Inventory Control Models
Content
Inventory Control Models
CHAPTER 6
TRUE/FALSE 6.1
Inv Invent entory ory is such such an expen expensiv sivee asset asset that that it may account account for as as much much aass 40 perce percent nt of a firm's firm's invested capital. ANSW!" #!$
6.%
It is impo imposs ssi& i&le le to have have la&or la&or stored stored in inve invent ntory ory.. ANSW!" A(S
6.)
#he o& o&*ec *ectiv tivee of inven inventor tory y con control trol is is to mi minim nimi+e i+e cust custom omer er dissati dissatisfact sfaction ion due due to inv invent entory ory ccont ontrol rol outa,es- called stocouts. ANSW!" A(S
6.4
Whi While le most most lar,e lar,e or,a or,ani+ ni+atio ations ns do don't n't need need invent inventory ory plann plannin, in, and contro controll- it is nearly nearly es essen sentia tiall for manufacturin, firms. ANSW!" A(S
6./
e ene neral rally ly-- ssupp upply ly and and d dem eman and d il illl &e cons constan tantt for for a prod product uct.. ANSW!" A(S
6.6
Inv Invent entory ory control control may &e consi consider dered ed a commo common n thread thread that ties ties all all of of the functio functions ns and and departm department entss of an or,ani+ation to,ether. ANSW!" #!$
6.2
3e 3elet lettt acard acard develo developed ped an inv invent entory ory mode modell &ased on dif differ ferent ent marets. marets. ANSW!" #!$
6.5
6.
In th thee decou decoupli plin, n, fun functio ctionn- som somee inven inventor tory y ma may y &e stored stored &etee &eteen n eeach ach produ productio ction n process process to to act as a &uffer. ANSW!" #!$ co conom nomic ic order order 7u 7uanti antity ty 89:; 89:; analys analysis is has recentl recently y &eco &ecome me practical practical as as a conse7 conse7uen uence ce of hi,h hi,h<< speed computers. ANSW!" A(S
6.10
When a firm receive receivess its inventory inventory over a period of timetime- a model model is neede needed d that that doe doess not not re7uire re7uire the instantaneous receipt assumption. ANSW!" #!$
1)
Inventory Control Models Models
6.11 6.1 1
CHAPTER 6
In the the &asi &asicc 9: 9: model odel-- iiff the the =0 is dou&led- the resultant 9: is dou&led. ANSW!" A(S
6.1% 6.1 %
#he reord reorder er poi point nt occ occurs urs duri durin, n, a sto stoc cou outt situa situatio tion. n. ANSW!" A(S
6.1)
Safety stoc stoc is i,nore i,nored d hen hen ccom omputi putin, n, the reorder reorder point. point. ANSW!" A(S
6.14
A>= analys analysis is cate,ori cate,ori+es +es inven inventor tory y int into o %6 diff differe erent nt cate,or cate,ories ies for for computer computer analy analysis. sis. ANSW!" A(S
6.1/
Service Service level level is is the chancechance- measu measured red in in percen percentt- that there there ill ill &e a stocou stocout. t. ANSW!" A(S
6.16
A stocou stocoutt is a si situati tuation on that that occurs occurs hen hen there there is no no inven inventory tory on hand hand.. ANSW!" #!$
6.12
Not all or,ani or,ani+ati +ations ons are re7ui re7uired red to or or ith ith iinve nvento ntory ry.. ANSW!" A(S
6.15
#he first first step in devel developin opin, , an an inventory inventory control process is identi identifyin fyin, , a method method to forecast forecast demand. ANSW!" A(S
6.1
#he conce concept pt of in inve vento ntory ry is applica applica&le &le to &oth &oth manufa manufacturi cturin, n, and and service service or,a or,ani+ ni+atio ations. ns. ANSW!" #!$
6.%0
As the the amount amount of inve invento ntory ry rises rises-- the total total cos costt to the the firm also rises. rises. ANSW!" A(S
6.%1
#he purpose purpose of the 9: model model is to achieve achieve a &alance &alance &etee &eteen n the cost cost of holdin, holdin, inventory inventory and the cost of stocouts. ANSW!" A(S
140
Inventory Control Models
6.%%
CHAPTER 6
9ne of the the assumptions assumptions of the the 9: 9: model model is that orders for invent inventory ory are placed placed periodic periodically ally 8eely- monthly- etc.;. ANSW!" A(S
6.%)
ortunatelyortunately- the the 9: 9: model model is relatively relatively insen insensitiv sitivee to minor minor errors in our forecast forecast of dema demand. nd. ANSW!" #!$
6.%4
#he 9: 9: model model maes maes the the assump assumptio tion n that inve invento ntory ry spoila, spoila,ee and pilfe pilfera,e ra,e costs costs are +ero. +ero. ANSW!" A(S
6.%/
#he o&*e o&*ecti ctive ve of of most most inven inventory tory mode models ls is to to minim minimi+e i+e stoc stocou outs. ts. ANSW!" A(S
6.%6 6.% 6
#he 9: 9: is defi define ned d &y the the inte interse rsecti ction on of the the Order Ordering ing Cost Curve and the Total Cost Curve. ANSW!" A(S
6.%2
$nder $nder the the assumptions assumptions made to develo develop p the the 9 9: : modelmodel- avera,e inventory inventory is one one half the the maximum inventory. ANSW!" #!$
6.%5
#he 9: model model is relativel relatively y insensitiv insensitivee to minor minor violations violations of the the &asic assumptions. assumptions. ANSW!" #!$
6.%
#he production production run model model is also useful hen a firm purchases purchases invent inventory ory hich is then delivere delivered d over a period of time. ANSW!" #!$
6.)0
We can develop develop an 9: m model odel for any situation for hich hich e can can define define an ?orderin,? ?orderin,? cost 8order8ordersetup- etc.; and a holdin, cost. ANSW!" #!$
6.)1
If e ish to use use the 9: model model in a situation here there are 7uantity 7uantity discountsdiscounts- the optimal optimal solution is the 9: hich is appropriate for the loest- discounted- cost. ANSW!" A(S
6.)%
Safety stoc stoc can &e &e used to ?comp ?compens ensate? ate? for variati variation on in in deliv delivery ery lea lead d times. times. ANSW!" #!$
6.))
We can usually usually determine determine an appropriate safety stoc even if e are una&le to accurately assess the the actual cost of a stocout. ANSW!" #!$
141
Inventory Control Models Models
6.)4
CHAPTER 6
In A>= inventory inventory analysi analysiss- items in the the ?A? ?A? ,roup ,roup should should have have the the loes loestt dollar dollar value to the firm. ANSW!" A(S
@6.)/
9ne reason reason inventory inventory is re7uired re7uired is the uneven uneven fl flo o of resources resources throu,h throu,h a company company.. ANSW!" #!$
@6.)6
#he loer loer the level level of inven inventory tory-- the lo loer er the cost cost to ac7uire and store the the inventory inventory-- &ut the ,reater the effort to trac inventory re7uired to avoid stocouts. ANSW!" #!$
@6.)2
A loer loer level level of invento inventory ry saves saves costs in to ays. ays. It costs les lesss to ac7uire ac7uire and store the inventory inventory-and it decreases the effort re7uired to avoid stocouts. ANSW!" A(S
@6.)5
#he costs costs involve involved d in a typical inven inventory tory m model odel are" order costscosts- mana,ement mana,ement costs- and holdi holdin, n, costs. ANSW!" A(S
@6.)
$nderstandi $nderstandin, n, the inven inventory tory co control ntrol process process is a si,nificant si,nificant part of the pro&lem of of inventory inventory model model &uildin,. &uildin,. ANSW!" #!$
@6.40
#he conom conomic ic 9rder 9rder :uantity helps one estimate estimate the optimal optimal num&er num&er of units units to purchase purchase ith ith each order. ANSW!" #!$
14%
Inventory Control Models
CHAPTER 6
MULTIPLE CHOICE 6.41
Inventory 8a; 8&; 8c; 8d;
is any sto stored red resource resource used used to satisfy satisfy current or or future need. need. includ includes es ra materials- or<i or<in<proce n<processss- and finished finished ,oods. ,oods. level levelss for finis finished hed ,oods ,oods are a direct function function o off demand. demand. needs from ra materials throu,h finished ,oods can &e reasona&ly determineddetermined- once finished ,oods demand is determined. deter mined. 8e; all of the the aa&o &ove ve ANSW!" e 6.4%
xtra invent inventory ory that is used to avoid avoid stoco stocouts uts is no non n as 8a; 8&; 8c 8c;; 8d; 8d; 8e;
planned planned shorta, shorta,es. es. 7uantity 7uantity dis discou counts. nts. sa safe fety ty sto stoc c.. ser servi vice ce leve level. l. A>= analy analysis sis..
