# MANAGING SUPPLY CHAINS

a. What is Leaky Pipe’s optimal order quantity? information is available on the item. The firm operates

b. What is the optimal number of orders per year? so Weeks tn e Veer‘ r

c. What is the optimal interval (in working days) between Demand = 50’ooO umts/year l

Orders? Ordering cost = $35/order

d. What is the demand during the lead time? Herding eeer = $2/dnlr/Year

e. What is the reorder point? Average teed tnne = e Weeks

f. What is the inventory position immediately after an Standard devtetlon of Weekly demend = 125 umts

order has been placed? a. What is the economic order quantity for this item?

10. Sam’s Cat Hotel operates 52 weeks per year, 6 days per b. If Petromax wants to provide a 90 percent cycle-semim

week, and uses a continuous review inventory system. level, what should be the safety stock and the reorder

It purchases kitty litter for $1 1.70 per bag. The following point?

lnrerrnanen re avallanle about rneee bage 14. In a continuous review inventory system, the lead time 1

Demand = 90 bags/week for door knobs is 5 weeks. The standard deviation of de~

Order Cost ,_. $ 54 /Order mand drurinrg tlrlrtg lead time85 unitrs. Threrrdesirrercrl crycle

service eve 1S percent. e supp ier o oor o s

Annual holdme eoet ee 27 percent of Cost streamlined its operations and now quotes a one-week

Deeded eYele’3e1’V1ee leVel = 30 Percent lead time. How much can safety stock be reduced witbow

Lead time = 3 weeks (18 working days) r reducing the,99rpercent cycle-service level?

Standard deviation of weekly demand = 15 bags 15. In a two-bin inventory system, the demand for three-

Current on-hand inventory is 320 bags, with no open tnenleg bolts ennng tne e’Week leeornme ts notmeny

erdere er. beekerderer distributed, an average of 53 units per week. The

Wrr r rr Eo r Wrr rd b V rr r_ standard deviation of weekly demand 1S 5 units.

e” at le t e Q ‘. at Wee e t e eeeteee eee a. What is the probability of demand exceeding the reor-

between orders (in weeks)?

der point when the normal level in the second bin is

b. What Should Set units? are ‘ t

G. An inventory withdrawal Of 10 bags was just made. IS it b_ What is the probability of demand exceeding the

time to reorder? 130 units in the second bin if it takes 3 weeks to reca‘w

d. The store currently uses a lot size of 500 bags a replenishment erderr

(i.e., Q = 500) . What is the annual holding cost of this 16. Nationwide Auto Parts uses a periodic review inventory I

policy? Annual ordering cost? Without calculating the control systemfor one of its stock items. The review inter-

EOQ, how can you conclude from these two calcula- val is 6 weeks, and the lead time for receiving the materials»

tions that the current lot size is too large?’ ordered from its wholesaler is 3-‘weeks. Weekly demand is I

e. What would be the annual cost saved by shifting from normenV_ tnstnonteo’ Wnn e mean or too nnns and e sten

the 500-bag lot size to the EOQ? onto oevtenon ot no nn1ts°

ll. Consider again the kitty litter ordering policy for Sam’s a‘ lrgehat lsdttrtre evetehee enttr the stentretdatrifvlatton of

Cat Hotel in Problem 10. Vrtrertrnan utmg e pm ecrlon In ere ’ r rr

a. Suppose that the weekly demand forecast of 90 bags is e’ deSeeeeteeeéepeegsfirtggeeelgfleerertregrtfiirereg It the He

incorrect and actual demand averages only 60 bags per _ _ r

Week HOW much higher will total Costs her Owing to c. If 3§O units were in stock at the time of a periodic

the distorted EOQ caused by this forecast error? reVleW» new nlanl’ llnlle enellla be Ordered?

b_ Suppose that actual demand is 60 bags but that Ordering 17. In a P system, the lead time for a box of weed-killer is

costs are cut to only $6 by using the Internet to automate 2 Weeks the revtew pertod ts 1 Week‘ Detnand dutme

Order placing. However’ the buyer does not ten anyone, the protection interval averages 218 boxes, with a standairim

and the EOQ is not adjusted to reflect this reduction in S. devtatton or 40 boxes‘

HOW much higher W111 total Costs be, Compared to What a. What is the cycle-service level when the target inventory“

they could be if the EOQ were adjusted? is Sell at 300 bexeer

12_ In a Q System, the demand rate for Strawberry ice Cream b. In the fall season, demand for weed-killer decreases

is normally distributed, with an average of 300 pints buttttso becomes more ntghly Vertebte’ Assume teat

per week. The lead time is 9 weeks. The standard deviation oormg tne ten season’ demand onnng tne ntoteenoe

of weekly demand is 15 pinte interval is expected to decrease to 180 boxes, but win:

a standard deviation of 50 boxes. What would be the

a. What is the standard deviation of demand during the CyC1e_SerViCe level if management keeps the target

9‘Week lead rlrner inventory level set at 300 boxes?

b- Vlrher is the eVeTe8e demand during The 9’Weel< lead dme? 18. You are in char e of invento control of a hi hl succw-

S FY 8 Y

c. What reorder point results in a cycle-service level of fill Prdddet rerelled by Vo111‘ fiTm- Weeldl’ demand for

99 percent; item varies, with an average of 200 units and a standard

I 3 Petromax Enter rises uses a Continuous review rrrVerr_ deviation of 16 units. It is purchased from a wholesaler E

p , . a cost of $12.50 per unit. The supply lead time is 4 weeks

tory control system for one of its SKUs. The following Placing an Order Costs $5er and the inventory Carrying

338 PART 3 MANAGING SUPPLY CHAINS

a. ‘vVhat is Leaky Pipe’s optimal order quantity? information is available on the item’ The firm operates

50 weeks in a year.

b, What is the optimal number of orders per year? :

Depand 50,000 units/Year

c. What is the optimal interval (in working days) between Ordering gs51 : $35/order

orders?

