Mfg Metrics-3e-S 11-24, 24/06, 06/04/07
Chapter 3 MANUFACTURING METRICS REVIEW REVIEW QUESTION QUESTIONS S 3.1
What What is the cycl cyclee time time in a manu manufa factu cturin ring g oer oerati ation! on! Answer " #s $efine$ in the te%t, the cycle time T c is the time that one &or' unit sen$s (eing rocesse$ or assem(le$. )t is the time (et&een &hen one &or' unit (egins rocessing *or assem(ly+ an$ &hen the ne%t unit (egins.
3.2 3.2
What What is a (ot (ottl tlen enec ec' ' sta stati tion on!! &or'station in a ro$uction line, an$ therefore therefore it limits Answer " he (ottlenec' station is the slo&est &or'station the ace of the entire line.
3.3 3.3
What What is is ro ro$u $uct ctio ion n ca caaacity city!! Answer " #s $efine$ in the te%t, ro$uction caacity is the ma%imum rate of outut that a ro$uction facility *or ro$uction line, &or' center, or grou of &or' centers+ is a(le to ro$uce un$er a gien set of assume$ oerating con$itions.
3.4
o& o& can can lant lant caac caacity ity (e increase increase$ $ or $ecrea $ecrease$ se$ in the short short term! term! Answer " #s liste$ in the te%t, the t&o &ays &ays that lant caacity can can (e increase$ or $ecrease$ $ecrease$ in the short term are *1+ change the num(er of &or' shifts er &ee' S w or *2+ change the num(er of hours &or'e$ er shift H sh.
3.
What What is utili utiliat ation ion in a manu manufa factu cturin ring g lant! lant! ro roi$e i$e a $efin $efinitio ition. n. Answer " tiliation is the amount of outut of a ro$uction facility relatie to its caacity. %ressing this as an euation, U 5 5 Q/ PC , &here U 5 5 utiliation, Q 5 actual outut uantity ro$uce$ $uring the erio$ of interest, an$ PC is is the ro$uction caacity $uring the same erio$.
3.6 3.6
What What is is aa aail ila( a(il ilit ity y an$ an$ ho& ho& is it $ef $efin ine$ e$!! Answer " #aila(ility is a relia(ility metric that in$icates the roortion of time that a iece of euiment is u an$ &or'ing roerly. )t is $efine$ as follo&s" A 5 * MTBF MTTR+/ MTBF , &here A 5 aaila(ility, aaila(ility, MTBF 5 5 mean time (et&een (et&een failures, an$ MTTR 5 mean time to reair.
3.7 3.7
What What is is manu manufa fact ctur urin ing g lea lea$ time time!! Answer " #s $efine$ in the te%t, manufacturing lea$ time is the total time reuire$ to rocess a gien art or ro$uct through the lant, lant , inclu$ing i nclu$ing any lost time $ue to $elays, time sent in storage, relia(ility ro(lems, an$ so on.
3. 3.
What What is &or' &or'-i -inn-r roc oceess ss!! Answer " #s $efine$ in the te%t, &or'-in-rocess *W)+ is the uantity of arts or ro$ucts currently locate$ in the factory that are either (eing rocesse$ or are (et&een rocessing oerations. W) is inentory that is in the state of (eing transforme$ from ra& material to finishe$ ro$uct.
3.8
o& o& are are fi%e fi%e$ $ cost costss $isting $istinguish uishe$ e$ from from aria(l aria(lee costs costs in manufac manufacturing turing!! Answer " 9i%e$ costs remain constant for any leel of ro$uction outut. %amles inclu$e the cost of the factory (uil$ing an$ ro$uction euiment, insurance, an$ roerty ta%es. :aria(le costs ary in roortion to the leel of ro$uction outut. #s outut increases, aria(le costs increase. %amles inclu$e $irect la(or, ra& materials, an$ electric o&er to oerate the ro$uction euiment.
