Pizza Pazza Case 1. What is the minimum time to fll a rush rush order, assuming assuming that all steps o the the process are started only ater the order is received? Without spending money, how can you reduce this response time? The minimum time to to fll an order order o 2 pizzas pizzas is: 2 + 3 + 2 + 1 + 15 + 3 + 2 + 2 =30
inutes.
Ways to reduce !ow time include: a" #ac$ueline can process process the payment while while the pizzas pizzas are are %a&ing, which can save 2 minutes. %" #ean and #ac$ueline #ac$ueline can can 'rep 'rep sauce and and dough at the same time, saving 2 minutes. c" #ean and #ac$ueline #ac$ueline can can put the the pizzas in the pan pan together %eore to save 1 minute. d" #ean can also also help #ac$ueline #ac$ueline load the pizzas pizzas into the %o( %o(es, es, which will will save 1 minute. The process process time or a single order order could %e shaved down to to 2) minutes. 2. What is the ma(imum num%er o orders orders that the ta&e*out ta&e*out acility can fll per hour in steady state? +ssume that there are sucient pizza pans to ensure that no order has to wait or pans to %ecome availa%le. -ow does your answer change i the cooling time is increased rom to / minutes?
0esourc e
nit oad
0esource 3apacity Total Total
0esource
3apacity
tilizatio n7
4time5ord er"
nit 3apacity 4orders5hou r"
#ean
28829
;<5 9 =.;
1
=.;
./5=.; 9 )>
#ac$ueli ne
182829 /
;<5/ 9 12
1
12
./512 9 1>
181/
;<51; 9 ./
1
./
ven
6 o units
'rocess
./ order5hr ./ pizza5hr
1<<>
While the frst order ta&es thirty minutes, the second ta&es thirty plus seven 4prep time delay" plus the %a&ing delay o nine minutes or a fnish time at the orty*si(th
minute. The third order will have a prep time delay o seven minutes plus the si(teen minute %a&e time o the second order plus two minutes o @dead timeA ater prepping the second and third orders, and waiting or the frst to fnish 41; minutes B 472" 9 2" to fnish at minute seventy*one. Thereore, in a single hour, only two orders can %e ulflled. +n increase in cooling time doesnCt aDect the %ottlenec& 4%a&ing time", which is what adds the most to the process time. +n increase in cooling time will merely increase the fnish o the frst order rom the oth minute to the 2 nd minute, and the fnish o the second order rom the ); th minute to the )= th minute. . +ssume that there is one order waiting to %e processed, #ean is Eust a%out to start mi(ing the sauce or a second order and #ac$ueline is Eust a%out to start loading the two pizza pans o a third order into the oven. + customer calls in with a new order or two pizzas and wants to &now when she can pic& up her order. What due-date time should #ean promise assuming that they process all orders in the se$uence received? #ac$uelineCs 1 st order 9 1; minutes or loading and %a&e. Within these 1; mins, #eanCs second order would %e waiting to %e loaded. Then, 1; minutes or the 2 nd order to %a&e. While the second order is %a&ing, frst order will %e %illed and #ean would have processed the third order, which will %e waiting again to %e loaded. Then, 1; minutes or rd order. Fimilarly, the 1; minutes or the new order and then adding cooling, unloading, pac&ing, and %illing time. 16 + 16 + 16 + 16 + 3 + 2 + 2 =71minutes
). G #ac$ueline calls in sic&, what is the ma(imum num%er o orders that can %e flled per hour? G #ac$ueline is sic&, #ean would %e in charge o every tas&. -e canCt cycle through preparation wor& every seven minutes and has to complete the entire process 4all thirty minutes" %eore starting another order. Hecause the oven is still the %ottlenec&, this change merely increases the wait time rom one order to the ne(t rom nine minutes to thirty minutes B so instead o completing the second order at the orty* si(th minute, the second order will %e completed at minute si(ty.
