Case Problem: Specialty Toys: 1. Information Provided by The Forecaster
Case Problem: Specialty Toys: 1. Information Provided by The Forecaster
Case Problem: Specialty Toys: 1. Information Provided by The Forecaster
1.
Informationprovidedbytheforecaster
Atx=30,000,
z
1.96
20, 000
Normaldistribution
2.
5102
+15,000
z
P(stockout)=0.3365+0.5000=0.8365
+18,000
z
P(stockout)=0.1517+0.5000=0.6517
+24,000
z
P(stockout)=0.50000.2823=0.2177
+28,000
z
P(stockout)=0.50000.4418=0.0582
3.
Profitprojectionsfortheorderquantitiesunderthe3scenariosarecomputedbelow:
OrderQuantity:15,000
UnitSales
10,000
20,000
30,000
TotalCost
240,000
240,000
240,000
at$24
240,000
360,000
360,000
Sales
at$5
25,000
0
0
Profit
25,000
120,000
120,000
OrderQuantity:18,000
UnitSales
10,000
20,000
30,000
TotalCost
288,000
288,000
288,000
at$24
240,000
432,000
432,000
Sales
at$5
40,000
0
0
Profit
8,000
144,000
144,000
OrderQuantity:24,000
UnitSales
10,000
20,000
30,000
TotalCost
384,000
384,000
384,000
at$24
240,000
480,000
576,000
Sales
at$5
70,000
20,000
0
Profit
74,000
116,000
192,000
OrderQuantity:28,000
UnitSales
10,000
20,000
30,000
TotalCost
448,000
448,000
448,000
at$24
240,000
480,000
672,000
Sales
at$5
90,000
40,000
0
Profit
118,000
72,000
224,000
4.
Weneedtofindanorderquantitythatcutsoffanareaof.70inthelowertailofthenormalcurvefordemand.
Q 20, 000
0.52
5102
Q=20,000+0.52(5102)=22,653
Theprojectedprofitsunderthe3scenariosarecomputedbelow.
OrderQuantity:22,653
UnitSales
10,000
20,000
30,000
5.
TotalCost
362,488
362,488
362,488
at$24
240,000
480,000
543,672
Sales
at$5
63,265
13,265
0
Profit
59,183
130,817
181,224
Avarietyofrecommendationsarepossible.Thestudentsshouldjustifytheirrecommendationbyshowingthe
projectedprofitobtainedunderthe3scenariosusedinparts3and4.Anorderquantityinthe18,000to
20,000rangestrikesagoodcompromisebetweentheriskofalossandgeneratinggoodprofits.
Whilethestudentsdon'thavethebenefitofthefollowing,asingleperiodinventorymodel(sometimescalled
thenewsvendormodel)showshowtofindanoptimalsolution.Weoutlinethatsolutionbelow.
Asingleperiodinventorymodelrecommendsanorderquantitythatmaximizesexpectedprofitbasedonthe
followingformula:
P(Demand Q* )
where
istheprobabilitythatdemandislessthanorequaltotherecommendedorder
Q* cu
co
quantity, . isthecostofunderestimatingdemand(havinglostsalesbecauseofastockout)and isthe
costperunitofoverestimatingdemand(havingunsoldinventory).SpecialtywillsellWeatherTeddyfor$24
cu
perunit.Thecostis$16perunit.So, =$24$16=$8.Ifinventoryremainsaftertheholidayseason,
co
Specialtywillsellallsurplusinventoryfor$5aunit.So, =$16$5=$11.
8
P(Demand Q* )
0.4211
8 11
Q* 20, 000
0.20
5102
Theprofitprojectionsforthisorderquantityarecomputedbelow:
OrderQuantity:18,980
Sales
UnitSales
10,000
20,000
30,000
TotalCost
303,680
303,680
303,680
at$24
240,000
455,520
455,520
at$5
44,900
0
0
Profit
18,780
151,840
151,840