3.10
;ame fie fie tyical tyical fact factory ory oerhe oerhea$ a$ e%en e%enses ses!! Answer " a(le 3.1 in the te%t lists the follo&ing e%amles of factory oerhea$ e%enses" lant suerision, alica(le ta%es, factory $ereciation, line foremen, insurance, euiment $ereciation, maintenance, maintenance, heat an$ air con$itioning, fringe (enefits, (enefits, custo$ial custo$ial serices serices,, light, material han$ling, security ersonnel, o&er for machinery, shiing an$ receiing, tool cri( atten$ant, ayroll serices, an$ clerical suort.
3.11
;ame fie fie tyical tyical cor cororate orate oerhea oerhea$ $ e%ense e%enses! s!
Mfg Metrics-3e-S 11-24, 24/06, 06/04/07 Answer " a(le 3.2 in the te%t lists the follo&ing e%amles of cororate oerhea$ e%enses" cororate e%ecuties, engineering, alica(le ta%es, sales an$ mar'eting, research an$ $eeloment, cost of office sace, accounting $eartment, suort ersonnel, security ersonnel, finance $eartment, insurance, heat an$ air con$itioning, legal counsel, fringe (enefits, an$ lighting.
PROBLEMS Production Concepts and Mathematical Models 3.1
# certain art is route$ through si% machines in a (atch ro$uction lant. he setu an$ oeration times for each machine are gien in the ta(le (elo&. he (atch sie is 100 an$ the aerage nonoeration time er machine is 12 hours.
Setu time *hr.+
=eration time *min.+
1
4
.0
2
2
3.
3
10.0
4
3
1.8
3
4.1
6
4
2.
Solution " #erage T su 5 *4 > 2 > > 3 > 3 > 4+/6 5 24/6 5 4.0 hr #erage T c 5 * > 3. > 10 > 1.8 > 4.1 > 2.+/6 5 27/6 5 4. min *a+ MLT 5 6*4.0 > 100*4./60+ > 12+ 5 6*23.+ 5 ! hr
*(+ R p for oeration 3" T p 5 ?.0 > 100*10/60+@/100 5 24.67/100 5 0.2467 hr/c 3.1
R p 5 !"#$ pc%hr
Suose the art in the reious ro(lem is ma$e in ery large uantities on a ro$uction line in &hich an automate$ &or' han$ling system is use$ to transfer arts (et&een machines. ransfer time (et&een stations 5 1 s. he total time reuire$ to set u the entire line is 10 hours. #ssume that the oeration times at the in$ii$ual machines remain the same. 10 5 $"#&$ hr for first art inclu$ing setu
*(+ T p for oeration 3 5 10.2 min, R p 5 60/10.2 5 $"'$3( pc%hr *c+ heoretical ro$uction rate for line 5 $"'$3( pc%hr since station 3 is the (ottlenec' station on the line. 3.2
he aerage art ro$uce$ in a certain (atch manufacturing lant must (e rocesse$ seuentially through si% machines on aerage. &enty *20+ ne& (atches of arts are launche$ each &ee'. #erage oeration time 5 6 min., aerage setu time 5 hours, aerage (atch sie 5 2 arts, an$ aerage nonoeration time er (atch 5 10 hr/machine. here are 1 machines in the lant &or'ing in arallel. ach of the machines can (e set u for any tye of Ao( rocesse$ in the lant. he lant oerates an aerage of 70 ro$uction hours er &ee'. Scra rate is negligi(le. 2*0.1+ > 10+ 5 #$ hr
*(+ T p 5 * > 2 % 0.1+/2 5 0.30 hr/c, R p 5 3.333 c/hr. PC 5 70*1+*3.333+/6 5 )## pc%wee* *c+ arts launche$ er &ee' 5 20 % 2 5 00 c/&ee'.
tiliation U 5 00/700 5 0.7143 5 )"!3+
*$+ #s utiliation increases to&ar$s 100B, &e &oul$ e%ect the nonoeration time to increase. When the &or'loa$ in the sho gro&s, the sho (ecomes (usier, (ut it usually ta'es longer to get the Ao(s out. #s utiliation $ecreases, &e &oul$ e%ect the nonoeration time to $ecrease. 3.3
Case$ on the $ata in the reious ro(lem an$ your ans&ers to that ro(lem, $etermine the aerage leel of &or'-in-rocess *num(er of arts-in-rocess+ in the lant.
