Ch. 1 Competing with Operations. Ch. 2 Project Management. Ch. 3 Process !trateg" Ch. 4 Process #na$"sis. Ch. %. &'a$it" an( Per)ormance Ch. 6. Capacit" P$anning Ch. 7. Constraint Management Ch. 8. *ean !"stems Ch. . !'pp$" Chain +esign. Ch. 10 !'pp$" Chain ntegration Ch. 11. *ocation. Ch. 12. nentor" Management. Ch. 13. orecasting. Ch. 14. Operations P$anning an( !che('$ing Ch. 1%. /eso'rce P$anning.
2, 3, 4 on p27-28 1, 6, 7, 8,10 on p7-80 1, 3, 4 on p116 10, 11, 20, 21, 2% on p147-14 3, 4, %, 6, 7, 8, 1% on p206-20 2, 3, 4 on p234-23% 3, 4, % on p282-283 3, 4, 7 on p317-318 2, %, on p346-347 2, 3, 4 on p381-382 1, 2, 3, 4, 8, 12 on p407-410 1, 7, , 10, 13, 14 on 440-442 2, 4, %, 11, 13 on p40-42 2, 3, 11, 16 on p%30-%34 1, 4, %, 14 M/P, 6 PM!
Ch1 2. a.
!'(s !'(s an( an( +'( +'(ss * *a' a'n( n(r" r" *ao *aorr pro( pro('c 'cti tii it" t" Number of Week Workers 1 2 2 2 3 3 4 3 % 2
Input (Labor-hours) 24 46 62 %1 4%
Output (Shirts) 68 130 1%2 12% 131
Output/Input Ratio 2.83 shirtsho'r 2.83 shirtsho'r 2.4% shirtsho'r 2.4% shirtsho'r 2.1 shirtsho'r
.
O'tp't O'tp't per perso person n (oes not not ar" m'ch m'ch whether whether it is !'(, +'(, +'(, or '( wor5ing wor5ing.. Pro('cti Pro('ctiit" it" (ec$in (ec$ines es when when a$$ three three are presen present. t. Perhaps Perhaps there there isnt isnt eno'gh eno'gh wor5 to 5eep 5eep three perso persons ns occ'pie occ'pie(, (, or perhaps perhaps there there is not eno'gh eno'gh wor5 wor5 space or e'ipment to accommo(ate three wor5ers. 3. Comp Compac actt (is (iscc p$a p$a" "ers ers a$'e a$'e o) O'tp't9 :300 a$'e a$'e o) np't9 *aor ; Materia$s ; Oerhea(
O'p't :300 = = 2.000 np't :30 + :70 + :%0 10< pro('ctiit" improement → 2. 00 00 × 1.10 = 2. 20 200 =ien pro('ctiit" = 2.20 , an( the a$'e o) o'tp't = :300, we so$e )or the cost o) inp'ts9 O'p't :300 = = 2.20 Pro('ctiit" = np't np't :300 = :136.36 or :136 np't = 2.2 Pro('ctiit"
>he cost o) inp'ts m'st (ecrease "
=
(:1%0 − :136) = :14 . :70 = 20.00<
a.
# :14 re('ct re('ction ion in materi materia$ a$ cost costss is :14
.
# :14 re('ction in $aor costs is
c.
# :14 :14 re(' re('ctio ction n in oer oerhea hea( ( is :14: :14:%0 %0 ? 28.00 28.00< <
4.
>he o'tp't o'tp't o) a process process is a$'e( a$'e( at :100 per 'nit. 'nit. >he cost cost o) $aor is :%0 per per ho'r inc$'( inc$'(ing ing ene)i ene)its. ts. >he acco'nting (epartment proi(e( the )o$$owing in)ormation ao't the process )or the past )o'r wee5s9
nits !ro"u#e" $ota% &a%ue Labor (')
:14 :30 = 46.67<
Week 1 1124 112,400 12,73%
Week 2 13 1 0 131,000 14,842
Week 3 102 10,200 10,603
.
Week 4 81 8,100 %26
2%4.7 21,041 8,2 2.63 4.41 'n 'nitshr
Labor (hrs) ateria% (') Oerhea" (') u%tifa#tor !ro"u#tiit* Labor !ro"u#tiit*
a.
26.8 24,%23 10,480 2.63 4.41'nitshr
212.1 20,442 8,736 2.7% %.1% 'n 'nitshr
10.% 18,364 7,848 2.7% %.1% 'n 'nitshr
@se the m'$ti)actor m'$ti)actor pro('ct pro('ctiit" iit" ratio to see see whether recent recent process process improeme improements nts ha( an" e))ec e))ectt an(, i) so, when the e))ect was noticea$e. a$'e o) o'tp't
1124'nits × :100 = :112, 40 4 00 a$'e a$'e o) inp't9 i np't9 $aor ; materia$ ; oerhea( :12,73% ; :21,041 ; :8,2 ? :42,768 Pro('ctiit" ratio9 *aor Pro('ctiit"
=
O'tp't np't
Aee5 1
Pro('ctiit"
=
O'tp't :112, 40 4 00 = = 2.628 np't :42, 76 768
Aee5 2
Pro('ctiit"
=
O'tp't :131,00 ,000 = = 2.628 np't :4, 84%
Aee5 3
Pro('ctiit"
=
O'tp't :10, 20 2 00 = = 2.74% np't :3, 78 781
Aee5 4
Pro('ctiit"
=
O'tp't :8,100 = = 2.74% np't :3%, 73 738
2.74% − 2.628 × 100< = 4.4%< 2.628 Improe" 4+4, - noti#eab%e in Week 3
.
Bas $aor pro('ctiit" change( @se the $aor pro('ctiit" ratio to s'pport "o'r answer. *aor-ho'rs o) inp't9 *aor :%0ho'r *aor costs Aee5 Aee5 1 ? Aee5 Aee5 2 ? Aee5 Aee5 3 ? Aee5 Aee5 4 ?
:12,73%:%0 ? 2%4.7 :14,842:%0 ? 26.84 :10,603:%0 ? 212.06 :,%26:%0 ? 10.%2
Pro('ctiit" ratio9 *aor Pro('ctiit"
Aee5 Aee5 1 ?
Aee5 Aee5 2 ?
Aee5 Aee5 3 ?
=
O'tp't np't
O'tp't 112 4 4.4130 ho'r ho'r = = 4.4130 np't 2%4.7 ho ho'rs O'tp't 131 0 = = 4.413 4.413 ho'r ho'r *aor Pro('ctiit" = np't 26.84 ho'rs O'tp't 1 02 %.14% % ho'r ho'r = = %.14 *aor Pro('ctiit" = np't 212.06 ho'rs *aor Pro('ctiit"
=
.
2%4.7 21,041 8,2 2.63 4.41 'n 'nitshr
Labor (hrs) ateria% (') Oerhea" (') u%tifa#tor !ro"u#tiit* Labor !ro"u#tiit*
a.
26.8 24,%23 10,480 2.63 4.41'nitshr
212.1 20,442 8,736 2.7% %.1% 'n 'nitshr
10.% 18,364 7,848 2.7% %.1% 'n 'nitshr
@se the m'$ti)actor m'$ti)actor pro('ct pro('ctiit" iit" ratio to see see whether recent recent process process improeme improements nts ha( an" e))ec e))ectt an(, i) so, when the e))ect was noticea$e. a$'e o) o'tp't
1124'nits × :100 = :112, 40 4 00 a$'e a$'e o) inp't9 i np't9 $aor ; materia$ ; oerhea( :12,73% ; :21,041 ; :8,2 ? :42,768 Pro('ctiit" ratio9 *aor Pro('ctiit"
=
O'tp't np't
Aee5 1
Pro('ctiit"
=
O'tp't :112, 40 4 00 = = 2.628 np't :42, 76 768
Aee5 2
Pro('ctiit"
=
O'tp't :131,00 ,000 = = 2.628 np't :4, 84%
Aee5 3
Pro('ctiit"
=
O'tp't :10, 20 2 00 = = 2.74% np't :3, 78 781
Aee5 4
Pro('ctiit"
=
O'tp't :8,100 = = 2.74% np't :3%, 73 738
2.74% − 2.628 × 100< = 4.4%< 2.628 Improe" 4+4, - noti#eab%e in Week 3
.
Bas $aor pro('ctiit" change( @se the $aor pro('ctiit" ratio to s'pport "o'r answer. *aor-ho'rs o) inp't9 *aor :%0ho'r *aor costs Aee5 Aee5 1 ? Aee5 Aee5 2 ? Aee5 Aee5 3 ? Aee5 Aee5 4 ?
:12,73%:%0 ? 2%4.7 :14,842:%0 ? 26.84 :10,603:%0 ? 212.06 :,%26:%0 ? 10.%2
Pro('ctiit" ratio9 *aor Pro('ctiit"
Aee5 Aee5 1 ?