0esour ce
nit oad 4time5order"
#ean ven
0esource 3apacity nit 3apacity 4orders5ho ur"
6 o units
Total
28828182 ;<512 9 / 8912
1
/
181/
1
./
;<51; 9 ./
'rocess
0esource
3apacity
tilization 7
./order5 hr ./
pizza5hr
/. +ssume #ean and #ac$ueline decide to hire two employees to perorm their respective tas&sI each paid J= per hour. What is the contri%ution margin 4revenue * varia%le costs" generated per hour o operation o the process i pizzas sell or J/ each? What is the minimum amount that #ean can charge per pizza, and still ma&e a proft? Kach employee costs J= per person totaling J1;.<< per hour. They sell ) pizzas an hour, J/.<< per pizza, J1.2< ingredients5pizza, J<.2< cents5%o(, which totals J1.)< or each pizza 7 )9 J/.;<. Total costs e$uals J21.;< Kuros per hour. Gn order to ma&e a proft, the minimum amount they can sell each pizza or J/.)1. To %rea& even, J/.)<. ;. What is the minimum num%er o pizza pans needed to ensure that no order has to wait or a pan? We need to have enough pans to supply pans or 21 minutes until the other pans ree up. G it ta&es them / minutes %eore they put the ingredients on the pan, minimum / sets o pans 9 1< total pans are needed. Gt ta&es 21 minutes rom when the pan is frst used to it %eing done with the cooling process and ready to go %ac& to the start where #ean puts the dough in the pan 8 spread the sauce. . The pizzas have %ecome wildly popular and #ean eels that they can easily sell thirty pizzas per hour. To increase capacity, he is thin&ing o renting additional industrial ovens, which would cost J1< or each hour that an oven is used. Fhould #ean rent more ovens, assuming the rest o the process is &ept as is? -ow many? What would %e the contri%ution margin rom each hour o operation o the process 4assume the employees do all the wor&"? +ssuming no change to the process, the prep time or each order is seven minutes. This means that the ma( num%er o orders that can %e prepared while the frst order is in the oven is two. This means that the ma( num%er o ovens that would still %e ecient is three. -owever, %uying and using two additional ovens gives a contri%ution margin o J<. The ma( num%er o orders with three ovens that can %e ulflled in an hour is fve, %ecause the frst order will %e completed at the < th minute, the second at the th minute, and the third at the )) th minuteI si(teen minutes remain, meaning that only two more orders can %e produced 41;5". +t fve orders, the revenue is J/<, with rental costs o J2<, varia%le costs o J2.=< per order 4J1.)< per pizza", and employee costs o J1; per hour 4assuming #ean and #ac$ueline are paid at the same rate as employees mentioned earlier". This gives a proft o J<. 4Fee, e.g., K(hi%it .1" Let, with two ovens, the ma( num%er o orders that can %e processed is our. The frst two orders can %e processed simultaneously with a seven minute delay. The
frst order ta&es si(teen minutes to %a&e, %y which point the third order has %een prepared or two minutes 472 9 1)I 1; B 1) 9 2". +gain, there is another two minute delay %etween the second order and the ourth order, with two rounds o preparation at seven minutes each and a %a&e time o si(teen minutes. The ourth order is completed at // minutes 41 st B <, 2nd B , rd B )) 8 2 9 );, ) th B /1 8 2 9 /". With a two*oven set up, the cost %ecomes J1< 4oven rent" 8 J1; 8 4J2.=<7)" 9 J.2<, and the total proft is J)< 4revenue: J1<7)" B J.2<, which is J2.=<. 4Fee, e.g., K(hi%it .2" Fince ma(imizing proft over product is more desira%le to %uy one additional oven with some ineciency 4two minutes wait time %etween orders one and three and orders two and our" rather than to purchase two ovens with %etter, more ecient production at a steeper cost. =. 3an #ean do %etter, relative to $uestion , %y restructuring the process? Mor e(ample, can he increase profts %y reallocating tas&s %etween the employees? 4+ssume all orders are or two pizzas." What is the contri%ution margin generated per hour as a result o the changes? What is the minimum amount that #ean can charge per pizza, and still ma&e a proft? With a new process cutting the total time down to twenty*fve minutes and with the addition o another employee, the time to prepare an order %eore it is loaded into an oven is cut down to our minutes %etween #ean and #ac$ueline. Thereore, the amount o ovens that need to %e used to ma( the product is 1; minutes %a&e time5) minutes prep 9 ). This allows #ean and #ac$ueline to produce eight orders an hour i they wor& on the prep %eore the pizzas go in the ovens and hire a third wor&er to do the wor& on the pizzas ater they e(it the ovens. Order Number 1st rder 2nd rder rd rder )th rder /th rder ;th rder th rder =th rder Nth rder
Completion Time 2/ mins 9 2/ mins 8 ) mins 9 2N mins 8 ) mins 9 mins 8 ) mins 9 mins 8 ) mins 9 )1 mins 8 ) mins 9 )/ mins 8 ) mins 9 )N mins 8 ) mins 9 / mins 8 ) mins
9 9 9 9 9 9 9 9
2N )1 )/ )N / /
mins mins mins mins mins mins mins mins