ANSW!" c 6.4) 6.4 )
As the the ser servi vice ce le leve vell incr increa ease sess8a; 8&; 8c; 8d; 8e;
safety stoc increases at a decreasin, decreasin, rate. safety sto stoc c increases increases at an increasin, increasin, rate. safety stoc decreases decreases at an increasin, increasin, rate. safety stoc decreases decreases at a decreasi decreasin, n, rate. none none of the the aa&ov &ovee
ANSW!" & 6.44 6.4 4
As the the ser servi vice ce le leve vell incr increa ease sess8a; carryin, cost increases increases at an increasin, increasin, rate. 8&; 8c; 8d; 8e;
carryin, cost cost decreases increases increasess at decre asin, rate. carryin, decrease at aa decreasin, decreasin, decreasin, rate. carryin, cost decreases decreases at an increasin, increasin, rate. none none of the the aa&ov &ovee
ANSW!" a
14)
Inventory Control Models Models
6.4/ 6.4 /
CHAPTER 6
Whic Which h of the the foll follo oin in, , is is not not a us usee of inv inven ento tory ry 8a; 8&; 8c; 8d; 8e;
the deco decoupl uplin, in, fun functio ction n the translu translucen centt functio function n an infl inflatio ation n hed,e hed,e allo for 7uantity 7uantity discounts discounts to avoid avoid stoc stocout outss and shorta, shorta,es es
ANSW!" & 6.46
In mai main, n, inv invent entory ory decisi decisions ons-- the purpose purpose of of the &asic &asic mo mode dell is to 8a; 8&; 8c; 8d; 8e;
mini minimi+e mi+e customer customer dissatisfaction. dissatisfaction. mini minimi+e mi+e stoc on hand. minim minimi+e i+e carryin, carryin, co costs. sts. mini minimi+e mi+e orderin, orderin, costs. mini minimi+e mi+e the sum of carryin, costs and orderin, orderin, costs.
ANSW!" e 6.42
Which Which of of the the fo follo lloi in, n, facto factors rs is 8are; 8are; not not inclu included ded in order orderin, in, cost cost 8a 8a;; &ill &ill pay payin, in, 8&; 8c; 8d; 8e;
o&sol o&soles esce cenc ncee purchasin, department department overhead overhead costs inspect inspectin, in, incom incomin, in, inven inventory tory devel developi opin, n, an and d sendin, sendin, purchase orders orders
ANSW!" & 6.45
Which Which of of the the fo follo lloi in, n, facto factors rs is 8are; 8are; not not inclu included ded in carry carryin, in, cost cost 8a 8a;; 8&; 8c; 8d; 8e;
spoi spoila la,e ,e.. o&sol o&soles esce cenc nce. e. cost cost of of ccap apita ital. l. inspect inspectin, in, incomi incomin, n, inventor inventory y. arehou arehousin sin, , overhe overhead ad costs. costs.
ANSW!" d 6.4
A false false statem statement ent a&out a&out 9: or econ econom omic ic order order 7uant 7uantity ity is that that iitt 8a; 8&; 8c; 8d; 8e;
is relativ relatively ely easy to use. use. is one of the most most commonly commonly used inventory control techni7ues. is one of th thee oldest oldest inventory inventory control control techni7 techni7ues. ues. as developed durin, the second World Wa War. r. is the 7uanti 7uantity ty here here the total annual annual carryin, cost and total total annual orderi orderin, n, costs costs are e7ual.
ANSW!" d 6./0
Which Which of the the follo folloi in, n, is n not ot an assumptio assumption n for for the &asic &asic 9: mod model el 8a; 9nly an iinte,e nte,err num&er num&er of orders can &e &e made each each year. year.
144
Inventory Control Models
8&; 8c; 8d; 8e;
CHAPTER 6
:uantity discounts discounts are not possi&le. possi&le. Inven Inventory tory receipt receipt is instantaneous instantaneous 8all at once;. With orders placed at the correct time- there there ill &e no shorta,es. shorta,es. Be Bema mand nd iiss n no on. n.
ANSW!" a 6./1
or the the &asic &asic 9: 9: model model-- h hich ich of the the follo folloi in, n, relatio relationsh nships ips is is not not true true 8a; 8&; 8c; 8d; 8e;
#he optimal nu num&er m&er of orders per year e7uals annual dem demand and div divided ided &y the 9:. #he reorder point e7uals daily demand demand times times the lead time in days. #he avera,e dol dollar lar level of of inventory inventory e7uals e7uals unit price times order order 7uantity 7uantity.. Avera,e Avera,e inventory inventory level level e7uals one<half the order si+e. At 9: 9:-- orderin, orderin, cost e7uals e7uals carryin, cost.
ANSW!" c 6./%
#he 9: ould ould dou&le dou&le if ever everyt ythin hin, , stayed stayed cons constant tant-- except except that 8a; 8&; 8c; 8d;
orderin orderin, , cost cost decreased decreased &y a factor of of four. four. carryin, cost increased increased &y a factor of four. four. annual d deman emand d increased increased &y a factor of of four. four. orderin orderin, , costs costs dou&led dou&led..
8e; carryin, carryin, cost dou&le dou&led. d. ANSW!" c 6. 6./ /)
#he #he re reo ord rder er point int is 8a; 8&; 8c; 8d; 8e;
the avera,e inventory inventory level. level. the 7uant 7uantity ity level level at hich to place an order order for :. the slo slope pe of the the inventory inventory level level curv curve. e. here orderin, orderin, cost cost e7uals carryin, cost. cost. found found &y a s7uare root formula. formula.
ANSW!" & 6./4
#he 9: 9: model model ith ithout out the the instanta instantaneo neous us receipt receipt assum assumptio ption n is commo commonly nly called called the the 8a; 8&; 8c; 8d; 8e;
7uantity 7uantity dis discou count nt model model.. safety safety stoc stoc model. model. planned planned shorta, shorta,ee model model.. producti production on ru run n model. model. none none of the the aa&ov &ovee
ANSW!" d 6.//
In the the productio production n run model model of 9:9:- the orderin, orderin, cost cost of the &asic model model is replaced replaced &y the the 8a 8a;; 8&; 8c; 8d; 8d;
se setu tup p cos cost. t. stoc stocou outt cost. cost. carryi carryin, n, cost. cost. mat materi erial al cost. cost.
14/
Inventory Control Models Models
CHAPTER 6
8e; none none of the the aa&ov &ovee ANSW!" a 6./6 6./ 6
Se Sens nsit itiv ivit ity y ana analy lysi siss of 9: 9: refe refers rs to to 8a; 8&; 8c; 8d; 8e;
the attitude o off top mana,emen mana,ementt toard the use of of the 9: model. model. an assessmen assessmentt of the impact impact of o&solescenc o&solescencee upon the the 9:. analysis of ho m much uch the 9: ill chan,e hen hen other other varia&les chan,e. chan,e. a study of the impact of storin, inc incompat ompati&le i&le products products in the same arehouse. arehouse. analysis of th thee impact of stoc stoc shorta,es on on customers customers or on production. production.