Mfg Metrics-3e-S 11-24, 24/06, 06/04/07 Solution " WIP 5 AU * PC +* MLT + / S w H sh 5
3.4
(1.0)( 0.7143)( 700)(10) 70
5 )$# pc
#n aerage of 20 ne& or$ers are starte$ through a certain factory each month. =n aerage, an or$er consists of 0 arts that are rocesse$ seuentially through 10 machines in the factory. he oeration time er machine for each art 5 1 min. he nonoeration time er or$er at each machine aerages hours, an$ the reuire$ setu time er or$er 5 4 hours. here are a total of 2 machines in the factory &or'ing in arallel. ach of the machines can (e set u for any tye of Ao( rocesse$ in the lant. =nly 0B of the machines are oerational at any time *the other 20B are in reair or maintenance+. he lant oerates 160 hours er month. o&eer, the lant manager comlains that a total of 100 oertime machine-hours must (e authorie$ each month in or$er to 'ee u &ith the ro$uction sche$ule. *a+ What is the manufacturing lea$ time for an aerage or$er! *(+ What is the lant caacity *on a monthly (asis+ an$ &hy must the oertime (e authorie$! *c+ What is the utiliation of the lant accor$ing to the $efinition gien in the te%t! *$+ 0%0.2 > + 5 &!$ hr%order
*(+ T p 5 *4 > 0%0.2+/0 5 16./0 5 0.33 hr/c, R p 5 3.0303 c/hr PC 5 *2%0.0+*160+*3.0303+/10 5 ,(,") pc%month arts launche$ er month 5 20%2 5 1000 c/month Sche$ule e%cee$s lant caacity (y 1000 - 868.7 5 30.3 c. his reuires oertime in the amount 5 *30.303 c % 10 machines+/*3.0303 c/hr+ 5 100 hr. *c+ tiliation U 5 *1000 c+/*868.7 c+ 5 1.0312 5 #3"&$+ *$+ WIP 5 *24 hr+*868.7 c/mo+*1.0312+/*160 hr/mo+ 5 $3"&$ parts 3.
he mean time (et&een failure for a certain ro$uction machine is 20 hours, an$ the mean time to reair is 6 hours.
3.6
=ne million units of a certain ro$uct are to (e manufacture$ annually on $e$icate$ ro$uction machines that run 24 hours er $ay, fie $ays er &ee', 0 &ee's er year. *a+ )f the cycle time of a machine to ro$uce one art is 1.0 minute, ho& many of the $e$icate$ machines &ill (e reuire$ to 'ee u &ith $eman$! #ssume that aaila(ility, utiliation, &or'er efficiency 5 100B, an$ that no setu time &ill (e lost. *(+ Sole art *a+ e%cet tha t aaila(il ity 5 0.80. Solution" *a+ otal &or'loa$ WL 5 1,000,000*1 min/60+ 5 16,666.7 hr/yr
ours aaila(le/machine 5 24 % % 0 5 6000 hr/yr er machine ;um(er of machines n 5 *(+ #t # 5 80B, n 5 3.7
16,666.7hr 6000hr / machine
5 2.7 → 3 machines
16,666.7hr 6000hr / machine* 0.80+
5 3.08 → ! machines
he mean time (et&een failures an$ mean time to reair in a certain $eartment of the factory are 400 hours an$ hours, resectiely. he $eartment oerates 2 machines $uring one -hour shift er $ay, fie $ays er &ee', 2 &ee's er year. ach time a machine (rea's $o&n, it costs the comany D200 er hour *er machine+ in lost reenue. # roosal has (een su(mitte$ to install a reentie maintenance rogram in this $eartment. )n this rogram, reentie maintenance &oul$ (e erforme$ on the machines $uring the eening so that there &ill (e no interrutions to ro$uction $uring the regular shift. he effect of this rogram is e%ecte$ to (e that the aerage MC9 &ill $ou(le, an$ half of the emergency reair time normally accomlishe$ $uring the $ay shift &ill (e erforme$ $uring the eening shift. he cost of the maintenance cre& &ill (e D100 er &ee'. o&eer, a re$uction of maintenance ersonnel on the $ay shift &ill result in a saings $uring the regular shift of D700 er &ee'. *a+ Eomute the aaila(ility of machines in the $eartment (oth (efore an$ after the reentie maintenance rogram is installe$. *(+