Aee5 Aee5 2 ?
Aee5 Aee5 3 ?
=
O'tp't np't
O'tp't 112 4 4.4130 ho'r ho'r = = 4.4130 np't 2%4.7 ho ho'rs O'tp't 131 0 = = 4.413 4.413 ho'r ho'r *aor Pro('ctiit" = np't 26.84 ho'rs O'tp't 1 02 %.14% % ho'r ho'r = = %.14 *aor Pro('ctiit" = np't 212.06 ho'rs *aor Pro('ctiit"
=
.
Aee5 Aee5 4 ?
*aor Pro('ctiit"
%.141 − 4.4130 4.4130
=
O'tp't 81 = = %.141 %.141 ho'r np't 10.%2 ho ho'rs
×100< = 16.68<
Improe" 1.+.
Ch2 1. a.
#OD #OD netw networ or5 5 (iag (iagra ram m
+ 2 F 4 !tart
# 2
E 1
= 3
8
B %
C % .
7
inish
4
>he critica$ path is #GCGGBG with a comp$etion time o) 27 (a"s.
c. #tiit* # F C + E = B
uration 2 4 % 2 1 8 3 % 4 7
0ar%iest Start 0 2 2 6 6 7 8 1% 1% 20
Latest Start 0 3 2 1% 16 7 17 1% 16 20
0ar%iest inish 2 6 7 8 7 1% 11 20 1 27
6. a.
>he >he #OD #OD (ia (iagram ram is9 is9
.
Latest inish 2 7 7 17 17 1% 20 20 20 27
S%a#k 0 1 0 10 0 0 1 0
On riti#a% !ath5 Hes Do Hes Do Do Hes Do Hes Do Hes
!tart
. c. (.
0
#
4
6
4
10
0
F
3
0
3
3
4
+
7
E! + E
10
3
13
*!
3
E
3
6
+@/ *
inish
0
C
%
7
11
4
%
13
4
17
=
17
17
B
2
8
17
17 12 2
>he critica$ path is9 FGEG=GB, which ta5es 2 wee5s. >he s$ac5 )or actiit" # ? 10 G 4 ? 6 wee5s. >he s$ac5 )or actiit" + ? 13 G 7 ? 6 wee5s. ) # ta5es % wee5s, then + wi$$ hae 10 G % ? % wee5s s$ac5.
7. Ae ent'res nc.
#tiit*
Optimisti# (a)
ost Like%* (m)
!essimisti# (b)
# F C + E
3 12 2 4 1
8 1% 6 4
1 18 16 20 7
7 1, 8 19 4
a.
te A = ( 3 + 4 ( 8 )
+ 1 ) 6 = %4 6 = (a"s
te B = ( 12 + 4 ( 1% )
+ 18) 6 = 0 6 = 1% (a"s
teC = ( 2 + 4 ( 6 )
+ 16) 6 = 42 6 = 7 (a"s
te D = ( 4 + 4 ( )
+ 20) 6 = 60 6 = 10 (a"s
te E = ( 1 + 4 ( 4 )
+ 7 ) 6 = 24 6 = 4 (a"s
. σ A = 2
2
σ B σ
2
2
σ D
2
= ( ( 18 − 12 ) 6) = 1.00 2
= %.44
2
= ( ( 20 − 4 ) 6 ) = 7.11
σ E = 2
2
( ( 1 − 3) 6) = 7.11
C = ( ( 16 − 2 ) 6 )
2
( ( 7 − 1) 6 ) = 1.00
8. a.
#tiit* Statisti#s 06pe#te" $ime &arian#e t (σ 2 ) ( e)
>he eIpecte( actiit" times in (a"s are9
.
8+11 1+99 ,+44 8+11 1+99
#tiit*
Optimisti#
ost Like%*
!essimisti#
t e
# F C + E
% 4 % 2 4
8 8 6 4 7
11 11 7 6 10
8.00 7.83 6.00 4.00 7.00
!ath #GC #G+GE FGE
2
σ
1.00 1.36 0.11 0.44 1.00
$ota% 06pe#te" $ime 8 ; 6 ? 14.00 8 ; 4 ; 7 ? 1.00 7.83 ; 7 ? 14.83
>he critica$ path is #G+GE eca'se it has the $ongest time ('ration. >he eIpecte( comp$etion time is 1 (a"s.
.
z =
T − T E σ
2
Ahere T ? 21 (a"s, T E ? 1 (a"s, an( the s'm o) the ariances )or critica$ path #G+GE is 1.00 ; 0.44 ; 1.00 ? 2.44.
z =
c.
21 − 1 2 = = 1.28 2.44 1%62 .
#ss'ming the norma$ (istri'tion app$ies which is 'estiona$e )or a samp$e o) three actiities, we 'se the ta$e )or the norma$ proai$it" (istri'tion. =ien z ? 1.28, the proai$it" that the project can e comp$ete( in 21 (a"s is 0.87, or ao't 0<. Feca'se the norma$ (istri'tion is s"mmetrica$, the proai$it" the project can e comp$ete( in 17 (a"s is 1 G 0. 87 ? 0. 1003, or ao't 10<.
10. a.
>he #OD (iagram is9
0
#
%
%
C
7
8
E
12
E! + E
4
%
2
11
11
4
1%
*!
!tart
. c.
+@/
*
inish
0
F
3
3
+
8
8
1%
0
3
3
3
%
8
8
7
1%
Critica$ path is FG+G. EIpecte( ('ration o) the project is 1% wee5s. #ctiit" s$ac5s )or the project are9
#tiit* # F C + E
Start 0ar%iest Latest 0 4 0 0 % 3 3 8 11
inish 0ar%iest Latest % 3 3 7 11 8 8 12 1%
.
S%a#k 4 0 4 0 3
riti#a% !ath5 Do Hes Do Hes Do
8
8
1%
1%
0
Hes
Ch3 1. +r. ='$a5owicJ iIe( cost, F = :1%0,000 /een'e per patient, p = :3,000 aria$e cost per 'nit, c = :1000 Frea5-een o$'me, Q
=
F p − c
=
:1%0,000 :3,000 − :1000
= 7% patients
3. Fa5er Machine Compan" %oseness epartment Ratin: !air wij 1G2 8 1G3 3 1G% 1G6 % 2G4 3 3G% 8 3G6 4G6 3 %G6 3
urrent !%an !ropose" !%an istan#e (d ij ) istan#e (d ij ) wij d ij wij d ij 3 24 3 24 1 3 1 3 1 2 18 2 10 1 % 1 3 1 3 2 16 3 24 3 27 2 18 2 6 1 3 1 3 1 3 wd ; wd ; 191 191 >here is no change in the weighte(-(istance score. >hese $a"o'ts can e assesse( 'sing the Layout so$er o) OM EIp$orer, as shown )o$$owing )or the c'rrent p$an.
4.
Fa5er Machine F$oc5 P$an # goo( p$an wo'$( $ocate the )o$$owing (epartment pairs c$ose together9 1G 2, 3G%, 1G%, 3G6, 1G6. >he )o$$owing $a"o't satis)ies these re'irements an( $eaes (epartment 3 'nmoe(. t a$so proi(es one-'nit (istances )or (epartment pairs 2G4 an( 4G6. 3
6
4
%
1
2
>he weighte(-(istance wd score is9 K8$ ; 32 ; $ ; %$ ; 3$ ; 8$ ; $ ; 3$ ; 32L ? %7, a 43.6< re('ction oer Pro$em 3s so$'tion. Ch4 10.
=aso$ine !tations a.
>he gas station in part has a more e))icient )$ow )rom the perspectie o) the c'stomer eca'se tra))ic moes in on$" one (irection thro'gh the s"stem.
.
11.
.
>he gas station in part a creates the possii$it" )or a ran(om (irection o) )$ow, there" ca'sing occasiona$ con)$icts at the gas p'mps.
c.
#t the gas station in part a c'stomer co'$( pa" )rom the car. Boweer, this practice co'$( e a so'rce o) congestion at pea5 perio(s.
'st *i5e Bome /esta'rant a. >he s'mmar" o) the process chart sho'$( appear as )o$$ows9
.
Each c"c$e o) ma5ing a sing$e-scoop ice cream cone ta5es 1.70 ; 0.80 ; 0.2% ; 0.%0 ? 3.2% min'tes. >he tota$ $aor cost is :10hrK3.2% mincone60 minL10 coneshr10 hr(a"363 (a""r ? :1,662.%0. >o ma5e this operation more e))icient, we can e$iminate (e$a" an( re('ce trae$ing " haing prec$eane( scoops aai$a$e. >he improe( process chart )o$$ows.
