=F2#;; B =B"" B

"=F2#;; ="" # =B""

=CDC2;= #

="";"D#2#

B= C=CDC2

;= F""" C

;"D#2#B= ;#"" D F"""

F###2##C D

;#"" FF###2#

#C FCB" F

;#"" 1" FCB" 1"

;#"" 11 FCB" 11

;#"" 1 FCB" 1

;#"" 1; FCB" 1;

;#"" 1= FCB" 1=

;#"" 1B FCB" 1B

;#"" 1# FCB" 1#;#"" 1C FCB" 1C

;#""BC==2"=

=; 1D FCB"1"""D2

;; 1DBC==2"=

=; C"" 1F1"""D2

;; 1"B"" 1F

C"" " 1"B""11"=12

#C "

C"" 111"=12

#C11;B"2

F 1


24/24

C"" A)o3e 11;B"2F

C"" ;

C"" =

C"" B

C"" #

C"" C

C"" D

C"" FC"" ;"

C"" ;1

C"" ;

C""FF=121F

1B ;;

A)o3e FF=121F ;=Ta)*e ;h

After a thoro/h ana*ysis of the data% it as deter,ined that the decision to )y ,ore car)on

credit o*d ha3e to )e ,ade dependin/ on the crrent sitation at the ti,e2 ith that )ein/said% the research shoed that price ran/es co*d )e ,ade >reference car)on credit price ran/es

in ta)*e ;h? and then co*d dictate ho ,any so*ar pane*s the co,pany sho*d insta**2

Referencin/ ta)*e ;h% the co,pany co*d *ook at the price of the crrent car)on credit and then

insta** the opti,a* choice of so*ar pane*s% fo**oed )y prchasin/ ,ore car)on credits if need )e2

This so*tion to the pro)*e, o*d a**o the M$S $orporation the a)i*ity to esti,ate ho ,any

car)on credits and so*ar pane*s to )y in the ftre2

Documents

OR Final Project Back Work