Solutions to Inventory Management Practice Problems

KRM Pg 338, Prob 10 Sam’s Cat Hotel

a. Economic order quantity d 

 = 90/week   D = (90 bags/week)(52 weeks/yr) = 4,!0 S = "54 #rice = "$$.%0  H = (2%&)("$$.%0) = "'.$  EOQ =

2 DS   H 

=

2(4,!0)("54) "'.$

=

$59,949.'%  = '99.9', or 400 bags.

ime between orders, in weeks Q 400 = = 0.0!54% years = 4.44 weeks  D 4!0  b. eorder *oint,    R = demand during *rotection inter+a - saety stock  d 

emand during *rotection inter+a =  L = 90  ' = 2%0 bags 1aety stock = z σdLT   0.!4 . 3en t3e desired cyceser+ice e+e is !0&,  z  = 0!4 σ  dLT  = σ  d   L '  = $5 = 25.9! or 2 1aety stock = 0.!4  2 = 2$.!2, or 22 bags  R  = 2%0 + 22 = 292 c. nitia nitia in+ent in+entory ory *osi *ositi tion on = 67 - 1 8 6 6 = '20 '20 - 0 8 0 '20 8 $0 = '$0. ecause in+entory *osition remains abo+e 292, 292 , it is not yet time to *ace an order. d. :nnua :nnua 3odin 3oding g cost cost :nnua :nnua orderi ordering ng cost cost  D 4,!0 S  = "54 500 Q Q 500 (2%& )("$$.%0)  H  = 2 2 = "505.44 = "%!9.%5 3en t3e E6; is used t3ese two costs are equa. 3en Q  = 500 , t3e annua 3oding cost is arger t3an t3e ordering cost, t3ereore Q is too arge. ota costs are "%!9.%5 "505.44 = "$,295.$9. e. :nnua :nnua 3odin 3oding g cost cost :nnua :nnua orderi ordering ng cost cost Q 400  D 4,!0 )("$$.%0)  H  =   (2%&)( S  "54 = 2 2 Q 400 = "'$.!0 = "'$.!0 ota o ta cost using E6; is "$,2'.0, w3ic3 is "'$.59 ess t3an w3en t3e order quantity is 500  bags.

KRM Pg 339, Prob 19

1amrom #robem $0, in+entory *osition, # = '20. 3e amount to reorder is T  8 # = %$0 8 '20 = '90.

KRM Pg 339, Prob 24, ood ounty 7os*ita a.  D = ($000 bo?es/wk)(52 wk/yr) = 52,000 bo?es  H  = (0.5)("'5/bo?)="5.25/bo?

2 DS 

 EOQ = C

=

C 900

=

C 545

=

 H 

Q

2

H

900 2 545 2

+

=

D Q

2 ( 52,000) ( "$5) "5.25

=

545.$ or 545 bo?es

S 

"5.25 + "5.25 +

52, 000 900 52, 000 545

"$5.00 = "', 229.$ "$5.00 = "2, !$.!2

3e sa+ings woud be "',229.$ 8 "2,!$.!2 = "'%.'4.  b. 3en t3e cyceser+ice e+e is 9%&, z  = $.!!. 3ereore,  z σ  d   L 2 1aety stock =  = ($.!!)($00)  = $.!!($4$.42) = 25.!%, or 2 bo?es d   R =  L - 1aety stock = $000(2) - 2 = 2,2 bo?es c. n a *eriodic re+iew system, ind target in+entory T , gi+en@  P  = 2 weeks  L = 2 weeks 1aety stock =  z σ   P + L σ   P   L = σ  d  +

σ   P + L =

 P +  L

($00) 2 + 2

 = 200 units. 1aety stock = $.!!(200) = '% units T  = :+erage demand during t3e *rotection inter+a - 1aety stock  T  = $000(2 - 2) - '% T  = 4,'% units

KRM Pg 356, Prob 4. (a a! b" Step 1: acuate t3e E6; at t3e owest *rice (".50)@  EOQ =

2 DS   H 

=

2('50)(50)($00) .'!(.5)

= $$90.4 or $$90 balls

3is soution is ineasibe. e cannot buy $$90 bas at a *rice o ".50 eac3. 3ereore we cacuate t3e E6; at t3e ne?t owest *rice ("%.25)@ 2 DS  2('50)(50)($00)  EOQ = = = $$2%.$' or $$2% balls .'!(%.25)  H  3is soution is easibe. Step 2: acuate tota costs at t3e easibe E6; and at 3ig3er discount quantities@ C=

Q

2

C $$2% =

H+

D Q

$,$2% 2

S + PD

A.'!("%.25)B +

$%,500 $,$2%

("$00) + "%.25($%,500)

C $$2% = "$,552.44 + "$,552.%9 + "$2,!%5.00 = "$29, 9!0.2' C 5000 =

5, 000 $%, 500 A.'!(".50)B + ("$00) + ".50($%,500) 2 5, 000

C 5000 = ",$%5.00 + "'50.00 + "$$', %50.00 = "$20,2%5.00

a. t is ess costy on an annua basis to buy 5,000 basebas at a time.  b. 3e tota annua costs associated wit3 buying 5,000 bas at a time are "$20,2%5.00