20. Perrottis PiJJa Pareto chart a. #$tho'gh the )re'enc" o) part$" eaten piJJa is $ow, it is a serio's 'a$it" pro$em eca'se it is (e$ierate rather than acci(enta$. t is $i5e$" to ca'se eItreme $oss o) goo(wi$$. # common root ca'se o) man" o) these pro$ems co'$( e miscomm'nication etween the c'stomer an( the or(er ta5er, etween the or(er ta5er an( pro('ction an( etween pro('ction an( (istri'tion. >his chart was create( 'sing OM EIp$orer.
.
Ca'se-an(-e))ect (iagram
.
(a#hines Car tro'$e
(ateria%s *ate pro('ction *ost in-oice
Dot )ami$iar with ser-ice area Mis'n(erstoo( a((ress !erson
.
!er-ice area too $arge !che('$ing too man" (e$i-eries on one trip (etho"s
Late 3e%i)er*
21. !mith, !chroe(er, an( >orn short moes a. >he ta$$" sheet gien in the pro$em is essentia$$" a horiJonta$ ar chart. >o create a Pareto (iagram, the categories are arrange( in or(er o) (ecreasing )re'enc". >his (iagram was create( 'sing OM EIp$orer.
.
Ca'se-an(-e))ect (iagram
2%.=rin(we$$, nc. a. !catter (iagram
. c.
Corre$ation coe))icient ρ = − 0.%47 . >here is a negatie re$ationship etween permeai$it" an( caron content, a$tho'gh it is not too strong. Caron content m'st e increase( to re('ce permeai$it" in(eI.
.
>he c"c$e time is re('ce( to 1.6% ; 0.4% ; 0.2%, or 2.3% min'tes. >he tota$ $aor cost is : 10hrK2.3% mincone60 minL10 coneshr10 hr(a"363 (a""r ? :14,217.%0. >here)ore, the ann'a$ $aor saing is :1,662.%0 G :14,217.%0 ? :%,44%.00. Ch%. 3. =arcias =arage p = 0.10 , n ? 100, z ? 2
= p ( 1 − p ) n = 0.10 ( 0.0 ) 100 = 0.03 UCL p = p + zσ p = 0.10 + 2 ( 0.03) = 0.16 LCL p = p − z σ p = 0.10 − 2 ( 0.03 ) = 0.04 σ p
#t 8 o) 100, the n'mer o) ret'rns )or serice is e$ow aerage, 't this oseration is within the contro$ $imits. >he repair process is sti$$ in contro$. 4. Canine =o'rmet Compan"
x ? 4% grams, n ? 10, R ? 6 grams
a. rom >a$e %.1, A2 ? 0.308, D3 ? 0.223, D4 ? 1.777 UCL R = D4 R ? 1.7776 grams ? 10.662 grams LCL R = D3 R ? 0.2236 grams ? 1.338 grams
UCL x = x + A2 R ? 4% grams ; 0.3086 grams ? 46.848 grams .
LCL x
= x − A2 R ? 4% grams G 0.3086 grams ? 43.1%2 grams
. >he range is in statistica$ contro$ howeer, the aerages o) samp$es 2, 4, an( % are o't o) statistica$ contro$, there)ore, the process is o't o) contro$. %.
Mar$in Compan"
1
2
3
4
x
R
1 2 3 4 % 6
.604 .%7 .%81 .620 .%0 .%8%
.612 .601 .%70 .60% .614 .%83
.%88 .607 .%8% .%% .608 .617
.600 .603 .%2 .%88 .604 .%7
.601 .602 .%82 .602 .604 .%1
.024 .010 .022 .032 .024 .038
R = 0.02% or a 'ic5 oeriew o) the (ata, we can 'se the Statistics mo('$e o) POM )or Ain(ows, which shows among other x
=
0.%7
things that x = 0.%7N an( σ ? 0.0128. >he graph trac5s the cap (iameters oer the 6 samp$es, with )o'r in each samp$e.
.
.
a.
x = 0.%7N , n ? 4, R = 0.02%N
rom >a$e %.1,
= 0.0 , D4 = 2.282 UCL R = D4 R = 2.282 ( 0.02%N) = 0.0%7 N LCL R = D3R = 0.0 ( 0.02%N) = 0.0N A2 = 0.72 , D3
UCL x
= x + A2 R = 0.%7 N+ 0.72 ( 0.02%N) = 0.61%N
LCL x = x − A2 R = 0.%7 N− 0.72 ( 0.02%N) = 0.%7 N .
) the process passes the process capai$it" in(eI test, the process is capa$e. Process capai$it" in(eI9
C pk = Minim'm o)
x − *ower speci)ication @pper speci)ication − x , 3σ 3σ 0.%7 − 0.%%0 = 1.21 30.013
0.6%0 − 0.%7 30.013
= 1.36
C pk ? 1.21 >he process is not capa$e o) )o'r-sigma 'a$it". >he target is 1.33. Conse'ent$", we test to see i) the process ariai$it" is too $arge.
C p
=
@pper speci)ication − *ower speci)ication 6σ C p =
0.6%0 − 0.%%0 60.013
.
= 1.28
>he process ariai$it" is e$ow )o'r-sigma 'a$it", which has a target o) 1.33. Management an( emp$o"ees sho'$( $oo5 )or wa"s to re('ce the ariai$it" in the process an( then rechec5 the process capai$it" in(eI. 6.
Ae initia$$" ass'me the historica$ gran( aerage is a(e'ate Stu"ent =ear 1 2 3 4 , . 1 63 %7 2 87 70 61 2 0 77 % 88 48 83 3 67 81 3 %% 71 71 4 62 67 78 61 8 3 % 8% 88 77 6 %8 0 6 60 %7 7 83 64 4 7 4 8% %6 77 8 72 8 7 86 83 88 6% 87 4 0 76 88 6% 3 10 88 1 71 8 7 7
)or the centra$ $ine o) the chart9 8 7% 63 86 71 7 86 71 76 86 3
%8 4 8 % 72 64 61 84 87 87
7 63 72 60 3 64 2 2 81 4 6
19 71 70 0 84 60 74 7 71 63 8%
era:e 6.7 74.4 77.2 7%.7 76.0 7%.3 7.4 81.8 83.6 84. x = 77.8
>he aerage )or the process, x =
77.8, an( the stan(ar( (eiation o) the 100 historica$ (ata points in >a$e
%.2 is 13. σ x
=
σ
n
=
13 10
= 4.1
UCL x
= x + zσ x = 77.8 + ( 2 × 4.1) = 86.0
LCL x
= x − z σ x = 77.8 − ( 2 × 4.1) = 6.6
#$tho'gh the process is in contro$, the $ast )o'r oserations are a$$ aoe the aerage an( eIhiit an eerincreasing tren(. Mega-F"te sho'$( eIp$ore )or ca'ses o) corr'ption, s'ch as instr'ctor or per)ormance meas'res, which gie incenties )or improe( test scores. t is possi$e that st'(ents are getting righter or are ecoming more high$" motiate(. Perhaps a(missions stan(ar(s hae een raise(. t is possi$e that teaching metho(s hae improe(. >he point shown here i s9 the process m'st e sta$e whi$e (ata are co$$ecte( )or setting contro$ $imits. 7.
Bospita$ a(ministrator p ? >ota$ asent>ota$ oserations a. ? 41%64 ? 0.0%1 σ p
= p ( 1 − p ) n = 0.0%1( 1 − 0.0%1) 64 ? 0.027%
UCL p = p + zσ p ? 0.0%1 ; 2.%80.027% ? 0.121 LCL p = p − z σ p ? 0.0%1 G 2.%80.027% ? G 0.01%, a(j'ste( to Jero. .
>he (ata )rom the $ast three wee5s )a$$ within the contro$ $imits. >here)ore we accept the estimate o) %.1< asenteeism. Ho' m'st now assess whether this amo'nt o) asenteeism is t"pica$ )or n'rses ai(es.
.
8.
>eIti$e man')act'rer a. c = 10.2%
UCLc LCLc .
= c +3 = c −3
c c
= 10.2% + 3 10.2% = 1.8% = 10.2% − 3 10.2% = 0.6%
Feca'se the $ast two samp$es with 22 an( 21 irreg'$arities p$ot o'tsi(e the 'pper contro$ $imit, we conc$'(e that the process is o't o) contro$.
1%. >he Mone" Pit *ower !peci)ication Ca$c'$ation
13.066 − %.00 = 0.64 ( 3 ) ( 4.21)
@pper !peci)ication Ca$c'$ation
2%.00 − 13.066 = 0.4 ( 3) ( 4.21)
a.
C pk = min ( 0.64, 0.4 )
C p
=
2% − % 6 ( 4.21)
Feca'se
.