Mfg Metrics-3e-S 11-24, 24/06, 06/04/07 Solution " *a+ Without reentie maintenance *M+, aaila(ility A 5 *400 - +/400 5 0.8 5 ,'"#+" With M, aaila(ility A 5 *00 - +/00 5 0.88 5 ,,"#+" his 88B alue ignores the fact that half the reair time is on the eening shift. )f &e use time of reair $uring the $ay to calculate aaila(ility, MTTR 5 4 hr, an$ #aila(ility A 5 *00 - 4+/00 5 0.88 5 ,,"$+"
*(+ otal oerating hours er year 5 % % 2 5 200 hr/year. Without M, MTBF 5 400 hr. We e%ect 200/400 5 .2 (rea'$o&ns/year for each machine. With 2 machines, (rea'$o&ns/year 5 .2 % 2 5 130. otal $o&ntime hours 5 130 % 5 #!# hr%-ear. With M, MTBF 5 00 hr. his means 200/00 5 2.6 (rea'$o&ns/yr for each machine. With 2 machines, (rea'$o&ns/year 5 2.6%2 5 6. otal $o&ntime hours 5 6 % 4 5 &(# hr%-ear" *c+ Without M, cost of $o&ntime 5 D200 % 1040 $o&ntime hr/yr 5 .&#'/###%-ear With M, cost of $o&ntime 5 D200 % 260 $o&ntime hr/yr 5 D2,000/year #$$itional la(or cost of M rogram 5 100 - 700 5 D00/&ee' #$$itional la(or cost of M rogram/year 5 D00 % 2 5 D41,600/yr otal cost er year f M 5 D2,000 > 41,600 5 .,3/(##%-r" Since this is su(stantially lo&er than D20,000/yr, M rogram is Austifie$. 3.
here are nine machines in the automatic lathe section of a certain machine sho. he setu time on an automatic lathe aerages 6 hours. he aerage (atch sie for arts rocesse$ through the section is 80. he aerage oeration time 5 .0 minutes. n$er sho rules, an oerator can (e assigne$ to run u to three machines. #ccor$ingly, there are three oerators in the section for the nine lathes. )n a$$ition to the lathe oerators, there are t&o setu &or'ers &ho erform machine setus e%clusiely. hese setu &or'ers are 'et (usy the full shift. he section runs one -hour shift er $ay, 6 $ays er &ee'. o&eer, an aerage of 1B of the ro$uction time is lost is lost $ue to machine (rea'$o&ns. Scra losses are negligi(le. he ro$uction control manager claims that the caacity of the section shoul$ (e 136 ieces er &ee'. o&eer, the actual outut aerages only 1440 units er &ee'. What is the ro(lem! Fecommen$ a solution. Solution " ours/&ee' 5 6 $ays/&' % hr/$ay % *1 - 0.1+ 5 40. hr/&ee'. T p 5 *6 > 80 % /60+/80 5 1 hr/80 c 5 0.2 hr/c, R p 5 c/hr. ro$uction caacity of automatic lathe section PC 5 *40. hr/&'+* c/hr+*8 machines+ 5 '3( pc%w* . Cut the actual outut 5 1440 c/&'. Why! Eonsi$er &or'loa$ of the setu men. ;um(er of (atches set u er &ee' 5 *2 setu men+*4 hr/&'+/*6 hr/setu+ 5 16 (atches/&'. #t 80 c/(atch, total c/&ee' 5 16 % 80 5 !!# pc%wee* . he ro(lem is that the setu &or'ers reresent a (ottlenec'. o sole the ro(lem, hire one more setu &or'er.