ANSW!" c 6./2
In the the A>= A>= analy analysis sis of of inven inventor tory y- the the A ,rou ,roup p items items 8a; 8&; 8c; 8d; 8e;
are critical to the functionin, functionin, of the or,an or,ani+ation i+ation.. are the m most ost expensiv expensivee class of items. items. typicall typically y account for over over 20 percent of the company's company's &usiness in dollars. typicall typically y account for a&out 10 percent percent of a company's company's inventory inventory items. items. all of the the aa&o &ove ve
ANSW!" e 6./5
!olf Steps Steps is the the product production ion mana mana,er ,er for for a local local manuf manufactur acturin, in, firm. firm. #his company company produce producess staplers and other items. #he annual demand for a particular particula r stapler is 1-600 units. #he holdin, holdin, cost is C% per unit per per year. #he cost of settin, up the production line for this is C%/. #here are %00 orin, days per year. #he production rate for this product is 50 per day. day. If !olf decided to produce %00 units each time he started production production of the staplerstapler- hat hat ould his maximum maximum inventory level &e 8a; 8&; 8c; 8d; 8e;
%00 150 100 0 none none of the the aa&ov &ovee
ANSW!" &
146
Inventory Control Models
6./
CHAPTER 6
!olf Steps Steps is the the product production ion mana mana,er ,er for for a local local manuf manufactur acturin, in, firm. firm. #his company company produce producess staplers and other items. #he annual demand for a particular particula r stapler is 1-600 units. #he holdin, holdin, cost is C% per unit per per year. #he cost of settin, up the production line for this is C%/. #here are %00 orin, days per year. #he production rate for this product is 50 per day. day. If !olf decided to produce %00 units each time he started production production of the staplerstapler- ho ho lon, lon, ould ould it tae tae to produce produce %00 units 8a; 8&; 8&; 8c 8c;; 8d; 8d; 8e;
1 ye year %./ %./ day dayss 4 day days 10 da day ys none none of the the aa&ov &ovee
ANSW!" & 6.60
!olf Steps Steps is the the product production ion mana mana,er ,er for for a local local manuf manufactur acturin, in, firm. firm. #his company company produce producess staplers and other items. #he annual demand for a particular particula r stapler is 1-600 units. #he holdin, holdin, cost is C% per unit per per year. #he cost of settin, up the production line for this is C%/. #here are %00 orin, days per year. #he production rate for this product is 50 per day. day. 3o many many units should !olf produce each time he starts production of this product if he ishes to minimi+e total inventory cost 8round anser to nearest unit; 8a; %00 8&; 8c; 8d; 8e;
50 100 %11 none none of the the aa&ov &ovee
ANSW!" d 6.61
With With an annual annual dem demand and of %-400 %-400 unitsunits- dail daily y deman demand d of 10 unit unitss- and daily daily producti production on rate rate of 40 units- a company has determined that each production run ill &e for %00 units. If production starts hen the inventory level is at +ero- ho many units ould actually &e in the arehouse at the end of the first day of production 8round anser to nearest unit; 8a; 1% 8&; %0 8d c; 4 )0 8e; none none of the the aa&ov &ovee ANSW!" c
142
Inventory Control Models Models
6.6%
CHAPTER 6
!.=. >arer maes maes purchas purchasin, in, dec decisi isions ons for his his co compa mpany ny.. 9ne prod product uct that that he &uys &uys costs costs C/0 per per unit hen the order 7uantity is less than /00. When the 7uantity ordered is /00 or more- the price per unit drops drops to C45. #he orderin, orderin, cost is C)0 per order and and the annual annual demand demand is 2-/00 2-/00 units. #he holdin, cost is 10 percent of the purchase cost. If !.=. ishes to minimi+e minimi+e his total annual inventory costs- he must evaluate the total cost for to possi&le order 7uantities. What are these to possi&le 7uantities 8round anser to nearest unit; 8a 8a;; 8& 8&;; 8c 8c;; 8d 8d;; 8e;
)00 )00 and and )06 )06 )00 )00 aand nd /00 /00 )0 )06 6 and and /0 %00 %00 aand nd )06 )06 none none of the the aa&ov &ovee
ANSW!" & 6.6)
!.=. >arer maes maes purchas purchasin, in, dec decisi isions ons for his his co compa mpany ny.. 9ne prod product uct that that he &uys &uys costs costs C/0 per per unit hen the order 7uantity is less than /00. When the 7uantity ordered is /00 or more- the price per unit drops drops to C45. #he orderin, orderin, cost is C)0 per order and and the annual annual demand demand is 2-/00 2-/00 units. #he holdin, cost is 10 percent of the purchase cost. If !.=. orders /00 units each time he places an order- hat ould the total annual holdin, cost &e 8a; C4/0 8& 8&;; C1-% C1-%00 00 8c 8c;; C1-% C1-%/0 /0 8d; C%-4 C%-400 00 8e; none none of the the aa&ov &ovee ANSW!" &
6.64
!.=. >arer maes maes purchas purchasin, in, dec decisi isions ons for his his co compa mpany ny.. 9ne prod product uct that that he &uys &uys costs costs C/0 per per unit hen the order 7uantity is less than /00. When the 7uantity ordered is %00 or more- the price per unit drops drops to C45. #he orderin, orderin, cost is C)0 per order and and the annual annual demand demand is 2-/00 2-/00 units. #he holdin, cost is 10 percent of the purchase cost. 3o many units shoul should d !.=. order to minimi+e his total annual inventory cost 8round anser to nearest unit; 8a; )00 8&; )06 c;; % /0 00 0 88d 8e; none none of the the aa&ov &ovee ANSW!" c
145
Inventory Control Models
6.6/
CHAPTER 6
=onsider =onsider an inventory inventory situation here here all all the the 9: assumptions assumptions are met met except there are 7uantity 7uantity discounts. When a person orders more than the 9: so that the discoun discountt price can &e had- hich of the folloin, is true 8a; 8&; 8c; 8d; 8e;
#o #otal tal orderin, orderin, cost usually usually decreases decreases relative relative to 9: cost. #o #otal tal purchase cost usually usually incr increases eases relative relative to 9: 9: cost. #o #otal tal holdin, holdin, cost cost usually decreases decreases relative relative to 9: cost. 3oldi 3oldin, n, cost cost per unit usually increases increases relativ relativee to 9: cost. none none of the the aa&ov &ovee
ANSW!" a 6.66
#he annu annual al de deman mand d for for a product product is 1-000 units. units. #he company company orders orders %00 unit unitss each time time an orde order r is placed. #he lead time is 6 days- and the company has determined that %0 units should &e held as a safety stoc. #here are %/0 orin, orin, days per year. year. What is the reorder point point 8a; 8&; 8c; 8d; 8e;
%0 %4 44 1%0 none none of the the aa&ov &ovee
ANSW!" c 6.62
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. days. =urrently =urre ntly-- the company is orderin, /00 units each time an order is placed. What is the avera,e inventory level under the current policy 8a; 8&; 8c; 8d; 8e;
/0 100 %/0 /00 none none of the the aa&ov &ovee
ANSW!" c
14
Inventory Control Models Models
6.65
CHAPTER 6
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. days. =urrently =urre ntly-- the company is orderin, /00 units each time an order is placed. What is the total holdin, cost for the year usin, this policy 8a; 8& 8&;; 8c 8c;; 8d; 8e;
C400 C%-0 C%-000 00 C4-0 C4-000 00 C5-0 C5-000 00 none none of the the aa&ov &ovee
ANSW!" & 6.6
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. days. =urrently =urre ntly-- the company is orderin, /00 units each time an order is placed. What is the total orderin, cost for the year usin, this policy 8a; C400 8&; C160 8c; C40 8d; C50 8e; none of the a&ove ANSW!" d
6.20
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. days. =urrently =urre ntly-- the company is orderin, /00 units each time an order is placed. What is the reorder point under the current policy 88a&;; 1 40 50 8c; 6 8d; %4 8e; none of the a&ove ANSW!" a
1/0
Inventory Control Models
6.21
CHAPTER 6
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. days. =urrently =urre ntly-- the company is orderin, /00 units each time an order is placed. 3o many orders ould &e placed each year usin, the current policy 8a; 8&; 8c; 8d; 8e;
100 6 4 5 none none of the the aa&ov &ovee
ANSW!" c 6.2%
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. 3o many units should the company order each time an order is placed if the company ishes to minimi+e total inventory cost 8a; 100 8&; %00 8c; %/0 8d; /00 8e; none of the a&ove ANSW!" a
6.2)
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. #he cost of placin, an order is C40- hile the holdin, cost is C%0 per unit per year. 3o many units should Dar order o rder to minimi+e total inventory costs for the year 8a; /00 8&; 1%0 8c; 600 88e; d; none )00 of the a&ove ANSW!" &
1/1
Inventory Control Models Models
6.24
CHAPTER 6
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. #he cost of placin, an order is C40- hile the holdin, cost is C%0 per unit per year. #here are )60 orin, days per year and the lead time is 6 days. What is the reorder point 8a; 56 8&; 60 8c; 1%0 8d; %00 8e; none of the a&ove ANSW!" &
6.2/