= 0.64
= 0.7
C p an( C pk hae a$'es $ess than 1, the process is not capa$e o) meeting speci)ications. Hes,
a$i( eca'se the process is 'n(er statistica$ contro$, as can e shown " p$otting the $ast 1% oserations on contro$ charts. #s5 st'(ents to (emonstrate that the process is in statistica$ contro$. >he ariai$it" o) the process m'st e great$" re('ce(. #$so, the process sho'$( e etter centere(
c. etween the speci)ication $imits. Ch6. 2. Capacit" re'irements in )ie "ears >his "ears capacit" re'irement, a$$owing instea( )or j'st a %-percent capacit" c'shion, is %2.63 or %0 K1.0 G 0.0%L c'stomers per (a". Essentia$$" "o' sho'$( (ii(e " the (esire( 'ti$iJation rate. ie "ears )rom now, i) (eman( is on$" 7% percent o) the c'rrent $ee$, the c'stomer re'irement wi$$ e 3.47 or %2.63 × 0.7% c'stomers per (a". 3.
#ir$ine compan"
>his "ears capacit" re'irement, a$$owing )or a 2%-percent capacit" c'shion, is 3.3 or 70 K1.0 − 0.2%L c'stomers per (a". >hree "ears )rom now, i) (eman( increases " 20 percent, the c'stomer re'irement wi$$ e ao't 112 or 3.3 × 1.2 c'stomers per (a" )or this )$ight segment. 4.
#'tomoi$e ra5e s'pp$ier a. >he tota$ machine ho'r re'irements )or a$$ three (eman( )orecasts9 !essimisti# ore#ast 06pe#te" ore#ast Optimisti# ore#ast !ro#ess Setup !ro#ess Setup !ro#ess Setup omponent $ime $ime $ime $ime $ime $ime p (/>)s p (/>)s p (/>)s # 7%0 2%0.0 00 300.0 1,2%0 416.7 F 2,000 %62.% 2,600 731.3 3,400 %6.3 C 8%0 1,161.7 1,2%0 1,708.3 2,000 2,733.3 3,600 ; 1,74.2 4,7%0 ; 2,73.6 6,6%0 ; 4,106.3 %,%74.2 7,48.6 10,7%6.3 Demand >he n'mer o) ho'rs N proi(e( per machine is9
.
N ? 2 shi)ts(a" × 8 ho'rsshi)t × % (a"swee5 × %2 wee5s"ear1.0 G 0.2 ? 3,328 ho'rsmachine >he capacit" re'irements )or three )orecasts are9 Pessimistic9 ? %,%74.23328 ? 1.67 or 2 machines EIpecte(9 ? 7,48.63328 ? 2.2% or 3 machines Optimistic9 ? 10,7%6.33328 ? 3.23 or 4 machines . >he c'rrent capacit" is s'))icient )or the pessimistic an( eIpecte( )orecasts. Boweer, there is a gap o) one machine )or the optimistic )orecast. >he gap (rops to Jero when the 20 percent increase )rom short-term options is inc$'(e(. 3 machines × 3,328 ho'rsmachine × 1.2 ? 11,81 ho'rs. >his is greater than 10,7%6 ho'rs re'ire(.
Ch7 3.
CQC Aor5 !tation A R H
4.
!tation R is the ott$enec5 G 2600 min'tes Pro('ct # Pro('ct F >ota$ *oa( 10S0?00 14S8%?110 200 10S0?00 20S8%?1700 2600 1%S0?13%0 11S8%?3% 228%
CQC a. >ra(itiona$ Metho(9 Pro('ct F has the higher contri'tion margin'nit Pro('ct # Pro('ct F Price %%.00 6%.00 /aw an( P'rchase( Parts %.00 10.00 Contri'tion Margin %0.00 %%.00
Aor5 !tation A R H
Min'tes at !tart 2400 2400 2400
Mins. *e)t a)ter Ma5ing 8% Fs 1210 700 146%
Mins. *e)t a)ter Ma5ing 0 #s 310
Can On$" Ma5e 70 #s 70010 ? 70
11%
8% 'nits o) F an( 70 'nits o) # Pro('ct F wi$$ 'se 1700 min'tes at station R $eaing 700 )or Pro('ct #. Pro('ct # F >ota$s
Oerhea(
/aw Mat$
3%00
70 I 2 ?140 8% I % ? 42% %6%
*aor
P'rchase Parts
3 I :6 I 40 hrs ? 720
70 I 3 ? 210 8% I % ? 42% 63%
>ota$ Costs
%420
/een'es 70 I :%% ? 38%0 8% I :6% ? %%2% 37%
/een'e G costs ? pro)it :,37% - :%,420 ? :3,%% . Fott$enec5-ase( approach9 Pro('ct # has the higher contri'tion margin'nit at the ott$enec5 Pro('ct # Pro('ct F Margin %0.00 %%.00 >ime at ott$enec5 10 min 20 min Contri'tion margin per min'te %.00 2.7% Aor5 !tation A
Min'tes at !tart 2400
Mins. *e)t a)ter Ma5ing 0 #s 1%00
.
Mins. *e)t a)ter Ma5ing 8% Fs 310
Can On$" Ma5e 7% Fs
R H
2400 2400
1%00 10%0
1%0020 ? 7% 11%
.
Ma5e 0 'nits o) # 00 min'tes 'se( G $eaes 1%00 min'tes can ma5e 7% 'nits o) F Pro('ct Oerhea( /aw Mat$ *aor P'rchase Parts >ota$ /een'es Costs # 0 I 2 ? 180 0 I 3 ? 270 0 I :%% ? 4%0 F 7% I % ? 37% 7% I % ? 37% 7% I :6% ? 487% >ota$s 3%00 %%% 3 I :6 I 40 hrs ? 640 %41% 82% 720 Pro)it?/een'e G costs :,82% G :%,41% ? :4,410 c.
:4,410- :3,%% ? :4%% increase 'sing >OC, which is a 12< increase
%. !t'(ent answers wi$$ ar" - this is one possi$e so$'tion. #ssem$"-$ine a$ancing with $ongest wor5 e$ement r'$e to pro('ce 40 'nits per ho'r.
1 1 ho'r 3600 sec sec = = = 0 'nit ! 40 'nits 40 'nits
a.
c=
.
T =
c.
!1 ? T#, C, EU, !2 ? TFU, !3 ? T=, +U, !4 ? TB, , U, !% ? T, QU
Station !1
!2 !3 !4
!%
∑ t =
41%
c
0
an"i"ate(s) # C E F +, , = +, , , B, , Q
= 4.611 or %
hoi#e # C E F = + B Q
Work 0%ement $ime (se#) 40 30 20 80 60 2% 4% 1% 10 7% 1%
( t ) 41% = ∑ (100< ) = = 22< . nc %(0) Fa$ance (e$a" (< ) = 100< − E))icienc" = 100< − 2.2< = 7.8< (.
E))icienc" <
Ch8 3. *eAin a. !o$ing )or imp$ie( po$ic" aria$e, α k"
d w + ρ 1 + α
12 =
c
1,800 1.0% + 0.003 ( 300) ( 1 + a )
(1+ a) =
300 12 ( 300 ) 1, 800 1.0% + 0.003 ( 300)
= 1.02%6
.
umu%atie $ime (se#) 40 70 0 80 60 8% 4% 60 70 7% 0
I"%e $ime ( c = 0 se#) %0 20 0 10 30 % 4% 30 20 1% 0
α = 1.02%6 − 1 = 0.02%6
.
/e('ction in waiting time
1,800 ( w + 0.0 ) ( 1.02%6) 1, 846w + 1, 661.47 = 11 = 300 300 1,846w = 3, 300 − 1, 661.47 w = 0.888 (a"s >he re('ction in waiting time is9
(10% . − 0.888) 10% .
. = 1%43<
4. =a(jits an( Ai(jits a. Containers )or ga(jits k" k"
.
d w + ρ 1 + α c
80030.0 + 0.061 + 0.0 80
? 4.0%
k"% Containers )or wi(jits k" k"
d w + ρ 1 + α c
80020.14 + 0.201 + 0.08 %0
? 11.7%0
k " 12
7. an'ar"s container nee(s k" k"
d w + ρ 1 + α c
1, 20040.16 + 0.101 + 0.1% 200
? 7.16 or 8 containers
er'ar"s container nee(s k"
d w + ρ 1 + α
c k ? 00S4 0.16;0.12%1;0.1% 200 k ? %.8% or 6 containers per (a"
2.
Ch. Prince E$ectronics a. a$'e o) each +Cs pipe$ine inentor" ? 7% 'nitsw52 w5:3%0'nit ? :%2,%00 .
>ota$ inentor"
? c"c$e ; sa)et" ; pipe$ine ? %K4002 ; 2S7% ; 2S7%L ? 2,%00 'nits
%. Precision Enterprises. #erage aggregate inentor" a$'e ? /aw materia$s ; AP ; inishe( goo(s
.
a.