3.8
# certain Ao( sho secialies in one-of-a-'in$ or$ers $ealing &ith arts of me$ium-to-high comle%ity. # tyical art is rocesse$ seuentially through ten machines in (atch sies of one. he sho contains a total of eight conentional machine tools an$ oerates 3 hours er &ee' of ro$uction time. he machine tools are interchangea(le in the sense that they can (e set u for any oeration reuire$ on any of the arts. #erage time alues on the art are" machining time er machine 5 0. hour, &or' han$ling time er machine 5 0.3 hour, tool change time er machine 5 0.2 hour, setu time er machine 5 6 hours, an$ nonoeration time er machine 5 12 hours. # ne& rogramma(le machine has (een urchase$ (y the sho that is caa(le of erforming all ten oerations in a single setu. he rogramming of the machine for this art &ill reuire 20 hoursG ho&eer, the rogramming can (e $one off-line, &ithout tying u the machine. he setu time &ill (e 10 hours. he total machining time &ill (e re$uce$ to 0B of its reious alue $ue to a$ance$ tool control algorithmsG the &or' han$ling time &ill (e the same as for one machineG an$ the total tool change time &ill (e re$uce$ (y 0B (ecause it &ill (e accomlishe$ automatically un$er rogram control. 9or the one machine, nonoeration time is e%ecte$ to (e 12 hours. *a+ 1 > 12+ 5 ,# hr. ;e& metho$" MLT 5 1*10 > .3 > 12+ 5 &)"3 hr.
Mfg Metrics-3e-S 11-24, 24/06, 06/04/07 *(+ resent metho$" 9or 1 machine, T c 5 *6 > 1+/1 5 7 hr, Rc 5 1/7 5 0.1428 c/hr 9or machines, lant caacity PC 5 * machines+*3 hr+*0.1428 c/hr+/*10 os/c+ 5 ! orders%wee* ;e& metho$" 9or each machines, T c 5 *10 > .3+/1 5 1.3 hr, Rc 5 1/1.3 5 0.0636 c/hr 9or 2 machines, lant caacity PC 5 *2 machines+*3 hr+*0.0636 c/hr+/*1 o/c+ 5 !"$)$ orders%wee* *c+ resent metho$" WIP 5 *4 or$ers/&ee'+*180 hr/or$er+/*3 hr/&'+ 5 &") orders ;e& metho$" WIP 5 *4.7 or$ers/&ee'+*27.3 hr/or$er+/*3 hr/&'+ 5 3"$) orders *$+ #utomation strategies reresente$" Strategy 2 - com(ine$ oerationsG Strategy - increase$ fle%i(ilityG Strategy 6 - imroe$ material han$lingG Strategy - rocess controlG Strategy 8 - lant oerations control. 3.10
# factory ro$uces car$(oar$ (o%es. he ro$uction seuence consists of three oerations" *1+ cutting, *2+ in$enting, an$ *3+ rinting. here are three machines in the factory, one for each oeration. he machines are 100B relia(le an$ oerate as follo&s &hen oerating at 100B utiliation" *1+ )n cutting , large rolls of car$(oar$ are fe$ into the cutting machine an$ cut into (lan's. ach large roll contains enough material for 4,000 (lan's. ro$uction cycle time 5 0.03 minute/(lan' $uring a ro$uction run, (ut it ta'es 3 minutes to change rolls (et&een runs. *2+ )n indenting , in$entation lines are resse$ into the (lan's to allo& the (lan's to later (e (ent into (o%es. he (lan's from the reious cutting oeration are $ii$e$ an$ consoli$ate$ into (atches &hose starting uantity 5 2,000 (lan's. )n$enting is erforme$ at 4. minutes er 100 (lan's. ime to change $ies on the in$entation machine 5 30 min. *3+ )n printing , the in$ente$ (lan's are rinte$ &ith la(els for a articular customer. he (lan's from the reious in$enting oeration are $ii$e$ an$ consoli$ate$ into (atches &hose starting uantity 5 1,000 (lan's. rinting cycle rate 5 30 (lan's/min. Cet&een (atches, changeoer of the rinting lates is reuire$, &hich ta'es 20 minutes. )n-rocess inentory is allo&e$ to (uil$ u (et&een machines 1 an$ 2, an$ (et&een machines 2 an$ 3, so that the machines can oerate in$een$ently as much as ossi(le. Case$ on this $ata an$ information, $etermine the ma%imum ossi(le outut of this factory $uring a 40-hour &ee', in comlete$ (lan's/&ee' *comlete$ (lan's hae (een cut, in$ente$, an$ rinte$+! #ssume stea$y state oeration, not startu. Solution " 4000 c*0.03 min/c+ 5 3 > 120 5 1 min./(atch * 4000 c / (atch+* 60 min./ hr + 5 $!'"! pc%hr R p 5 1 min./ (atch =eration *2+ - in$enting" T b 5 30 min. > 2000 c*4./100 min./c+ 5 30 > 80 5 120 min./(atch * 2000 c / (atch+* 60 min./ hr + 5 ### pc%hr R p 5 120 min./ (atch 1000 c =eration *3+ - rinting" T b 5 20 min. > 5 20 > 33.33 5 3.33 min./(atch 30 c / min. R p 5
*1000 c / (atch+* 60 min./ hr +
5 &$ pc%hr 333 . min./ (atch Cottlenec' rocess is oeration *2+. Wee'ly outut 5 *40 hr/&'+*1000 c/hr+ 5 !#/### 0lan*s%w* .