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. #he cost of placin, an order is C40- hile the holdin, cost is C%0 per unit per year. #here are )60 orin, days per year and the lead time is / days. If Dar orders %00 units each time he places an order- hat ould his avera,e inventory &e 8in units; 8a; 100 8&; %00 8c; 60 8d; 1%0 8e; none of the a&ove ANSW!" a
6.26
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. #he cost of placin, an order is C40- hile the holdin, cost is C%0 per unit per year. #here are )60 orin, days per year and the lead time is / days. If Dar orders %00 units each time he places an order- hat ould his total orderin, cost &e for the year 8a 8a;; 8& 8&;; 8c; 8d; 8e;
C%-0 C%-000 00 C%-2 C%-2%0 %0 C%00 C2%0 none none of the the aa&ov &ovee
ANSW!" d
1/%
Inventory Control Models
6.22
CHAPTER 6
Andre =andess mana,es mana,es an office office supply store. 9ne product in the store is computer computer paper. Andre Andre nos that 10-000 &oxes ill &e sold this year at a constant ra rate te throu,hout the year. year. #here are %/0 orin, days per year year and the lead time is ) days. #he cost of placin, an order is C)0- hile the holdin, holdin, cost is C1/ per &ox per y year. ear. What is the daily demand demand for paper 8a; 8&; 8c; 8d; 8e;
40 %/0 1%0 %00 none none of the the aa&ov &ovee
ANSW!" a 6.25
Andre =andess mana,es mana,es an office office supply store. 9ne product in the store is computer computer paper. Andre Andre nos that 10-000 &oxes ill &e sold this year at a constant ra rate te throu,hout the year. year. #here are %/0 orin, days per year year and the lead time is ) days. #he cost of placin, an order is C)0- hile the holdin, holdin, cost is C1/ per &ox per year. If Andre Andre orders /00 &oxes each time he orders from his supplier- hat ould his total relevant inventory cost &e 8holdin, cost plus orderin, cost; 8a 8a;; 8& 8&;; 8c 8c;; 8d;
C)-0 C)-000 00 C4-) C4-)/0 /0 C)-0 C)-02/ 2/ C)-2 C)-2/0 /0
8e; none none of the the aa&ov &ovee ANSW!" & 6.2
Andre =andess mana,es mana,es an office office supply store. 9ne product in the store is computer computer paper. Andre Andre nos that 10-000 &oxes ill &e sold this year at a constant ra rate te throu,hout the year. year. #here are %/0 orin, days per year year and the lead time is ) days. #he cost of placin, an order is C)0- hile the holdin, cost is C1/ per &ox & ox per year. 3o many units should Andre order each time to minimi+e his annual inventory cost 8a; 8&; 8c; 8d;
%00 400 /00 100
8e; none none of the the aa&ov &ovee ANSW!" a
1/)
Inventory Control Models Models
6.50
CHAPTER 6
Baniel Baniel #rumpe #rumpe has comp compute uted d th thee 9: 9: for a product product he sells sells to &e 400 units. units. 3o 3oev everer- due to recent events he has has a cash ca sh flo pro&lem. #herefore- he only orders 100 units each time he places an order. Which of the folloin, folloin, is true for this situation 8a; 8&; 8c; 8d; 8e;
#o #otal tal orderin, cost cost ill &e hi,her hi,her than total holdin, holdin, cost. #o #otal tal orderin, cost cost ill &e loer loer than total holdin, holdin, cost. cost. #o #otal tal orderin, cost ill e7ual total holdin holdin, , cost. Nothin Nothin, , can &e determined determined ithout ithout more information information.. none none of the the aa&ov &ovee
ANSW!" a 6.51
A person is usin, usin, the normal normal distri&utio distri&ution n to determ determine ine the safety stoc for a product. What ?+? value ould &e associated ith a 0 percent service level 8a; 0.0 8&; 1.%5 .%5 8c; 0./) 8d; −0.0 8e; none none of the the aa&ov &ovee ANSW!" &
6.5%
A person is usin, usin, the normal normal distri&utio distri&ution n to determ determine ine the safety stoc for a product. What ?+? value ould &e associated ith a / percent service level 8a; 0./ 8&; 1.%5 .%5 8c; 1.6/ 8d; −0./ 8e; none none of the the aa&ov &ovee ANSW!" c
6.5)
A person is usin, usin, the normal normal distri&utio distri&ution n to determ determine ine the safety stoc for a product. What ?+? value ould &e associated ith a percent service level 8a; 0.0 8&; 1.6/ .6/ 8c; %.)% 8d; −0. 8e; none none of the the aa&ov &ovee ANSW!" c
1/4
Inventory Control Models
6.54
CHAPTER 6
Bemand Bemand for a product is constantconstant- &ut &ut the lead time fluctuates. #he demand demand durin, the lead time is normally distri&uted ith a mean of 40 and a standard deviation of 4. If the company ishes to maintain a 0 percent service level- ho much safety stoc should &e held 8a; 8& 8&;; 8c; 8d; 8e;
4/.1% .1% 41.% 41.%5 5 1.%5 /.1% .1% none none of the the aa&ov &ovee
ANSW!" d 6.5/
Eac Spratt is the producti production on man mana,er a,er for a local local man manufact ufacturin urin, , firm. firm. #his #his company company produce producess i++y<,ad,ets and other items. #he annual demand demand for a particular i++y<,ad,et is 1-600 units. #he holdin, cost is C% per unit per year. #he cost of settin, up the production line for this is C%/. #here are %00 orin, days per year. #he production rate for this product is 50 per day. day. If his maximum inventory level is 150 units- ho many units did he produce each time he started production producti on of the the i++y<,ad,e i++y<,ad,ets ts 8a; 8&; 8c; 8d;
%00 150 100 0
8e; none none of the the aa&ov &ovee ANSW!" a 6.56
!ose Arena Arena is is the the product production ion man mana,er a,er for a local local manuf manufactur acturin, in, firm. firm. #his company company produces produces &u,,y hips and other items. items. #he annual annual demand demand for a particular &u,,y hip is 1-600 units. #he holdin, cost is C% per unit per year. #he cost of settin, up the production line for this is C%/. #here are %00 orin, days per year. !ose decided to produce %00 units each time she started production producti on of the the &u,,y hips. hips. If it too her her four days to produce produce the the %00 units- hat hat as her production producti on rate 8a 8a;; 50 uni units tsFd Fday ay 8&; 60 unitsFday 8c 8c;; 40 uni units tsFd Fday ay 8d; 8d un 8e;; 100 none noneunit ofitsFd the tsFday heay aa&ov &ovee ANSW!" e
1//
Inventory Control Models Models
6.52
CHAPTER 6
!olf Steps Steps is the the product production ion mana mana,er ,er for for a local local manuf manufactur acturin, in, firm. firm. #his company company produce producess staplers and a nd other items. #he holdin, holdin, cost is C% per unit per year. #he cost of settin, up the production producti on line line for th this is is C%/. #here are %00 orin, orin, days per year. year. #he production production rate for this product is 50 per day. day. If the production production order 7uantity 7uantity is %00 unitsunits- hat as the daily d deman emand d 8rounded to the nearest hole unit; 8a 8a;; 8&; 8&; 8c 8c;; 8d; 8d; 8e;
6 un units 2 unit unitss 5 un units un unit itss none none of the the aa&ov &ovee
ANSW!" & 6.55
#he annu annual al de deman mand d for for a product product is 1-000 units. units. #he company company orders orders %00 unit unitss each time time an orde order r is placed. #he lead time is six days. days. #here are %/0 orin, orin, days per year. year. If the reorder point is /0- hat safety stoc are they usin, 8a; 8&; 8c; 8d; 8e;
%% 4 %6 %5 none none of the the aa&ov &ovee
ANSW!" c 6.5
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. If the avera,e inventory is 400 units- ho many units is the company orderin, at a time 8a; 8&; 8c; 8d; 8e;
)00 400 /00 600 none none of the the aa&ov &ovee
ANSW!" e
1/6
Inventory Control Models
6.0
CHAPTER 6
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. =urrently=urrently- the purchase purchase cost is C40 per per unit. #here are %/0 orin, orin, days per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. If the total holdin, cost for the year is C%-000- ho many units does the company order at a time 8a; 8&; 8c; 8d; 8e;
)00 400 /00 600 none none of the the aa&ov &ovee
ANSW!" c 6.1
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. #he purchase purchase cost is C40 per unit. unit. #here are %/0 orin orin, , days per per year. Whenever Whenever an order is placed- it is non that the entire order ill arrive on a truc in 6 days. =urrently =urrentl y- the company is orderin, /00 units each time an order is placed. What level of safety stoc ould ,ive a reorder point of 60 units 8a; 10 8&; 8c; 8d; 8e;
14 15 %% none none of the the aa&ov &ovee
ANSW!" e 6.%
#he annu annual al de deman mand d for for a product product has has &een &een pro*ec pro*ected ted to &e %-000 units units.. #hi #hiss deman demand d is assum assumed ed to to &e constant constant throu,hout throu,hout the year. year. #he orderin, orderin, cost is C%0 per orderorder- and the the holdin, holdin, cost is %0 percent of of the purchase purchase cost. #he purchase purchase cost is C40 per unit. unit. #here are %/0 orin orin, , days per per year. =urrently =urrentl y- the company company is orderin, /00 units each time time an order is placed. Assumin, the company uses a safety stoc of %0 units resultin, in a reorder point of 60 units- hat is the expected lead time for delivery 8a 8a;;; 8& 8&; 8c 8c;; 8d; 8e;
4 day da yss / day days 6 day days 2 day dayss none none of the the aa&ov &ovee
ANSW!" &
1/2
Inventory Control Models Models
6.)