? :3,12,%00 ; :6,237,000 ; :2,686,%00 ? :12,0%3,000 ? Cost o) goo(s so$(%2 wee5s per "ear ? :32,%00,000%2 ? :62%,000 ? #erage aggregate inentor" a$'e Aee5$" sa$es ? :12,0%3,000:62%,000 ? 1.28 w5
!a$es per wee5
Aee5s o) s'pp$"
.
.
nentor" t'rnoer
!ter$ing nc. a. !art Number
? #nn'a$ sa$es at cost#erage aggregate inentor" a$'e ? :32,%00,000:12,0%3,000 ? 2.664 t'rns"ear
era:e Inentor* (units)
/M-1 /M-2 /M-3 /M-4 AP-1 AP-2 =-1 =-2
&a%ue ('/unit)
20,000 %,000 3,000 1,000 6,000 8,000 1,000 %00
$ota% &a%ue (')
1.00 %.00 6.00 8.00 10.00 12.00 6%.00 88.00
20,000 2%,000 18,000 8,000 60,000 6,000 6%,000 44,000
#erage aggregate inentor" a$'e9 :336,000 .
#erage wee5$" sa$es at cost Aee5s o) s'pp$"
? :6,%00,000%2 ? :12%,000 ? :336,000:12%,000 ? 2.688 wee5s.
c.
2.
nentor" t'rnoer ? #nn'a$ sa$es at cost #erage aggregate inentor" a$'e ? :6,%00,000:336,000 ? 1.34 t'rns. Ch10 Eight $ags. Ae app$" the e'ation )or tota$ ann'a$ cost ana$"sis to each s'pp$ier9 >ota$ #nn'a$ Cost ; pD ; reight costs ; Q2 ; d L # ; #(ministratie costs. >he aerage re'irements per wee5 are 30,000%0 ? 600 ga$$ons. or !harps an( a shipping 'antit" o) %,000, the tota$ ann'a$ cost is9 >ota$ #nn'a$ Cost ? :430,000 ; :%,000 ; %,0002 ; 600 4:0.80 ; :4,000 ? :132,20. >he tota$ ann'a$ costs )or the other a$ternaties are gien in the )o$$owing ta$e. Shippin: >uantit*
3.
Supp%ier
,?999
19?999
1,?999
Sharps
:132,20
:132,%20
:133,20
:12,136 :128,736 Wink%er Ain5$er, with a shipping 'antit" o) 10,000, is t he $owest cost a$ternatie. Fennet a. Each s'pp$iers per)ormance can e ca$c'$ate( as9 !erforman#e Wei:hte" Ratin:
.
:130,336
riterion
Wei:ht
Supp%ier
Supp%ier <
1.
Price
0.2
0.60.2 ? 0.12
0.%0.2 ? 0.10
2.
&'a$it"
0.2
0.60.2 ? 0.12
0.40.2 ? 0.08
3.
+e$ier"
0.3
0.60.3 ? 0.18
0.30.3 ? 0.0
0.1
0.%0.1 ? 0.0%
0.0.1 ? 0.0
0.1
0.70.1 ? 0.07
0.80.1 ? 0.08
0.1
0.0.1 ? 0.0
0.0.1 ? 0.0
0.63
0.%3
4.
Pro('ction )aci$ities V capacit" %. Enironmenta$ protection 6.
inancia$ position
Tota$ wei%&ted sco!e
Supp%ier 0.0.2 ? 0.18
0.80.2 ? 0.16 0.80.3 ? 0.24 0.60.1 ? 0.06 0.60.1 ? 0.06 0.70.1 ? 0.07 0.77
.
!'pp$iers # an( C s'rie( the h'r($e. !'pp$ier # wo'$( receie 4%< o) the or(ers an( !'pp$ier C wo'$( receie %%< o) the or(ers. c. Fens s"stem proi(es some ass'rance that or(ers are p$ace( with 'a$i)ie( s'pp$iers. >he or(ers are (ii(e( etween two s'pp$iers, so there is a rea(" a$ternatie i) a stri5e, )ire, or other pro$em preents one s'pp$ier )rom per)orming. >he s"stem a$so rewar(s s'pp$iers with more or(ers i) the" improe per)ormance.
4.
Feag$e C$othiers. >he weights )or the )o'r criteriaWprice, 'a$it", (e$ier", an( )$eIii$it"Wsho'$( e 0.2, 0.2, 0.2, an( 0.4, respectie$". >he weighte( scores are Supp%ier Supp%ier < Supp%ier 8 × 0.2 ? 1.6 6 × 0.2 ? 1.2 6 × 0.2 ? 1.2 × 0.2 ? 1.8 7 × 0.2 ? 1.4 7 × 0.2 ? 1.4 7 × 0.2 ? 1.4 × 0.2 ? 1.8 6 × 0.2 ? 1.2 % × 0.4 ? 2.0 8 × 0.4 ? 3.2 × 0.4 ? 3.6 >ota$ weighte( score 6.8 7.6 7.4 !'pp$ier F sho'$( e se$ecte(. Ch11
1.
Pre)erence matriI $ocation )or #, F, C, or +
Lo#ation a#tor 1. *aor c$imate 2. &'a$it" o) $i)e 3. >ransportation s"stem 4. ProIimit" to mar5ets %. ProIimit" to materia$s 6. >aIes 7. @ti$ities >ota$
a#tor Wei:ht % 30 % 2% % 1% 1% 100
% 2 3 % 3 2 %
2% 60 1% 12% 1% 30 7% 34%
a#tor S#ore for 0a#h Lo#ation < 4 20 3 1% 3 0 % 1%0 4 20 3 1% 3 7% 4 100 2 10 3 1% % 7% % 7% 4 60 2 30 3%0 400
% 1 % 4 % 4 1
2% 30 2% 100 2% 60 1% 280
*ocation C, with 400 points. 2.
ohn an( ane +ar$ing
Lo#ation a#tor 1. /ent
a#tor Wei:ht 2%
3
a#tor S#ore for 0a#h Lo#ation < 7% 1 2% 2 %0 %
.
12%
2. &'a$it" o) $i)e 3. !choo$s 4. ProIimit" to wor5 %. ProIimit" to recreation 6. Deighorhoo( sec'rit" 7. @ti$ities >ota$
20 % 10 1% 1% 10 100
2 3 % 4 2 4
40 1% %0 60 30 40 310
% % 3 4 4 2
100 2% 30 60 60 20 320
% 3 4 % 4 3
100 1% 40 7% 60 30 370
4 1 3 2 4 %
80 % 30 30 60 %0 380
*ocation +, the in-$aws (ownstairs apartment, is in(icate( " the highest score. >his points o't a criticism o) the techni'e9 the +ar$ings (i( not inc$'(e or gie weight to a re$eant )actor. 3.
ac5son or +a"ton $ocations ac5son W
:2%030,000 − K:1,%00,000 + :%0× 30,000L = :7,%00,000− :3,000,000
= :4,%00,000 +a"ton W
:2%040,000 − K:2,800,000 + :8% × 40,000L = :10,000,000 − :6, 200, 000
= :3,800,000 4.
ac5son "ie$(s higher tota$ pro)it per "ear. a$$-*ine, nc. a. P$ot o) tota$ costs in : mi$$ions ers's o$'me in tho'san(s
18 16
#spen
14 12
Me(icine *o(ge
Fro5en Fow
10 8 Ao'n(e( Qnee 6 4 2 0 0
.
c.
10
20
30
40
%0
60
70
80
o$'me Me(icine *o(ge Fro5en Ao'n(e( Qnee Fow Me(icine *o(ge is the $owest-cost $ocation )or o$'mes 'p to 2%,000 pairs per "ear. Fro5en Fow is the est choice oer the range o) 2%,000 to 44,000 pairs per "ear. Ao'n(e( Qnee is the $owest-cost $ocation )or o$'mes oer 44,000 pairs per "ear. #spen is not the $ow-cost $ocation at an" o$'me. #spen W
:%0060,000 − K:8,000,000 + :2%0 × 60,000L = :30,000,000 − :23,000,000 = :7,000,000 Me(icine *o(ge W
:3%04%,000 − K:2,400,000 + :130 × 4%,000L = :1%,7%0,000− :8, 2%0, 000 = :7,%00,000 Fro5en Fow W
.
:3%043,000 − K:3,400,000 + :0 × 43,000L = :1%,0%0,000 − :7, 270, 000 = :7,780,000 Ao'n(e( QneeW
:3%040,000 − K:4,%00,000 + :6% × 40, 000L = :14,000,000 − :7,100, 000 = :6,00,000 (.
#spen wo'$( s'rpass Fro5en Fow when the #spen pro)it is :7,780,000.
:%00Q − ( :8, 000, 000 + ( :2%0Q ) ) = :7, 780, 000 :2%0Q = 1%, 780, 000 Q = 63,120 #spen wo'$( e the est $ocation i) sa$es wo'$( eIcee( 63,120 pairs per "ear. Bo$(ing a$$ other sa$es o$'mes constant. 8. Cent'ra Bigh !choo$ @sing the Cente! o' (!a)ity !o$er o) OM EIp$orer, we get9
Solver - Center of Gravity
Enter the names of the towns and the coordinates ( x and y ) and population (or load, l ) of each town.