Costs o1 Manu1acturin2 perations 3.11
heoretically, any gien ro$uction lant has an otimum outut leel. Suose a certain ro$uction lant has annual fi%e$ costs FC 5 D2,000,000. :aria(le cost VC is functionally relate$ to annual outut Q in a manner that can (e $escri(e$ (y the function VC 5 D12 > D0.00Q. otal annual cost is gien (y TC 5 FC > VC % Q. he unit sales rice for one ro$uction unit P 5 D20. *a+ *12 > 0.00H+H 5 2,000,000 > 12 H > 0.00 H2 UC 5
TC Q
d ( UC ) dQ
5
5
2,000,000 Q
−2,000,000
Q2
> 12 > 0.00 Q
>0.00 5 0
Mfg Metrics-3e-S 11-24, 24/06, 06/04/07 Q 5 20 % 103 5 &#/### pc 0.00Q2 5 2,000,000 Q2 5 400 % 106 rofit 5 20*20,000+ - *2,000,000 > 12*20,000+ > 0.00*20,000+ 2+ 5 .)(#/###%-r
*(+ rofit Π5 20 Q -*2,000,000 > 12 Q > 0.00 Q2+ 5 23 Q - 2,000,000 - 0.00 Q2 d Π dQ
5 23 2*0.00 Q+5 23 - 0.010 Q 5 0
Q 5 23/0.010 5 &3/'## pc
rofit 5 20*23,00+ - *2,000,000 > 12*23,00+ > 0.00*23,00+ 2+ 5 .'3&/&##%-r 3.12
Eosts hae (een comile$ for a certain manufacturing comany for the most recent year. he summary is sho&n in the ta(le (elo&. he comany oerates t&o $ifferent manufacturing lants, lus a cororate hea$uarters.
%ense category
lant 1
lant 2
Eororate hea$uarters
D1,000,000
D1,70,000
Materials
D3,00,000
D4,000,000
9actory e%ense
D1,300,000
D2,300,000
Eororate e%ense
D,000,000
Solution " *a+ lant 1" 9actory oerhea$ rate FOHR1 5
lant 2" 9actory oerhea$ rate FOHR2 5
1,300,000 1,000,000
5 1.30 5 3#+
2,300,000
5 1.3143 5 3"!3+ 1,70,000 ,000,000 *(+ Eororate oerhea$ rate COHR 5 5 1.12 5 '"'&+ 1,0 00,000 + 1,7 0,000 3.1
he hourly rate for a certain &or' center is to (e $etermine$ (ase$ on the follo&ing $ata" $irect la(or rate 5 D1.00/hrG alica(le factory oerhea$ rate on la(or 5 3BG caital inestment in machine 5 D200,000G serice life of the machine 5 yearsG rate of return 5 1BG salage alue in fie years 5 eroG an$ alica(le factory oerhea$ rate on machine 5 40B. he &or' center &ill (e oerate$ t&o -hour shifts, 20 $ays er year.