CHAPTER 6
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. #he holdin, cost is C%0 per unit per year. If Dar Dar is minimi+in, minimi+in, total inventory cost and is orderin, in lots of 0 units- hat is his total order cost per year 8a; 8&; 8c; 8d; 8e;
/00 200 00 11-1 100 ins insuff uffici icient ent informa informatio tion n
ANSW!" c 6.4
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. year. #he holdin, holdin, cost is C%0 per unit per y year. ear. #here are )60 orin, days per year and the lead time is / days. or hat order cost ould Dar order %00 units each time he placed an order 8a; 8&; 8c; 8d; 8e;
%0 40 60 50 none none of the the aa&ov &ovee
ANSW!" e 6./
Dar Achin Achin sells )-600 electric electric motors each year. year. #he cost of these is C%00 each each-- and deman demand d is constant throu,hout the year. #he holdin, cost is C%0 per unit per year. #here are )60 orin, days per year and the lead time is / days. Assumin, that Dar orders o rders %00 units 8the 9:; each time he places an order- hat ould &e his total orderin, cost per year 8a 8a;; 8& 8&;; 8c; 8d; 8e;
C%-0 C%-000 00 C%-2 C%-2%0 %0 C%00 C2%0 none none of the the aa&ov &ovee
ANSW!" a 6.6
Andre =andess mana,es mana,es an office office supply store. 9ne product in the store is computer computer paper. Andre Andre nos that 10-000 &oxes ill &e sold this year at a constant ra rate te throu,hout the year. year. #here are %/0 orin, days per year. #he cost of placin, an order is C)0- hile the holdin, cost is C1/ per &ox per year. year. What is the the delivery delivery lead time time 8a 8a;; 8& 8&;; 8c; 8d; 8e;
6.2
/ day days 6 day dayss ins insuff uffici icient ent informa informatio tion n 5 day dayss none none of the the aa&ov &ovee
ANSW!" c Andre =andess mana,es mana,es an office office supply store. 9ne product in the store is computer computer paper. Andre Andre nos that 10-000 &oxes ill &e sold this year at a constant ra rate te throu,hout the year. year. #here are %/0 orin, days per year and the lead time is ) days. #he holdin, cost is C1/ per &ox & ox per year.
1/5
Inventory Control Models
CHAPTER 6
Andre orders /00 &oxes each time he orders from his supplier. If his total relevant inventory cost 8holdin, cost plus orderin, cost; is C4-)/0- hat is his cost for each order 8a 8a;; 8& 8&;; 8c 8c;; 8d 8d;; 8e;
C/0F C/0For orde der r C40F C40For orde der r C)0F C)0For orde der r C%0F C%0F0r 0rde der r none none of the the aa&ov &ovee
ANSW!" c 6.5
A person is usin, usin, the normal normal distri&utio distri&ution n to determ determine ine the safety stoc for a product. #he ?+? value of 1.%5 ould &e associated ith hat service level 8a 8a;; 8& 8&;; 8c 8c;; 8d 8d;; 8e;
40 perc percen entt / perc percen entt 20 perc percen entt 0 perc percen entt none none of the the aa&ov &ovee
ANSW!" d 6.
A person is usin, usin, the normal normal distri&utio distri&ution n to determ determine ine the safety stoc for a product. #he ?+? value of 1.6/ ould &e associated ith hat service level 8a 8a;; 8& 8&;; 8c 8c;; 8d 8d;; 8e;
0 perc percen entt / perc percen entt 100 100 p per erce cent nt %./ %./ pe perc rcen entt none none of the the aa&ov &ovee
ANSW!" & 6.100
A person is usin, the normal normal distri&utio distri&ution n to determ determine ine the safety stoc for for a product. #he ?+? ?+? value of %.)% ould &e associated ith hat service level 8a 8a;; / perc percen entt 8& 8&; 8c 8c;;; 8d 8d;; 8e;
2./ 2./ perc rcen ent 5 perc pepe rcen ent t t perc percen entt none none of the the aa&ov &ovee
ANSW!" d
1/
Inventory Control Models Models
6.101
CHAPTER 6
Bemand Bemand for a product is constant- &ut &ut the lead time fluctuates. #he demand demand durin, durin, the lead lead time is normally distri&uted ith a mean of 40 and a standard deviation of 4. If they have calculated a reorder point of 4/.1% units- hat service level are they assumin, 8a 8a;; 8& 8&;; 8c 8c;; 8d 8d;; 8e;
5/ perc percen entt 0 perc percen entt / perc percen entt 2./ 2./ pe perc rcen entt none none of the the aa&ov &ovee
ANSW!" & @6.10% Which of the folloin, folloin, is not an assumption of the simple 9: inventory inventory model model 8a; 8&; 8c; 8d; 8e;
Bemand is no non n and constant. constant. (ead tim timee is non non an and d is +ero. +ero. :uantity :uantity disco discounts unts are not possi& possi&le. le. er unit unit cost cost is cons constant tant.. none none of the the aa&ov &ovee
ANSW!" & @6.10) Which of the folloin, folloin, circumstances re7uires that ad*ustments &e made to the simple simple 9: model 8a; 8&; 8c; 8d; 8e;
Service Service level levelss are spec specifi ified. ed. (ead tim timee is nonnon- &ut n non<+e on<+ero. ro. !eceipt of iinven nventory tory occu occurs rs over time time rather than instantaneously instantaneously.. 9rders are placed so as to limit the num&er num&er of stocouts. stocouts. c aan nd d
ANSW!" e @6.104 #he Gpoint at hich to reorderH does not depend on hich of the folloin," 8a 8a;; (e (ead ad tim time. 8&; orderi orderin, n, cos costt 88d c;; Sto 9: . e cos 8d; Stora, ra,e costs. ts. 8e; none none of the the aa&ov &ovee ANSW!" a
160
Inventory Control Models
CHAPTER 6
@6.10/ #he 9: is particularly sensitiv sensitivee to hich hich of the follo folloin, in, 8a; early demand demand.. 8& 8&;; 9rde 9rderr cost cost.. 8c; 3old 3oldin in, , cost. cost. 8d; roductio roduction n cost. cost. 8e; none none of the the aa&ov &ovee ANSW!" e @6.106 #o evaluate 7uantity discounts- one uses the 9: modelmodel- and modifies the model model so that 8a; 8&; 8c; 8d; 8e;
hold holdin, in, co cost st is considered considered as a percenta,e percenta,e of unit cost rather than a separa&le dol dollar lar cost. the 9: is calculate calculated d to lie ithin ithin one o off the cost corridors. corridors. hold holdin, in, cost is calcul calculated ated on an Gavera,e &asisH &asisH across the discounts. discounts. any one of the a&ove a&ove approaches approaches could &e used. none none of the the aa&ov &ovee
ANSW!" a @6.102 Which of of the folloi folloin, n, does does not impact impact on 9: 8a 8a;; sa safe fety ty stoc stoc 8&; demand demand per unit unit time time 8c 8c;; or orde derr cost cost 8d; 8d; all of the the aa&o &ove ve 8e; none none of the the aa&ov &ovee ANSW!" a
PROBLEMS 6.105
ast Jal Jalve ve Bistri&utors distri&utes distri&utes industrial industrial valves valves and and control control devices devices.. #he astern control control device has an annual demand of -)2/ units and sells for C100 per unit. #he cost of orderin, is C40 per order and the avera,e carryin, cost per unit per year is C0.2/. Betermine the economic order 7uantity. ANSW!" 9: K 1-000 units
6.10
ast Jal Jalve ve Bistri&utors distri&utes distri&utes industrial industrial valves valves and and control control devices devices.. #he astern valve valve has an annual demand of 10-000 units and a cost co st of C50 per unit. #he cost of orderin, is C2% per order and inventory carryin, carr yin, cost is estimated to &e / percent of the cost of each valve. (ead time is four orin, days. Betermine 8assume %/0 orin, days;" 8a; 8&; 8c; 8d;
the econo economi micc order order 7uantity 7uantity the reorder reorder point point the optimal optimal num&er num&er of orders per year year the optim optimal al num&er num&er of days &eteen &eteen any to to orders
161
Inventory Control Models Models
CHAPTER 6
ANSW!" 8a 8a;; 8&; 8c; 8d; 6.110
9: 9: K 600 600 unit unitss !9 K 4084 4084;; K 160 unit unitss num&e num&err of orders orders per year K BF: K 10-000F600 K 16.62 orders num&e num&err of days days &eteen &eteen orders orders K %/0F16.62 K 1/ days days
urniture Danufacturers Inc.- uses %0-000 %0-000 loads of lum&er lum&er per year. year. A load of lum&er lum&er costs C/00 C/00 and the carryin, cost is 10 percent of the unit cost. #he cost to order is C%00 per order and the lead time is three orin, days. days. Betermine 8assume %00 orin, days;" 8a; 8&; 8c; 8d;
the econo economi micc order order 7uantity 7uantity the reorder reorder point point num&er num&er o off orders orders per year year days days &ete &eteen en orders orders
ANSW!" 8a 8a;; 8&; 8c; 8d; 6.111
9: 9: K 400 400 unit unitss !9 K 1008); 1008); K )00 unit unitss num&e num&err of orders orders per year K BF: K %000F400 K /0 /0 orders days &et &eteen een orders K %00F/0 K 4 days days
We use use 1-/00 per per year of a certain su&assem&l su&assem&ly y that has an annual annual holdin holdin, , cost cost of C4/ per unit. unit. ach order placed costs us C1/0. We operate )00 days per year and have found that an order must &e placed ith our our supplier 6 orin, orin, days &efore &efore e can expect expect to receive receive that order. order. or this su&assem&ly- find" 8a; 8&; 8c; 8d;
the econo economi micc order order 7uantity 7uantity the annual annual hold holdin in, , cost cost the annual annual order orderin, in, cos costt the reorder reorder point point
ANSW!" 8a 8a;; 9: 9: K 10 100 0 8&; annual holdin, holdin, cost K 8100F%;84/; K %%/0 8c; annu ord Ks 81/00F100 81/00F100;1/0 ;1/0 K %%/0 8d; 8d; annual !9al K orderin /86; /86erin, ;K, )0cost un unit its 6.11%
We use use 1-%00 of of a certain spare part that costs C%/ for each order and and has a C%4 annual holdi holdin, n, cost. =alculate the total cost for order si+es of" %/- 40- /0- 60- and 100. Identify the economic economic order 7uantity and consider the implications for main, an error in calculatin, the economic order 7uantity.