Holding : $2/unit/Year

d. lVhat is the demand during the lead time? “ss1

Average lead time : 3 weeks

e. ‘vVhat is the reorder Point?

Standard deviation of weeklydem4nd

: 125 units

l. What is the inventory position immediateli after an

order has been Placed? a. ‘vVhat is the economic order quantity for this item?

10. Sam’s Cat Hotel operates 52 weeks per yellr, 6 days per b. If Petromaxwants to provide a90 percent

level, what should be the safety stock and the reork

week, and uses a continuous review inventory system’

point?

It purchases kitty litter for $11.70 per bag’ The following

information is available about these bags’ t 4. In a continuous review inventory system, the lead time

: 90 bags/week

for door knobs is 5 weeks. The standard deviation ofde-

Demand

mand during the lead time is 85 units’ The desired ry*-

Order cost: 954/order service level is 99 percent. The supplier ofdoor knobs

Annual holding cost : 27 percent of cost streamlined its operations and now quotes a one-weel

Desired cycle-service level : 80 percent Iead time. How much can safety stock be reduced wi

reducing the-99 percent cycle-service level?

Lead time : 3 weeks (18 working daYs)

deviation of weekly demand : 15 bags 15. In a two-bin inventory system, the demand for three-

Standard

inch lag bolts during the 2-week lead time is normally

Current on-hand inventoryis 320 bags, with no open distribited, with an average of 53 units per week’ The

orders or backorders. standard deviation of weekly demand is 5 units’

a. rVhat is theEOQ? rVhat would be the average time a. Mhat is the probability o! tlbmand exceeding the reo

between orders (in weeks)?

b. What should Rbe? set at 130 units?

c. An inventory withdrawal of 10 bags was justmade’ Is it b. Mhat is the probability of demand exceeding the

time to reorder? 130 units in ihe second bin if it takes 3 weeks to

a replenishment order?

d. The store currently uses a lot size of 500 bags

(i.e., Q : 500).What is the annual holding cost of this 16. Nationwide Auto Parts uses a periodic review inventory

policy? Annual ordering cost?Without’calculating the control systemfor one of its stockitems. The reviewinter-

iOQ, t o- you conclude from these two calcula- val is 6 wleks, and the lead time for receiving the materi*

“uncurrent lot sizeis too large?

tions that the ordered from its wholesaler is 3weeks. Weekly demandir

normally distributed, with a mean of 100 units and a star

e. What would be the annual cost saved by s$ifting from dard deviation of20 units.

the 500-bag lot size to the EoQ?

a. lVhat is the average and the standard deviation of

11. Consider again the kitty litter ordering policy for Sam’s demand during the protection interval?

Cat Hotel in Problem 10.

b. ‘vVhat shoutd be the target inventorylevel if the firm

a. Suppose that the weekly demand forecast of 90 bags is desires 97.5 percent stockout protection?

iniorrect and actual demand averages only 60 bags per were in stock at the time of a periodic

c. If 350 units

week. How much higher will total costs be, owing to review, how many units should be ordered?

the distorted EOQ caused by this forecast error?

17. In a Psystem, the lead time for a box of weed-killer is

b’ Suppose that actual demand is 60 bags but that ordering 2 weeks and the reviewperiod is 1 week Demand during

costs are cut to only $6 by using the Intemet to automate the protection interval averages 218 boxes, with a

order placing. However, the buyer does not tell anyone’ deviation of40 boxes.

and the EOQ is not adjusted to reflect this reduction in S’

a. What is the cycle-service levelwhen the target

How much higher wili total costs be, compared to what

is set at 300 boxes?

they could be if the EOQ were adjusted?

b. In the fall season, demand for weed-killer decreases

12. In a Q system, the demand rate for strawberr!’ ice cream but also becomes more highlyvariu6ls’ 655urns that

is normally distributed, with an average of 300 pints during the fall season, demand during the protection

per week.ihe lead time is 9 weeks. The standard deviation intervll is expected to decrease to 180 boxes, butwift

of weekly demand is 15 Pints. a standard deviation of 50 boxes. lVhatwould be the

a. lVhat is the standard deviation of demand during the cycle-service level if management keeps the target

9-weeklead time? inventorylevel set at 300 boxes?

b. What is the average demand during the 9-weeklead time? t B. You are in charge of inventory control of a highly

succtr

ful product retailed by your firm. Weekly demand for tffi

c. What reorder point results in a cycle-service level of item varies, with an average of 200 units and a standard

deviation of 16 units. It is purchased from a wholesalert

99 Percent?

13. Petromax Enterprises uses a continuous review inven- a cost of $12.50 per unit. The supply lead time is 4 weelc”

tory control tysi”m for one of its SI(Us’ The following Placing an ordei costs $50, and the inventory carrying

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