+t this level o production, our contri%ution per order is J.2< 49 J1< B J2.=<" 7 = 9 J;2.=<, su%tracting costs o J< 49 7J1<, oven rental" and J2) 4 9 7J=, la%or cost" gives an overall proft o J=.=<. The amount they can charge per pizza and still ma&e a proft is e$ual to the e(cess proft divided %y the num%er o pizzas that theyCre producing in an hour, which is J.;<51; 9 .J22/, su%tracted rom the current price o J/ per pizza, or a %rea&*even price o J)./. To ma&e minimum proft, they can charge J).=. 4Fee, e.g., K(hi%it =.1" N. ver time, 'izza 'azza has also started to accept orders or one pizza. Gn eDect, hal o all orders are or only one pizza and those have %een pushed through the
system as @emergency ordersA resulting in only one pizza in the oven. Fhould #ean consider a @rush chargeA or such orders? G hal o all orders are or a single pizza only, then the opportunity cost o %eing a%le to ulfll a complete order must %e considered. Mor e(ample, using the set up that was generated or pro%lem 6=, i hal o all orders are or a single pizza then output alls to 12 4=52 9 ) Oorders or one pizza onlyP71 9 ) Onum%er o pizzas @lostA B no longer produced %ecause the order comes in or a single pizzaPI 1; B ) 9 12". The cost o potentially ulflling other orders with the @lostA num%er o pizzas is ) pizzas52 pizzas per order 9 2 orders 7 J.2< contri%ution margin per order 9 J1).)<. Qividing this cost among the single pizzas reasona%ly e(pected to %e sold per hour gives you an additional J.;< per pizza. Thereore, single orders should cost the original J/ per pizza plus J.;<, or J=.;<. 1<. 0ealizing the importance o %atch economies, should #ean oDer a discount to encourage all orders to %e or three pizzas? G so, how much? G he starts producing three pizzas per process cycle instead o two pizzas, he will need more ovens and each third pizza will incur wait time %eore another pizza is produced at which point %oth may %e loaded into an oven. Kach third pizza will %e loaded into an oven every our minutes, meaning that an order or three pizzas will ta&e twenty*our minutes 4streamlined process or a single order o two pizzas" plus our minutes, or twenty*eight minutes to complete, assuming the process has %een streamlined according to the answer in 6=. G not, then completing an order will ta&e even more time: at seven minutes o prep wor& or each %atch o three and a total process time o thirty minutes, an order or three pizzas will %e completed every thirty*seven minutes. This will lead to an inventory %uild*up at the %ottlenec& point o the ovens, %ecause the ovens only have a capacity o two pizzas at a time. Kven with three ovens and a preparation time %eore entering the oven o our minutes, each additional pizza will have a delay time o our minutes. 0unning the calculation or inventory %uild*up using the streamlined process generated or pro%lem 6=, %y the end o an hour there will %e inventory %uild*up o nine pizzas. 41 letover pizza rom frst cycle plus 1 letover pizza rom each su%se$uent cycle producing %atches o 9 N cycles 7 1 letover per cycle 9 N pizzas". This translates to a cost o N52 or )./ orders 7 J.2< contri%ution per order 9 J2.)
11. +ssume that deep-dish pizzas sell or J./< and re$uire J1.N< worth o ingredients. Which o these two products should #ean push to customers that call in and are undecided?
0esourc e
nit oad
0esource 3apacity Total
0esource
3apacity
tilizatio n7
4time5ord er"
nit 3apacity 4orders5hou r"
#ean
28829
;<5 9 =.;
1
=.;
./5=.; 9 )>
#ac$ueli ne
182829 /
;<5/ 9 12
1
12
./512 9 1>
182N
;<5< 9 2
1
2
ven
6 o units
'rocess
2 orders5hr
1<<>
) pizzas5hr
Gn this scenario, %ecause the %a&e time is e(tended to thirty minutes and the prep time is increased to ten minutes, each order now ta&es thirty minutes plus ourteen plus three which is orty*seven minutes. nce #ean is fnished prepping one order, he can immediately move onto the ne(t, which gives a delay o ten minutes %etween orders in prep time. -owever, since %a&e time ta&es thirty minutes, the ne(t order has to wait twenty minutes %eore it can %e %a&ed, meaning that it wonCt %e fnished until minute si(ty*seven. Thereore, since only one pizza can %e completed per hour, the contri%ution margin per pizza is 1/ B ).2< 4O1.N< materials 8 .2< %o(esP 7 2" 9 1<.=<. Whereas with thin*crust pizza #ean can produce two orders an hour or a proft o J1< per order B J2.=< cost 4OJ1.2< materials 8 J.2< %o(esP 7 2" 9 J.2<72 orders 9 J1).)<. 12. What is the proft rate i orders or thin-crust and deep-dish are in a ratio o 4a" :1 4%" 1:1 4c" 1:? + ratio o :1 would give you a process time o 1 8 1< 8 1 minutes wait time 8 < minutes %a&e time 8 minute process time 9 1/ minutes. The total proft will %e J.2<7 4contri%ution margin or thin*crust" 8 J1<.=< 4contri%ution margin or deep*dish" 9 J2.)<51/ 9 J.2) per minute or J1).)< an hour 4the same as the proft rom two thin*crusts, which is the average production per hour".