16%
Inventory Control Models
CHAPTER 6
ANSW!" #otal =ost K total orderin, cost L total holdin, cost : K %/ : K 40 : K /0 : K 60 : K 100
#= K 1%00 L )00 K C1-/00 #= K 2/0 L 450 K C1-%)0 #= K 600 L 600 K C1-%00 #= K /00 L 2%0 K C1-%%0 #= K )00 L 1%00 K C1-/00
Small variations in order 7uantity ill not have a si,nificant impact on total costs. 6.11)
Dar >arry forecasts forecasts annual annual demand demand of his his ne ne computer computer softare softare to to &e 6-%/0 units. units. #his should &e relatively relatively constant constant throu,ho throu,hout ut the year. year. #he cost cost of placin, placin, an order is C40C40- hile the holdin holdin, , cost per unit is C% per unit per year. (ead time is constant at four daysd ays- and there are %/0 orin, days per year. 8a; #o minimi+e total cost- ho many units should >arry order each time he places an order 8&; What is the reorder point ANSW!" 8a; 9: K /00 units 8&; !9 K 486%/0F%/0; K 100 units
6.114
Bavid and >eth >eth She&a run a health health food food store. #heir top sellin sellin, , item is called called 3eavenly 3eavenly Melp. #he annual demand for this is 510 units- and demand demand is constant throu,hout the y year. ear. #he cost of placin, an order is C%0C%0- hile the holdin holdin, , cost p per er unit per year year is C4. 8a; 3o many orders per year should &e placed if they ish to minimi+e minimi+e their total cost 8&; What is the mi minimu nimum m possi&le possi&le annual annual holdin, holdin, cost cost ANSW!" 8a; 9: K 0 units. #herefore#herefore- the num&er num&er of orders orders per year year is 510F0 K orders per per year. year. 8&; 80F%;4 80F%;4 K C150 total hold holdin in, , cost cost
6.11/
#he annual 3.A.(. 3.A.(.demand =omputer =omputis erforecasted Store sellstoa &e printer C%00. C%00 . Bemand Beman d cost for for this is constant co nstant dper urin, thehile yearand 600 for units. #he holdin, is C%0 per unit durin, yearthe cost of orderin, is C60 per order. =urrently =urrentl y- the company company is orderin, 1% times times per year 8/0 units each time;. #here are %/0 orin, days per year year and the lead time is 10 days.
16)
Inventory Control Models Models
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8a; iven the current policy policy of orderin, orderin, /0 /0 units at a time- hat hat is the total of the annual annual orderin, orderin, cost and the annual holdin, cost 8&; If the company used the a&solute &est inventory policypolicy- hat ould the total of the orderin, and holdin, cost &e 8c; What is is the the reorde reorderr po point int ANSW!" 8a; #9= #9= L #3= #3= K 2%0 L /00 /00 K C1%%0 C1%%0 8&; If e order 9: 9: K 60 unitsunits- #9= #9= L #3= K 600 600 L 600 K C1-%00. 8c; !9 K 8600F%/0 8600F%/0;10 ;10 K %4 units units 6.116
urinnerds urinnerds Bo, ood is a very popular product product at May nein' nein'ss corner corner ,rocery ,rocery.. Bemand Bemand for for this is is relatively constant- and the total demand for the year is 1-%00 &a,s &a,s.. #he cost of placin, an order is C/0- hile the holdin, cost is C) per unit per year. #he store is open )00 days per year. (ead time for this is 5 days. 8a; If May places /0 orders per year- hat ould ould her her orderin, orderin, and holdin holdin, , costs &e 8&; If May ishes to minimi+e minimi+e her total inventory cost- ho many units should she order each time an order is placed 8c; What is is the the reorde reorderr po point int ANSW!" 8a; With /0 orders orders per year- :K%4. #= K #9= #9= L #3= K %/00 %/00 L )6 K C%-/)6 8&; 8&; 9: 9: K %0 %00 0 8c; !9 K 81%00F)0 81%00F)00;5 0;5 K )% units units
6.112
verett Dann's Bream Bream Store sells ater &eds &eds and assorted supplies. #he &est sellin sellin, , &ed &ed in the store has an annual demand of 400 units. #he orderin, cost is C40- hile the holdin, cost is C/ per unit per year. #here are %/0 orin, days per yearyear- and the lead time is 6 days. 8a; #o minimi+e minimi+e total cost- ho many units should &e ordered each time an order is placed 8&; If the holdin, holdin, cost per unit as C6 instead of C/- hat ould the optimal order 7uantity &e ANSW!" 8a 8a;; 9: 9: K 50 50 uni units ts 8&; 9: K 2).0% 2).0% unit unitss if =hK6.
6.115
#he 3andy Danufacturin, =ompany manufactures small air conditio conditioner ner compressors. compressors. #he estimated demand demand for the year is 1%-000 units. #he setup cost for the production process is C%00 per run- and the carryin, carryin, cost is C10.00 C10.00 per unit per year. year. #he dai daily ly production production rate is 100 units per dayday- and demand demand has &een /0 units per day. day. Betermine Betermine the the num&er num&er of units units to produce produce in each &atch. 8ro&lem assumes %40 operatin, operatin, days.; days.; ANSW!" 9ptimum production 7uantity K 2.5 units
6.11
#he Ne Ne =ompany =ompany inventori inventories es product product !. #he carryin, cost of one unit per per year is C5.00- and the the cost of a stocout is C%0.00 per unit. $sin, the lead time demand pro&a&ility distri&ution ,iven &elo &elo - determine determine the appropriate appropriate safety stoc. stoc. Assume Assume the the optimum optimum num&er num&er of orders orders is non non to &e 1/.
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Inventory Control Models
!9K
(ead #ime Bemand 8$nits; %00 %/0 )00 )/0
ro&a&ility
400
0.10
CHAPTER 6
0.10 0.%0 0.40 0.%0
ANSW!" 6.1%0
9ptimum safety stoc K 100 units #otal #otal cost for safety stoc of 100 units K C500 #otal #otal cost for safety stoc of /00 units K C%-/00 #otal #otal cost for safety stoc of 0 units K C6-000
=andy Incorporated Incorporated stocs stocs &u&&le &u&&le ,um ,ame cards- an item that has a normally normally distri&uted distri&uted demand durin, the reorder period ith a mean of 1% do+en &oxes and a standard deviation of to do+en &oxes. If it is desira&le to experience a stocout only 10 percent of the time- hat is the appropriate safety stoc ANSW!" or 0 percent service level- e must have O K 1% L 1.%58%; K 14./6 do+en. Since the mean is 1%- the safety stoc K 14./6 < 1% K %./6
6.1%1
Susan 3olland 3olland sells hand<painted hand<painted shirts to vacationer vacationerss ho ho enter her ,ift ,ift shop. 3er supplier supplier can only deliver 10 of these per day- &ut if she orders more than this- the supplier ill deliver 10 each day until the entire entire order is met. 3er annual demand for these is 1-000- and the sales are relatively constant for each of the %/0 days that her store is open. #he cost of placin, an order is C%0- hile the holdin, cost per unit per year is C%. If she ishes to minimi+e minimi+e her annual inventory cost- ho many units should she order each time she places an order ANSW!" : K 15%./ units ill minimi+e costs.