City/Town Name Boelus Cairo annero*
x
10.!" 10.% 10.!!
y
#.$1 #.$! #.$#
Center+of+ra-ity Coordinates
12.
+ais, Ca$i)ornia, Post O))ice a. Center o) =rait" S
x =
∑ $i xi i
∑ $ i i
an( y
S
=
∑ $i yi i
∑ $ i i
.
l
""% !$! $&
lx
1$"1
"#$$".1 !%"$.1 $%010.1" 0 0 1#0'&.#
x* y*
10.!1 #.$&
ly
10&&%.% $#1!#.' 1#'!.0# 0 0 1"$0.#1
xS
=
(6 × 2) + (3 × 6) + (3 × 8) + (3 × 13) + ( 2 × 1%) + ( 7 × 6) + ( %× 18) + ( 3× 10) (6 + 3 + 3 + 3 + 2 + 7 + % + 3)
xS
=
28%
yS
=
207 = 6.% 32
= 8. 32 (6 × 8) + (3 × 1) + (3 × %) + (3 × 3) + (2 × 10) + ( 7 × 14) + (% × 1) + ( 3× 3) yS = (6 + 3 + 3 + 3 + 2 + 7 + % + 3)
.
*oa( (istance scores ai% Sour#e !oint 1 2 3 4 % 6 7 M
Roun" $rips per a* (l ) 6 3 3 3 2 7 % 3
xyoor" 2, 8 6, 1 8, % 13, 3 1%, 10 6, 14 18, 1 10, 3
Loa"-"istan#e to @ (19? 3) 68 ; % ? 78 34 ; 2 ? 18 32 ; 2 ? 12 33 ; 0 ? 2% ; 7 ? 24 74 ; 11 ? 10% %8 ; 2 ? %0 30 ; 0 ? 0 $ota% ; 27.
Loa"-"istan#e to A@ (+7? .+,) 66. ; 1.% ? %0.4 32. ; %.% ? 2%.2 30. ; 1.% ? 7.2 34.1 ; 3.% ? 22.8 26.1 ; 3.% ? 1.2 72. ; 7.% ? 72.8 %.1 ; %.% ? 73.0 31.1 ; 3.% ? 13.8 $ota% ; 24+4
Ch12 1. *oc5woo( n('stries irst we ran5 the !Q@s )rom top to ottom on the asis o) their (o$$ar 'sage. >hen we partition them into c$asses. >he ana$"sis was (one 'sing OM EIp$orer >'tor12.1W#FC #na$"sis. Cumulative Cumulative % % SKU Descripti Qty Value Dollar !ct of of Dollar of SKUsClass # on Used/Year Usae "otal Value
# ! & " % $ 1 Total
##,000 !0,000 '00 1"0,000 $&0 "00 100 1,"00
1.00 0.$0 #.&0 0.0$ 0.'0 1.&0 0.#& 0.01
##,000 "1,000 #,0&0 $,00 $1& $00 #& 1" !$,$""
.
0.0 "%. &.& #.' 0.# 0.# 0.1 0.0
0.0 %%.! '#." ''.1 ''.& ''.' 100.0 100.0
1".& "&.0 $!.& &0.0 ".& !&.0 %!.& 100.0
B B C C C C
SBs >he (o$$ar 'sage percentages (ont eIact$" match the pre(ictions o) #FC ana$"sis. or eIamp$e, C$ass # !Q@s acco'nt )or 88.7< o) the tota$, rather than 80<. Donethe$ess, the important )in(ing is that #FC ana$"sis (i( )in( the Xsigni)icant )ew. or the items samp$e(, partic'$ar$" c$ose contro$ is nee(e( )or !Q@s 4 an( 7. 7. !ams Cat Bote$ a. Economic or(er 'antit" d ? 0wee5 D " 0 agswee5%2 wee5s"r ? 4,680 S ? :%4 Price ? :11.70 # " 27<:11.70 ? :3.16
E*Q =
2 DS
=
24,680:%4
# :3.16 >ime etween or(ers, in wee5s
Q D .
=
400 4680
=
1%,4.37 ? 3.3, or 400 ags.
= 0.08%47 "ears = 4.44 wee5s
/eor(er point, / R ? (eman( ('ring protection intera$ ; sa)et" stoc5 +eman( ('ring protection intera$ ? d L ? 0 S 3 ? 270 ags !a)et" stoc5 ? z σdLT Ahen the (esire( c"c$e-serice $ee$ is 80<, z = 084 . . σ dLT
= σ d
L ? 1%
3
? 2%.8 or 26
!a)et" stoc5 ? 0.84 S 26 ? 21.82, or 22 ags
R = 270 + 22 = 22 c.
(.
nitia$ inentor" position ? OB ; !/ G FO ? 320 ; 0 G 0 320 G 10 ? 310. Feca'se inentor" position remains aoe 22, it is not "et time to p$ace an or(er. #nn'a$ ho$(ing cost #nn'a$ or(ering cost
%00 Q (27< )(:11.70) # = 2
D Q
2 = :78.7%
S =
4,680 %00
:%4
= :%0%.44
.
.
Ahen the EO& is 'se( these two costs are e'a$. Ahen Q = %00 , the ann'a$ ho$(ing cost is $arger than the or(ering cost, there)ore Q is too $arge. >ota$ costs are :78.7% ; :%0%.44 ? :1,2%.1. # Q s"stem a$so 5nown as a reor(er point s"stem d ? 300 pintswee5 ? 1% pints !tan(ar( (eiation o) (eman( ('ring the protection intera$9 σ dLT = σ d L ? 1% ? 4% pints σ d
a. .
#erage (eman( ('ring the protection intera$9 +eman( ('ring protection intera$ ? d L ? 300 S ? 2700 pints c. /eor(er point R ? aerage (eman( ('ring protection intera$ ; sa)et" stoc5 !a)et" stoc5 ? z σdLT Ahen the (esire( c"c$e-serice $ee$ is <, z ? 2.33. !a)et" stoc5 ? 2.33 S 4% ? 104.8% or 10% pints R ? 2,700 ; 10% G 0 ? 2,80% pints a. #nn'a$ ho$(ing cost #nn'a$ or(ering cost
Q
2
D
400 (27<)(:11.70) 2 = :631.80
# =
Q
S =
4,680 :%4 400
= :631.80
>ota$ cost 'sing EO& is :1,263.60, which is :31.% $ess than when the or(er 'antit" is %00 ags. 10. PetromaI Enterprises a. .
E*Q =
2 DS #
2
= 1,323 'nits
c. Or(er 'antit"
3
? 277.13 or 277 'nits
? aerage $ea( time (eman( ; sa)et " stoc5 ? 3%0,000%0 ; 277 ? 3,277 'nits
Dationwi(e #'to Parts a. Protection intera$ P #erage (eman( ('ring P !tan(ar( (eiation ('ring P
. Ta!%et in)ento!y
14.
2 ( %0, 000) ( 3%)
!a)et" stoc5 ? z σ( *> ? z σ d L ? 1.2812% /eor(er point
13.
=
? + ; L ? 6 ;3 ? wee5s ? 100 ? 00 'nits ? • 20 ? 60 'nits " d ,+-L. - z σ +-L ? 00 - 1.660 ? 1,018 ? >arget inentor" G P ? 1,018 G 3%0 ? 668 'nits pres'ming no !/ or FO
# + s"stem a$so 5nown as a perio(ic reiew s"stem. in( c"c$e-serice $ee$, gien9 L ? 2 wee5s + ? 1 wee5 d + - L " 218 oIes σ + + L " 40 oIes
T ? 300 oIes T ? #erage (eman( ('ring protection intera$ ; !a)et" stoc5 T ? 218 ; z 40 ? 300 oIes z ? 300 G 21840 ? 2.0% Ahen z ? 2.0% / c"c$e-serice $ee$ is 7.8 or 8<.
.
Ch13 2.
+a$worth Compan" a. >hree-month simp$e moing aerage onth
#tua% Sa%es ($housan"s)
$hree-onth Simp%e oin: era:e ore#ast
bso%ute 0rror
bso%ute < 0rror
SCuare" 0rror
an. 20 e. 24 Mar. 27 #pr. 31 Ma" 37 24;27;313 ? 27.33 .67 26.14 3.%1 'ne 47 27;31;373 ? 31.67 1%.33 32.62 23%.01 '$" %3 31;37;473 ? 38.33 14.67 27.68 21%.21 #'g. 62 37;47;%33 ? 4%.67 16.33 26.34 266.67 !ept. %4 47;%3;623 ? %4.00 0.00 0.00 0.00 Oct. 36 %3;62;%43 ? %6.33 20.33 %6.47 413.31 Do. 32 62;%4;363 ? %0.67 18.67 %8.34 348.%7 +ec. 2 %4;36;323 ? 40.67 11.67 40.24 136.1 >ota$ 106.67 267.83 1,708.47 #erage 13.33 33.48 213.%6 !'ch res'$ts a$so can e otaine( )rom t he Time Se!ies Fo!ecastin% So$)e! o) OM EIp$orer9
.