+ ratio o 1:1 would give you a process time o < minutes 8 1< minutes prep time 8 1) minutes additional %a&e time 8 ; minute wait time 9 ;< minutes or a proft o J.2< 8 J1<.=< 9 J1= an hour. + ratio o 1: would give you a process time o < minutes 8 1< minutes prep frst deep dish 8 ; minutes wait 8 1) minutes additional %a&e time 8 1< minutes prep second deep dish 8 2; minute wait 4< 8 ; B 1<" 8 1< minutes prep third deep dish 8 ); minute wait 42; 8 < B 1<" 9 1/2 minutes total prep or a proft o J.2< 8 J1<.=<7 9 JN.;<51/2 9 J.2;1 per minute or J1/.; an hour.
K(hi%it .1 n i m ) , ( n i m 2 ,
l l e ! & c a P
n i m 1 , ( n i m , *
"
n i m * * ( n i m ) 3 n i s m n % e v 3 O ( n 3 i $ m t i 1 ' 3 s s e c o r n P i m d r a + 3 d ( n n a i t ! m : 1 * 2 % t i b i $ # "
"
) l l ) 4 i e l ! s e e u & t u q n c c i a e " a J ) P ) 4 : a s B t e & u n d i a o L ; n
"
: l l . 4 i e l ! s e e u & t u q n c c i a e " a J : P . : a 4 s B t e & u n d i a o L ; n
"
< l l . 4 i e l ! s e e u & t u q n c c i a e " a J < P . : a 4 s B t e & u n d a i o L ; n
i l e u q c a e n i J m 3 2 ( n i m )
l 1 l 4 i n e / s l ! e e u & t u q n c c i a e " a J 1 P / 4 : a s B t e & u n d i a o L ; n
1
" .
2 a 4 s B e & t u n d i a o L ; 1
1
2 3 4 n a a z z e z i z v i O P P
s s " e / c . 4 o r s P t n e a n u e J e n v i O e : r P
s s " e = c 2 4 o r s P n e t a n u e J e n v i O e : r P
s s " e 1 c 2 4 o r s P n e t a n e e u J n v i O e r : P
s s " e ) c 1 4 o r s P t n e a n e e u J v n O i e : r P
s s " e n : i c 4 o m r s e P t % n ( a n u e n J e n i v i m O 1 e r : P : s e 1 1 2 t u a a z z n n e i z z i v i M O P P
1
1
3 5 6 n a a z z e z i z v i O P P
1 7 8 n a a z z e z i z v i O P P
2 9 0 1 n a a z z e z i z v i O P P
K(hi%it .2 "
l 2 l ; e 4 ! s e & t u n c a i P
n i m + . ( n i m * ,
:
n i m 3 , ( n i m % *
"
n i m . * ( n i m + * n i m 3 ( n i m ) s 3 n e v i n O 2 m % $ t i 3 ' ( n s s i m e c 1 o 3 r P d r a n d i n a m t + ! : 3 2 ( n % i t i m b * i $ # 2 "
"
l l ; 4 e ) ! s e n i & t u l n e c u i a q P c a e " : J ; ) 4 a s B t e & u n d i a o L
"
l l : 4 e . s ! e & t u n c a i P
4 a s B t e & u n d a i o L ; 1
:
i l e u q c a e " . n J i
2 a 4 s B t e & u n d i a o L ; 1
1
s s " e c 1 2 o r 4 P s n e t a e n u e J n v i O e r : P
s s " e c ) 1 o r 4 P s n e t a e n u e J n v i O e r : P
s s " n e i c : 4 m o r s e % n P t ( a u e n e n J i i v n m O 1 e r : P : s e 1 1 2 t u n a a n e z z i z z i v i M O P P
; 1
2 3 4 n a a e z z z z i v i O P P
1 5 6 n a a e z z z z i v i O P P
1
4 ) e 9 m 3 i ( T n t i a i M W
s s " e c / . o r 4 P s n e t a e n u e ) J n v i 2 0 t 3 i O ( a e e m n : r i W T i M P
s s " e c = 2 o r 4 s P n e a n t e u e ) J n 3 v 2 i t e 2 i O ( a m n e : r i W T i M P
"
l < l n 4 i e . s l ! e e u & t u q c n c a e " a i J < P . 4 : a s B t e & u n d a i o L ; n
m 3 2 ( n i m )
n i l e u q c a e " N J .