6.1%%
Ivonne Ivonne =allen sells &eauty supplies. 3er annual annual demand demand for a particular particular sin lotion lotion is 1-000 units. units. #he cost of placin, an order is C%0- hile the holdin, cost per unit per year is 10 percent of the cost. #his item currently costs C10 if the order 7uantity 7uantity is less than 100. or orders of )00 units or more- the cost falls to C.50. C. 50. #o minimi+e minimi+e total cost- ho many units should Ivonne order each time she places an order What is the minimum minimum total cost
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Inventory Control Models Models
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ANSW!" With 9: K %00- the total cost is C10-%00. With : K )00 to o&tain discount- the total cost is C10-01)-62. #herefore- she should order )00 units. 6.1%)
#he purchasin, purchasin, mana,er mana,er for a firm is tryin, tryin, to determine determine hat the the safety stoc should should &e for a particular product. She has develo developed ped the fol follo loin, in, ta&le- hich hich ,ives ,ives the distri&ution distri&ution of demand demand durin, the lead time and the pro&a&ilities" Bemand Burin, (ead #ime 40 /0 60 20 50
ro&a&ility
0.%0 0.%/ 0.%/ 0.%0 0.10
#he carryin, cost is C/ per unit per year- the orderin, cost is C)0 per order- and the stocout cost is C40 per unit. #he reorder point is 60 units- and 6 orders are placed each year. What level of safety stoc should &e maintained ANSW!" Safety Stoc 0 10 %0
Additional 3oldin, =ost 0 /0 100
Stocout =ost 810;80.%;840;810;L8%0;80.1;840;810; 810;80.1;840;810; 0
#otal =ost 1600 4/0 100
#herefore- %0 units of safety stoc should &e carried. 6.1%4
red rummer rummer is the the inventory inventory mana,er for rummer rummer !etail and Bistri&utors. Bistri&utors. 9ne productautomo&ile distri&utors- has an annual demand of 4-000 units. #he orderin, cost is C%/ per order and the holdin, cost is C/ per unit per year. If red uses *oint orderin,- the orderin, cost ould fall to C%0 per order. 8a; What is the optimal order 7uantity if *oint orderin, is not used 8&; What is the optimal order 7uantity if *oint orderin, is used 8c; What is the cost savin,s of usin, *oint orderin, ANSW!" 8a; 9: ith no *oint orderin, K %00 units 8&; 9: ith *oint orderin, K 125.5 8c; =ost savin,s K 1000 < 54.4) K 10/./2
6.1%/
Dartha Daples opened opened a ne &eauty products products retail store. #here are numerous numerous items items in inven inventory tory-and Dartha nos that there are costs associated a ssociated ith inventory. inventory. 3oever- her time time is limited- so she cannot carefully evaluate the inventory inventory policy for all products. Dartha Dart ha ants to classify the
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items accordin, to the dollars invested in these. #he folloin, folloin, ta&le provides information a&out the 10 items that she carries" Item Num&er 10% B%) B%2 !0%
$nit =ost 4.00 5.00 ).00 %.00
S!1102 S1%) $11 $%) J2/
5 6..0 00 0 1.00 2.00 1.00 4.00
Bemand 8units; 500 1-%00 200 1-000 %-0 /0 00 0 1-%00 500 1-/00 1-/00
$se A>= A>= analysis to classify class ify these items into cate,ories AA- >- and =. ANSW!" Item Num&er 10% B%) B%2 !0% !1 S102 S1%) $11 $%) J2/
$nit =ost
Bemand 8units;
Annual =ost 8C;
4.00 5.00 ).00 %.00 5.00 6.00 1.00 2.00 1.00 4.00
500 1-%00 200 1-000 %00 /00 1-%00 500 1-/00 1-/00
)-%00 -600 %-100 %-000 1-600 )-000 1-%00 /-600 1-/00 6-000
B%) ould &e a =lass A item. $11 and J2/ ould &e =lass > items- and the rest ould &e =lass = items. i tems. #he percenta,es are not exactly as descri&ed in the text&oo- &ut the relative importance is certainly evident from this ta&le. 6.1%6
ast Jal Jalve ve Bistri&utors distri&utes distri&utes industrial industrial valves valves and and control control devices devices.. #he astern control control device has an annual demand of -)2/ units and sells for C100 per unit. #he cost of orderin, is C40 per order. If the 9: is calculated to &e 1-000 units- hat is the avera,e carryin, cost per unit per year ANSW!" Avera,e carryin, cost K C0.2/ per unit
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6.1%2
CHAPTER 6
We use use 1-/00 per per year of a certain su&assem&l su&assem&ly y that has an annual annual holdin holdin, , cost cost of C4/ per unit. unit. ach order placed costs us C1/0. We operate )00 days per year and have found that an order must &e placed ith our our supplier 6 orin, orin, days &efore &efore e can expect expect to receive receive that order. order. What reorder point should e use ANSW!" reorder point K )0 units
6.1%5
Dar >arry forecasts forecasts annual annual demand demand his ne computer computer softare softare to &e 6-%/0 units. #his should should &e &e relatively constant throu,hout the year. #he cost of placin, an order is C40- hile the holdin, cost per unit is C% per unit unit per year year.. (ead time time is constant constant at 4 days- and there are %/0 orin, orin, days days per year. year. If lead time time can &e reduced reduced to % days- hat should should the the ne 9: &e ANSW!"