.
o'r-month simp$e moing aerage
onth
#tua% Sa%es ($housan"s)
our-onth Simp%e oin: era:e ore#ast
bso%ute 0rror
bso%ute < 0rror
an. 20 e. 24 Mar. 27 #pr. 31 Ma" 37 20;24;27;314 ? 2%.% 11.%0 31.08 'ne 47 24;27;31;374 ? 2.7% 17.2% 36.70 '$" %3 27;31;37;474 ? 3%.% 17.%0 33.02 #'g. 62 31;37;47;%34 ? 42.00 20.00 32.26 !ept. %4 37;47;%3;624 ? 4.7% 4.2% 7.87 Oct. 36 47;%3;62;%44 ? %4.00 18.00 %0.00 Do. 32 %3;62;%4;364 ? %1.2% 1.2% 60.16 +ec. 2 62;%4;36;324 ? 46.00 17.00 %8.62 >ota$ 124.7% 30.71 #erage 1%.% 38.71 !imi$ar$", 'sing Time Se!ies Fo!ecastin% So$)e! o) OM EIp$orer, we get9
c.−e. Comparison o) per)ormance >uestion
c. (. e.
easure
M#+ M#PE M!E
3-onth S 13.33 33.48 213.%6
4-onth S 1%.% 38.71 267.21
.
Re#ommen"ation
3-month !M# 3-month !M# 3-month !M#
SCuare" 0rror
132.2% 27.%6 306.2% 400.00 18.06 324.00 370.%6 28.00 2,137.68 267.21
4. +a$worth Compan" contin'e( c. >hree-month weighte( moing aerage weights o) 36, 26, an( 16 onth #tua% Sa%es $hree-onth Wei:hte" bso%ute bso%ute SCuare" (999s) oin: era:e ore#ast 0rror 0rror 0rror an. 20 e. 24 Mar. 27 #pr. 31 K3 × 27;2 × 24;$ × 20L6 ? 24.83 6.17 1.0 38.07 Ma" 37 K3 × 31;2 × 27;$ × 24L6 ? 28.%0 8.%0 22.7 72.2% 'ne 47 K3 × 37;2 × 31;$ × 27L6 ? 33.33 13.67 2.0 186.87 '$" %3 K3 × 47;2 × 37;$ × 31L6 ? 41.00 12.00 22.64 144.00 #'g. 62 K3 × %3;2 × 47;$ × 37L6 ? 48.33 13.67 22.0% 186.87 !ept. %4 K3 × 62;2 × %3;$ × 47L6 ? %6.%0 2.%0 4.63 6.2% Oct. 36 K3 × %4;2 × 62;$ × %3L6 ? %6.%0 20.%0 %6.4 420.2% Do. 32 K3 × 36;2 × %4;$ × 62L6 ? 46.33 14.33 44.78 20%.3% +ec. 2 K3 × 32;2 × 36;$ × %4L6 ? 37.00 8.00 27.% 64.00 >ota$ .34 2%0.% 1,323.1 #erage 11.04 27.84 147.0 >he res'$ts )rom Time Se!ies Fo!ecastin% So$)e! o) OM EIp$orer gie the same res'$ts9
.
(.
EIponentia$ smoothing α ? 0.6
onth
Dt
(t ) an. e. Mar. #pr. Ma" 'ne '$" #'g. !ept. Oct. Do. +ec. >ota$ #erage
(mi%%ions) 20 24 27 31 37 47 %3 62 %4 36 32 2
F t+1 = F t + ( Dt F t ) bso%ute bso%ute (ore#ast for Ne6t onth) 0rror < 0rror 22.00 20.80 20.80 22.72 22.72 2%.2 2%.2 28.72 %.71 18.41 28.72 33.6 8.28 22.38 33.6 41.67 13.31 28.32 41.67 48.47 11.33 21.38 48.47 %6.% 13.%3 21.82 %6.% %%.04 2.% 4.80 %%.04 43.62 1.04 %2.88 43.62 36.64 11.61 36.28 36.64 32.06 7.6% 26.38 3.0% 232.6% 10.34 2%.8% F t
SCuare" 0rror
32.60 68.%6 177.16 128.37 183.06 6.71 362.%2 134.7 %8.%2 1,1%2.2 128.03
c.−e. Comparison o) per)ormance >uestion
c. (. e. %.
easure
M#+ M#PE M!E
3-onth W 11.04 27.84 147.0
06ponentia% Smoothin: 10.34 2%.8% 128.03
Re#ommen"ation
EIponentia$ smoothing EIponentia$ smoothing EIponentia$ smoothing
Conenience !tore
= 0.2 Dt + 0.8 At −1 + T t −1 T t = 0 .1 A)e!a%e t&is pe!iod − A)e!a%e $ast pe!iod + 0 .T!end $ast pe!iod F t +1 = At + T t At
a*
AMa" = 0.2 ( 760 ) + 0.8 ( 700 + %0) = 7%2 T Ma" = 0.1( 7%2 − 7%0) + 0. ( %0) = %0.2
orecast )or 'ne = 7%2 + %0.2 = 802.2 or 802 Dune
A'ne
= 0.2 ( 800 ) + 0.8 ( 7%2 + %0.2 ) = 801.76 or 802
= 0.1( 801.76 − 7%2 ) + 0. ( %0.2) = %0.16 or %0 orecast )or '$" = 801.76 + %0.16 = 8%1.2 or 8%2
T 'ne Du%*
A'$"
= 0.2 ( 820) + 0.8( 801.76 + %0.16) = 84%.%4 or 846
= 0.1( 84%.%4 − 801.76) + 0.( %0.16) = 4.%2 orecast )or #'g'st = 84%.%4 + 4.%2 = 8%.06 or 8%
T '$"
11. !n"(ers =ar(en Center
>uarter
=ear 1
Seasona% a#tor
=ear 2
.
Seasona% a#tor
era:e Seasona% a#tor
1 2 3 4 >ota$ #erage
40 3%0 20 210 80 222.%0
0.17 1.%73 1.303 0.44
60 440 320 280 1,100 27%.00
0.218 1.600 1.164 1.018
0.1 1.%87 1.234 0.81
#erage 'arter$" sa$es in "ear 3 are eIpecte( to e 287.%0 1,1%04. @sing the aerage seasona$ )actors, the )orecasts )or "ear 3 are9 >uarter 1 2 3 4
0.1287.%0 1.%87287.%0 1.234287.%0 0.81287.%0
ore#ast %7 4%6 3%% 282
Aith the Seasona$ Fo!ecastin% So$)e! o) OM EIp$orer, we get the same res'$ts
13. =arcias =arage a. >he res'$ts, 'sing the Re%!ession Ana$ysis So$)e! o) OM EIp$orer, are9
.
>he regression e'ation is 0 ? 42.464 ; 2.4%2 1 orecasts 0 !ep ? 42.464 ; 2.4%2 ? 64.%32 or 6% 0 Oct ? 42.464 ; 2.4%2 10 ? 66.84 or 67 0 Do ? 42.464 ; 2.4%2 11 ? 71.888 or 72
Ch14 2. Fo Car$tons =o$) Camp a. >he $ee$ strateg"9 >he pea5 (eman( is 6,400 ho'rs in 'arter 2. #s each emp$o"ee can wor5 600 ho'rs per 'arter 480 on reg'$ar time an( 120 on oertime, the $ee$ wor5)orce that coers re'irements an( minimiJes 'n(ertime is 6,400600 ? 10.67 or 11 emp$o"ees.
.
ost /eg'$ar wages
Oertime wagesS Bire costs
a%#u%ation :7200 per 'arter118 'arters 1,120 hr in 'arter 2:20 per hr
mount :633,600 22,400
60 hr in 'arter 6:20 per hr :10,000 per hire3 hires >O>#*
1,200 30,000 :70%,200
S >he 11 wor5ers can pro('ce 11 480 ? %,280 ho'rs o) reg'$ar time in an" 'arter. >he 6,400-ho'r re'irement in 'arter 2 eIcee(s this amo'nt " 1,120 ho'rs. >he 6,240-ho'r re'irement in 'arter 6 eIcee(s this amo'nt " 60 ho'rs. >he tota$ 'n(ertime ho'rs can e ca$c'$ate( as9 &'arter 1 11480 G 4,200 &'arter 3 11480 G 3,000 &'arter 4 11480 G 4,800 &'arter % 11480 G 4,400 &'arter 7 11480 G 3,600 &'arter 8 11480 G 4,800 .
