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 - saety stock d
emand during *rotection inter+a = L = 90 ' = 2%0 bags 1aety stock = z σdLT 0.!4 . 3en t3e desired cyceser+ice e+e is !0&, z = 0!4 σ dLT = σ d L ' = $5 = 25.9! or 2 1aety stock = 0.!4 2 = 2$.!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 3odin 3oding g cost cost :nnua :nnua orderi ordering ng cost cost D 4,!0 S = "54 500 Q Q 500 (2%& )("$$.%0) H = 2 2 = "505.44 = "%!9.%5 3en t3e E6; is used t3ese two costs are equa. 3en Q = 500 , t3e annua 3oding cost is arger t3an t3e ordering cost, t3ereore Q is too arge. ota costs are "%!9.%5 "505.44 = "$,295.$9. e. :nnua :nnua 3odin 3oding g cost cost :nnua :nnua orderi ordering ng cost cost Q 400 D 4,!0 )("$$.%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
1amor an !0& cyceser+ice e+e z = 0.!4 σ P L = σ d P + L +
σ P + L =
(.$24) 2% + $! = 4$.0! z σ P + L
1aety stock = = 0.!4(4$.0!) = '4.5$ or '5 bags T = :+erage demand during t3e *rotection inter+a - 1aety stock T = ($545) - '5 = %$0 b. n #robem $0, t3e Q system required a saety stock o 22 bags to ac3ie+e an !0& cyce ser+ice e+e. 3ereore, t3e P system requires a saety stock t3at is arger by ('5 8 22) = $' bags. c. >rom #robem $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 woud be "',229.$ 8 "2,!$.!2 = "'%.'4. b. 3en t3e cyceser+ice e+e is 9%&, z = $.!!. 3ereore, z σ d L 2 1aety stock = = ($.!!)($00) = $.!!($4$.42) = 25.!%, or 2 bo?es d R = L - 1aety 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 1aety stock = z σ P + L σ P L = σ d +
σ P + L =
P + L
($00) 2 + 2
= 200 units. 1aety stock = $.!!(200) = '% units T = :+erage demand during t3e *rotection inter+a - 1aety stock T = $000(2 - 2) - '% T = 4,'% units
KRM Pg 356, Prob 4. (a a! b" Step 1: acuate t3e E6; at t3e owest *rice (".50)@ EOQ =
2 DS H
=
2('50)(50)($00) .'!(.5)
= $$90.4 or $$90 balls
3is soution is ineasibe. e cannot buy $$90 bas at a *rice o ".50 eac3. 3ereore we cacuate t3e E6; at t3e ne?t owest *rice ("%.25)@ 2 DS 2('50)(50)($00) EOQ = = = $$2%.$' or $$2% balls .'!(%.25) H 3is soution is easibe. Step 2: acuate tota costs at t3e easibe E6; and at 3ig3er discount quantities@ C=
Q
2
C $$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 costy on an annua basis to buy 5,000 basebas at a time. b. 3e tota annua costs associated wit3 buying 5,000 bas at a time are "$20,2%5.00