6.1%
9: K /00 units
#he 3.A.(. 3.A.(. =omputer =omputer Store sells a printer for C%00. C%00. Bemand Bemand for for this is constant constant durin, durin, the yearand annual demand is forecasted to &e 600 units. #he holdin, cost is C%0 per unit per year- hile the cost of orderin, is C60 per order. =urrently =urrentl y- the company company is orderin, 1% times times per year 8/0 units each time; ith ith a total annual orderin, and holdin, holdin, cost of C1-400. #here are %/0 orin, days per year and the lead time is 10 days. 8a; Is the annual total ord order er and holdin, holdin, cost cost more or less than than the optimal optimal 8&; If the company decides to eep a safety stoc e7ual to / units- hat is the reorder point ANSW!" 8a; 9: K 60- ,i ,ivin, vin, #9= L #3= #3= K C600 L C600 C600 K C1-%00. #herefore#herefore- present present cost cost is a&ove a&ove optimal. 8&; !9 K 8600F% 8600F%/0;@ /0;@10 10 L / K % unit unitss
6.1)0
verett Dann's Bream Bream Store sells ater &eds &eds and assorted supplies. #he &est sellin sellin, , &ed &ed in the store has an annual demand of 400 units. #he orderin, cost is C40. resent holdin, cost is C6 per year- &ut Dr. Dann &elieves that he can reduce this cost to C/. What impact ould this reduction in holdin, holdin, cost have on the 9: #here are %/0 orin, days per year- and the lead time is 6 days. ANSW!" 9: 8=hKC/; K 50 unitsP 9: 8=hKC6; K 2).0% units
6.1)1
Susan 3olland 3olland sells hand<painted hand<painted shirts to vacationer vacationerss ho ho enter her ,ift ,ift shop. 3er supplier supplier can only deliver 10 of these per day- &ut if she orders more than this- the supplier ill deliver 10 each day until the entire entire order is met. 3er annual demand for these is 1-000- and the sales are relatively constant for each of the %/0 days that her store is open. #he cost of placin, an order is C%0- hile the holdin, cost per unit per year is C%. If she could convince her supplier to deliver her entire order on a sin,le day- ould this increase or decrease her carryin, plus orderin, cost
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ANSW!" :8roduction model; model; K 15%./ units. #otal #otal carryin, cost" K 81F%;@815%./@%;@81 < 4F10; K 15%./@.6 K C10./ :8Simple 9: Dodel; K 141 units. #otal carryin, cost" K 20./@% K C141 #herefore- havin, the supplier deliver 10 units per day until he has filled her order is the alternative that minimi+es the total carryin, plus order costs. 6.1)%
#he purchasin, purchasin, mana,er mana,er for a firm is tryin, tryin, to determine determine hat the the safety stoc should should &e for a particular product. She has develo developed ped the fol follo loin, in, ta&le- hich hich ,ives ,ives the distri&ution distri&ution of demand demand durin, the lead time and the pro&a&ilities" Bemand Burin, (ead #ime 40 /0 60 20 50
ro&a&ility 0.10 0.%0 0.%/ 0.%/ 0.%0
#he carryin, cost is C/ per unit per year- the orderin, cost is C)0 per order- and the stocout cost is C40 per unit. #he reorder point is 60 units- and 6 orders are placed each year. What level of safety stoc should &e maintained ANSW!" Safety Stoc 0 10 %0
Additional 3oldin, =ost 0 /0 100
Stocout =ost 810;80.%/;840;810;L8%0;80.%;840;810; 810;80.%;840;810; 0
#otal =ost 8C; %600 5/0 100
#herefore- %0 units of safety stoc should &e carried. @6.1)) !ascalQs !ascal Qs Inc. stocs &eef *ery- an item that has a normally normally distri&uted distri&uted demand durin, the reorder period ith a mean mean of 2 do+en do+en &oxes &oxes and a standard deviatio deviation n of three three do+en do+en &oxes. &oxes. If it is desira&le to experience a stocout only 10 percent of the time- hat is the appropriate safety stoc ANSW!" or 0 percent service level e must have O K 2 L 1.%58); K ./6 do+en. Since the mean is 2- the safety stoc K ./6 < 2 K %./6 do+en
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Inventory Control Models Models
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@6.1)4 Art9r,anArt9r,an- (td. distri&utes distri&utes mechanical mechanical replacem replacements ents for for human mitral mitral heart valves. valves. #heir artificial artificial valve has a demand of 1%-26/ units per year and sells for C2-00 C2-0 0 per unit. #he cost of orderin, is C2/ per order and the avera,e carryin, cost per unit per year is C1/0. Betermine the economic order 7uantity. ANSW!" 9: K 11) units @6.1)/ Art9r,anArt9r,an- (td. distri&utes distri&utes porcine replacemen replacements ts for human mitral heart valves. #heir replacement replacement valve has a demand of 1%-26/ units per year and sells for C2-00 C2-0 0 per unit. #he cost of orderin, is C2/ per order and the avera,e carryin, cost per unit per year ors out to &e a&out /R of the cost of the valve. (ead time is 4 orin, days. Betermine 8assume %/0 orin, days;" 8a; 8&; 8c; 8d;
the econo economi micc order order 7uantity 7uantity the reorder reorder point point the optimal optimal num&er num&er of orders per year year the optim optimal al num&er num&er of days &eteen &eteen any to to orders
ANSW!" 8a 8a;; 8&; 8c; 8d;
9: 9: K 6.6 6.6 unit unitss !eorder !eorder point point K %04.%4 %04.%4 Num&er Num&er of of orders orders pe perr year year K 15).)4 9ptimal num num&er &er of days &eteen &eteen orders K 1.4 orin, days
@6.1)6 We use %-2/0 %-2/0 per year of a certain su&assem&ly su&assem&ly that has a purchase co cost st of C4/0- and an annual annual holdin, cost of C/00 per unit. ach order placed costs us C1/0. We operate )00 days per year and have found that an order must &e placed ith our supplier 6 orin, days &efore e can expect to receive that order. order. or this su&assem&ly- find" 8a; 8&; 8c; 8d;
econo economi micc order order 7uantity 7uantity K 40.6 40.6 annual h holdi oldin, n, cost 8usi 8usin, n, 9:; K C101 C101//.60 //.60 annual orderin, orderin, cost cost 8usin, 8usin, 9:; K C101//.60 reorder reorder point point K // //
@6.1)2 We use 1-)00 1-)00 of a certain spare part that costs C)/ for each ord order er and has a C)% annual holdin, holdin, cost. =alculate the total cost for order si+es of" %/- 40- /0- 60- and 100. Identify the economic economic order 7uantity and consider the implications for main, an error in calculatin, the economic order 7uantity. ANSW!" #otal =ost K total orderin, cost L total holdin, cost : K %/ #= K C%%%0.00 : K 40 #= K C1222./0 : K /0 #= K C1210.00 Q* K /).) #= K C1206.40 : K 60 #= K C1215.00 : K 100 #= K C%0//.00 ercent variation of total cost is certainly less than percent variation in order 7uantity. @6.1)5 #he 3.A.(. =omputer =omputer Store sells sells a printer printer for C400. Bemand Bemand for this this is constant constant durin durin, , the the yearyearand annual demand is forecasted to &e 1100 units. #he holdin, cost is C%0 per unit u nit per year- hile
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the cost of orderin, is C0 per order. =urrently =urrentl y- the company company is orderin, 1% times times per year 8% units each time;. #here are %/0 orin, days per year year and the lead time is 5 days. 8a; iven the current policy policy of orderin, orderin, % % units at a time- hat hat is the total of the annual annual orderin, orderin, cost and the annual holdin, cost 8&; If the company used the a&solute &est inventory policypolicy- hat ould the total of the orderin, and holdin, cost &e 8c; What is is the the reorde reorderr po point int 8d; 3o ma many ny days days &eteen &eteen orders orders ith 1% orders per year year ANSW!" 8a 8a;; 8&; 8c 8c;; 8d;
#= K C1- C1-6 6.0 .0 $sin, $sin, 9: o off ./ ./ units" units" #= K C10.00 C10.00 !9 !9 K )/.% )/.% unit unitss Num&er of days days &eteen &eteen orders K %%.6 %%.6
SHORT ANSWER/ESSAY 6.1)
xplain xplain in inven ventor toryQ yQss fin financ ancial ial role role in a company company.. ANSW!" Inventory often represents a considera&le amount of invested capital- thus inventory control is essential.
6.140
(ist three three ,ene ,eneral ral cate, cate,ori ories es of of inven inventor tory y. ANSW!" ra material- or<in<process inventory- finished ,oods inventory
6.141
xplain xplain h ho o inve invento ntory ry can act act as a &uffer &uffer in in the produ productio ction n process. process. ANSW!" >y storin, some inventory- it helps to decouple the manufacturin, process ithin the or,ani+ation.
6.14%
(ist three three disadvanta,es disadvanta,es of &uyin, &uyin, inventory inventory in lar,e 7uantities. 7uantities. ANSW!" hi,her stora,e cost- more spoila,e- dama,ed stoc- theft- insurance- less cash to investetc.
6.14)
(ist four si,nif si,nifican icantt inv invent entory ory costs. costs. ANSW!" the inventory itself- order cost- carry cost- stocout cost
6.144 6.1 44
(i (ist st thre threee carry carryin in,< ,<cos costt factor factors. s. ANSW!" taxes- insurance- spoila,e- theft- o&solescence- arehouse personnel a,es- etc.
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Inventory Control Models Models
6.14/ 6.1 4/
CHAPTER 6
(i (ist st three three order order cost cost facto factors. rs. ANSW!" sendin, a purchase purc hase order- inspectin, incomin, inventoryinventory- &ill payin,- inventory 7uestions- purchasin, department expenses- etc.
6.146
xplain xplain hat hat is meant meant &y reorder reorder point. point. ANSW!" #he reorder point is hen time to reorder an inventory item.
6.142 6.1 42
Wh Why y carr carry y ssaf afet ety y ssto toc c ANSW!" to prevent costly stocouts
6.145 6.1 45
Be Besc scri ri&e &e A>= anal analy ysi sis. s. ANSW!" Bivide inventory into three cate,ories &y importance of control- assi,n A items as the most important to control and = items ith little or no need of control.
@6.14 Bescri&e- in in ,eneral,eneral- the procedure procedure for findin findin, , 9:. ANSW!" Write the the e7uation to represent the e7uality" 9rder =ost K 3oldin, =ost- and solve for :. @6.1/0 xplain the &asic difference8s; difference8s; &eteen the simple 9: model and the roduction !un Dodel. ANSW!" In the simple 9:- inventory delivery is assumed to occur instantaneously- hile in the roduction !un Dodel- inventory is assumed to &e produced 8or GdeliveredH; over time. @6.1/1 Is the comment comment G#he only function of safety stoc is to protect a,ainst fluctuations in demand durin, lead timeH an accurate depiction of the purpose of the function of safety stoc ANSW!" Safety stoc certainly does miti,ate the effect of fluctuation in demand durin, lead time. It also helps miti,ate the effect of 7uality pro&lems and other such issues on the supply side.
12%