0.1/*1 + 0.1/+
/
5 0.283 / *1 + 0.1/+ − 1 UAC 5 D200,000*0.283+ 5 D8,663/yr ours/yr 5 *16 hr/$ay+*20 $ays/yr+ 5 4000 hr/yr, so C m 5 8,663/4000 5 D14.82/hr Iien C L 5 D1.00/hr, C o 5 1.00*1 > 0.3+ > 14.82*1 > 0.40+ 5 .!"3%hr 3.2
)n the reious ro(lem if the &or'loa$ for the cell can only Austify a one shift oeration, $etermine the aroriate hourly rate for the &or' center. Solution" Same UAC as in reious solution" UAC 5 D8,663/yr, C m 5 8,663/2000 5 28.3/hr C o 5 1.00*1 > 0.3+ > 28.3*1 > 0.40+ 5 .(&"#%hr
3.3
)n the oeration of a certain ro$uction machine, one &or'er is reuire$ at a $irect la(or rate 5 D10/hr. #lica(le la(or factory oerhea$ rate 5 0B. Eaital inestment in the system 5 D20,000, e%ecte$ serice life 5 10 years, no salage alue at the en$ of that erio$, an$ the alica(le machine factory oerhea$ rate 5 30B. he &or' cell &ill oerate 2000 hr/yr. se a rate of return of 2B to $etermine the aroriate hourly rate for this &or' cell. Solution " * A/ P ,2B,10+ 5
0.2*1 + 0.2+10 *1 + 0.2+10 − 1
5 0.201
Mfg Metrics-3e-S 11-24, 24/06, 06/04/07 UAC 5 20,000*0.201+ 5 70,02/year Machine rate C m 5 70,02/2000 5 D3.01 C o 5 10.00*1 > 0.0+ > 3.01*1 > 0.30+5 .(#"$&%hr
3.4
)n the reious ro(lem, suose that the machine &ill (e oerate$ three shifts, or 6000 hr/yr, instea$ of 2000 hr/yr. ;ote the effect of increase$ machine utiliation on the hourly rate comare$ to the rate $etermine$ in the reious ro(lem. Solution " * A/ P ,2B,10+ 5 0.201 as in reious ro(lem. UAC 5 20,000*0.201+ 5 70,02/year Machine rate C m 5 70,02/6000 5 D11.67 C o 5 10.00*1 > 0.0+ > 11.67*1 > 0.30+5 .3#")%hr
3.
he (rea'-een oint is to (e $etermine$ for t&o ro$uction metho$s, one a manual metho$ an$ the other automate$. he manual metho$ reuires t&o &or'ers at D8.00/hr each. ogether, they ro$uce at a rate of 36 units/hr. he automate$ metho$ has an initial cost of D12,000, a 4-year serice life, no salage alue, an$ annual maintenance costs 5 D3000. ;o la(or *e%cet for maintenance+ is reuire$ to oerate the machine, (ut the o&er reuire$ to run the machine is 0 'W *&hen running+. Eost of electric o&er is D0.0/'Wh. )f the ro$uction rate for the automate$ machine is 100 units/hr, $etermine the (rea'-een oint for the t&o metho$s, using a rate of return 5 2B. Solution " Manual metho$" aria(le cost 5 *2 &or'ers+*D8.00/hr+/*36 c/hr+ 5 D0.0/c otal cost as a function of Q is TC 5 0.0 Q assuming no fi%e$ costs.
#utomate$ metho$" * A/ P ,2B,4+ 5
0.2/*1 + 0.2/+
4
5 *0.4234+ 4 *1 + 0.2/+ − 1 UAC 5 12,000*#/,2B,4+ > 3000 5 12,000*0.4234+ > 3000 5 D,830/yr *0'&h / hr +*D0.0 / '&h+ :aria(le cost 5 5 0.02/c 100 c / hr otal cost as a function of Q 5 ,830 > 0.02 Q Crea'-een oint" 0.0 Q 5 ,830 > 0.02 Q, 0.47Q 5 ,830 Q 4 )/)!) pc%-r 117 ,747 c / yr ours of oeration er year" Manual" H 5 5 3270.76 hr/yr. 36 c / hr Comment" his &oul$ reuire t&o shifts. 117 ,747 c / yr #utomate$" H 5 5 1177.47 hr/yr. 100 c / hr Comment" lenty of a$$itional caacity in one shift (eyon$ the (rea'-een oint.