>he chase strateg"9 >uarter 1 2 3 4 % 6 7 8
eman" (hr) 4,200 6,400 3,000 4,800 4,400 6,240 3,600 4,800 >O>#*
ost /eg'$ar wages Bire costs *a"o)) costs
c.
1,080 ho'rs 2,280 480 880 1,680 480 6,880 ho'rs
Workfor#e 14 7 10 10 13 8 10 81
Eires 1 %
La*offs
7 3 3 % 0 12
2 14
a%#u%ation :7,200 per 'arter81 :10,000 per hire14 hires :4,000 per $a"o))12 $a"o))s >O>#*
mount :%83,200 140,000 48,000 :771,200
Propose( p$an9 >his p$an egins with j'st wor5ers )or &'arter 1, as with the chase strateg". Boweer, it increases temporari$" the wor5)orce to 11 emp$o"ees in &'arters 2 an( 6, ma5ing 'p the short)a$$ with oertime. >uarter 1 2 3 4 % 6 7 8
eman" (hr) 4,200 6,400 3,000 4,800 4,400 6,240 3,600 4,800 >O>#*
ost /eg'$ar wages Bire costs
Workfor#e 11 11 76
Eires 1 2
La*offs
Oertime (hr)
1,120 2 480 80 60
2 0 %
a%#u%ation :7,200 per 'arter76 :10,000 per hire% hires
.
2 0 4
480 3,120 mount :%47,200 %0,000
*a"o)) costs Oertime
:4,000 per $a"o))4 $a"o))s :20 per ho'r3,120 ho'rs >O>#*
16,000 62,400 :67%,600
>his p$an is more $i5e the $ee$ strateg", eIcept that on$" emp$o"ees are on the wor5)orce each 'arter, with another 2 hire( temporari$" in &'arters 2 an( 6. t a$so 'ses more oertime than with the $ee$ strateg". 3. Fo Car$tons =o$) Camp with part-time instr'ctors a. One o) man" p$ans that ta5e a(antage o) )$eIii$it" proi(e( " part-time instr'ctors, this p$an re('ces hiring an( $a"o))s o) certi)ie( instr'ctors, re('ces oertime, an( re('ces tota$ costs. eman" ertifie" ert ert !$ !$ !$ Oertime >tr (hr) Workfor#e Eires La*offs Work Eours Eires La*offs (hr) 1 4,200 1 2 6,400 10 1 720 3 880 3 3,000 8 2 3 4 4,800 8 720 3 240 % 4,400 8 %60 6 6,240 10 2 720 720 7 3,600 8 2 3 8 4,800 8 720 3 240 >O>#* 6 4 4 3,440 6 2,080 ost /eg'$ar wages Cert. hire costs Cert. $a"o)) costs P>. hire costs P>. $aor costs Oertime
a%#u%ation :7,200 per 'arter6 :10,000 per hire4 hires :4,000 per hire4 $a"o))s :2,000 per hire hires :12hr 3,440 hrs :20 per ho'r2,080 ho'rs >O>#*
11. Michae$s +istri'tion Center a* Requirement s
M 6
> 3
A %
>h 3
mount :46,800 40,000 16,000 18,000 41,280 41,600 :6%3,680
7
! 2
$
W
$h
S
Su
0mp%o*ee
6
3
%
3
7
2
3
1
%
2
4
2
6
2
3
2
4
1
3
1
%
2
3
3
3
1
3
0
4
1
2
4
2
0
2
0
3
1
2
%
1
0
2
0
2
0
1
6
0
0
1
0
1
0
1
7
.
!' 3
>he n'mer o) emp$o"ees is 7. >he" are sche('$e( to ta5e the oIe( (a"s o)). 16. Bic5or" Compan" a. !che('$es )or two r'$es C! r'$e9 ustomer SeCuen#e
Er Sin#e Or"er rrie"
Start $ime (hr)
a#hine $ime (hr)
inish $ime (hr)
ue ate (hr)
!ast ue (hr)
%oF $ime (hr)
1
6
0
;
10
?
10
12
9
1.
2
%
10
;
3
?
13
8
,
1
3
3
13
;
1%
?
28
18
19
31
4
1
28
;
?
37
20
18
3
%
0
37
;
7
?
44
21
23
44
16 + 18 + 31 + 38 + 44 ? 2.4 ho'rs %
#erage )$ow time ?
#erage ho'rs past ('e ?
0 + % + 10 + 17 + 23 ? 11.0 ho'rs %
E++ r'$e9 ustomer SeCuen#e
Er Sin#e Or"er rrie"
Start $ime (hr)
a#hine $ime (hr)
ue ate (hr)
Er !ast ate
%oF $ime (hr)
2
%
0
;
3
?
3
8
9
1
6
3
;
10
?
13
12
1
17
3
3
13
;
1%
?
28
18
19
31
4
1
28
;
?
37
20
18
3
%
0
37
;
7
?
44
21
23
44
#erage )$ow time ? #erage ho'rs past ('e ? .
inish $ime (hr)
8 + 1 + 31 + 38 + 44 ? 28.0 ho'rs % 0 + 1 + 10 + 17 + 23 ? 10.2 ho'rs %
>he E++ r'$e is etter than C! on oth aerage )$ow time 28.0 s. 2.4 an( aerage ho'rs past ('e 10.2 s. 11.0. t gies the etter sche('$e, a$tho'gh this is not a$wa"s tr'e.
Ch1%. 1.
Fi$$ o) materia$s, ig. 1%.24 a. tem has on$" one parent E. Boweer, item E has two parents F an( C. . tem # has 10 'ni'e components F, C, +, E, , =, B, , , an( Q. c. tem # has )ie p'rchase( items , , =, B, an( Q. >hese are the items witho't components. (. tem # has )ie interme(iate items F, C, +, E, an( . >hese items hae oth parents an( components. e. >he $ongest path is GEGCG# at 11 wee5s. 4. >he i$$ o) materia$s )or item # with $ea( times is shown )o$$owing. a. *ea( time is (etermine( " the $ongest path =-E-F-# ? 12 wee5s. . ) p'rchase( items +, , =, an( B are a$rea(" in inentor", the $ea( time is re('ce( to9 #GFGE ? 8 wee5s.
.
c.
tem = is the p'rchase( item with the $ongest $ea( time in the $ongest path. >his p'rchase( item co'$( e 5ept in stoc5 to re('ce the oera$$ $ea( time.
# *> ? 1 F1
C1
*> ? 2 +1
%.
*> ? 2
E1
1
*> ? 6
*> ? %
=1
B1
*> ? 4 /e)er to ig're 1%.1 an( !o$e( Pro$em 1.
*> ? 6
B1 *> ? 3
*> ? 3
FIGURE 15.19
# *> ? 1 F3
C1
*> ? 2 +1 *> ? 3
E2
*> ? 3 1
*> ? 6
+1
*> ? 1
*> ? 3
=1 *> ? 3 Materia$ re'irement to pro('ce % 'nits o) en(-item #9
( % A × 3B per A) = 1% B − 2 B on han( = 13 B ( % A ×1C per A) = %C Materia$ re'irement to pro('ce 13 B9
( 13 B ×1D per B ) = 13 D ( 13 B × 2 E per B ) = 2. E Materia$ re'irement to pro('ce % C 9
( %C ×1D per C ) = , D han( = 4 F ( %C ×1F per C ) = % F − 1F on Materia$ re'irement to pro('ce 4 F 9
( 4 F × 1( per F ) = 4G G 3G on han" ; 1 G P'rchase( materia$ re'irements net o) on-han( inentor"9
.
13 + % = 18 D , 26 E , an( 1(.
6. MP! recor( in ig. 1%.26. >he )o$$owing ta$e is )rom the Master Pro('ction !che('$ing !o$er in OM EIp$orer. >he #>P row is not re'ire( )or this pro$em.
Solver aster !roduction Sc$edulin
Enter data in yellow shaded areas. ot 2i3e ead Time
0 1
4uantity on 5and
$& 1
"
$
#
&
!
%
6orecast
"0 1% "% "% "$ $0 $$
%$Customer 7rders (Boo8ed)
1& 1!
' 1#
9ro:ected 7n+5and ;n-entory 1& &! "' <92 4uantity 0
-ailale+to+9romise ;n(T9)
"0 "0
7-erride 6ormulas
% $& &!
0
0 0
0
10 11 1" 1$ 1# 1&
!
1
%$0
<92 start
'
'
0 0 &1
&$ 0
=estore 6ormulas
14. nentor" recor(. >he ta$es )o$$owing were generate( wit h the !ing$e-tem M/P so$er )rom OM EIp$orer. a. iIe( or(er 'antit" ? 110
.
*4*
.
.