n
i l l l . / 4 e e ! s u q e c & t a u J n c " a i e / P / : a 4 B s e & t u n d a i o L ;
2 7 8 n a a e z z z i z v i O P P
1 9 0 1 n a a z z e z i z v i O P P
K(hi%it =.1 n i m % , ( n i m * ,
r l e l k e r o ! W & c w e a N P
n i m 3 , ( n i m + ,
r l l e k e r o ! W & c w e a N P
n i m * ( n m . *
r e l l k e r o ! W & c w e a N P
n i m , * ( n i m 2 *
r l l e k e r o ! W & c w e a N P
n i m 1 * ( n i m ) 3 n i r m e % 3 r o ( n i l m a n * o i t 3 i d d i n d m n a 3 s 3 n ( e n v i O m * + 0 3 ' s s e n c i o r m P t n 2 e ( i c i n / m " : . 1 2 ) t i b i i n $ # m r e l l " e , k r o ! 2 & ( W n i c e a m w 1 N P 2
r e l k e r o ! W & c w e a N P r e l l k e r o ! W & c w e a N P r l e l k e r o ! W & c w e a N P r l l e k e r o ! W & w c a e N P " / 2 4 s e t u n i
/
e
n a i l B e u & q c a a d J o L n i e m n a i l + B e 2 ( u q & d c n i a a J o m . L
L
; 1
; 1
s " n s i n l ) i c 4 e e o m u r s q P e c , t a n ( J u n n & e i v i m n O e ) 1 a r e P J : s e 1 1 2 t n z a u a z e n z i z i v i M O ' '
s n s i e l c e o u r q P c a n J e v & O n e a r e P J s n s i e l c e u o r q P c a n J e v & O n a e r e P J
s n s i e l e c o u r q P c a n J e v & O n a e r e P J " = 4 s e t u n i )
2 . ) n a z z z e a z v i ' ' O i
; 1
" 2 1 4 s e t u n i
)
3 / ; n a a z z e z i z v i O ' '
" ; 1 4 s e t u n i
)
* : = n z a z e a z i z v ' ' O i
e
L
" < 2 4 s e t u n i
)
1 N < 1 n a z a z e z i z v i O ' '
" ) 2 4 s e t u n i )
2 2 1 1 1 n z a z e a z z v i ' ' O i
" 2 / 4 s e t u n i ; 1
s n s i e l c e u o r q P c a n J e v & O n e a r e P J
" : . 4 s e t u n i )
" = ) 4 s e t u n i ; 1
" ) ) 4 s e t u n i
; 1
s n s i e l c e u o r q P c a n J e v & O n a e r e P J s n s i e l c e o u r q P c a J n e v & O n a e r e J P
s n s i e l c e o u r q P c n a J e v & O n a r e e J P
/
" < ) 4 s e t u n i ; 1
" ; . 4 s e t u n i ; 1
" 2 . 4 s e t u n i
" = 2 4 s e t u n i ; 1
" ) 2 4 s e t u n i
" < 2 4 s e t u n i
s n s i l e c e o u q P c r a J n e v & O n a r e e J P
/
e
e
/
e n a i l B e u & q c a a d J o L
n a i l e B u & q c a a d J o
n a i l B e u & q c d a a J o L
e n a i l B e u & q c a a d J o L
n a i l B e u q & c a a d J o L
e
n a i l e B u & q c a a d J o e n a i l e B u & q c a a d J o L
/
" : . 4 s e t u n i
" . . 4 s e t u n i
" N 2 4 s e t u n i /
" 1 ) 4 s e t u n i
" . / 4 s e t u n i /
" N ) 4 s e t u n i
" / ) 4 s e t u n i /
" = 2 4 s e t u n i
)
. ) 3 1 1 n z a a z e z i z v i O ' '
" : / 4 s e t u n i /
" 2 . 4 s e t u n i
)
; * / 1 1 n a a z z e z v z i ' ' O i
= 1 : 1 1 n a a z z e z z v i i O ' '
