Exercise 13-4: Champion
Inputs
Current Policy
South America Option
Anticipated demand 20,000 20,000
Standard deviation 10,000 10,000
Unit costs $30 $30
Sales price $60 $60
Disposal value $25 $30
Inventory holding costs $5 $5
South America sale price $35
Shipping costs $5
Salvage value $20 $25
Cost of understocking $30 $30
Cost of overstocking $10 $5
Outputs
Optimal cycle service level 0.7500 0.8571
Optimal lot size 26,745 30,676
Expected profits $472,889 $521,024
Expected overstock 8,236 11,407
Champion manufactures winter fleece jackets for sale in the United States. Demand for
jackets during the season is normally distributed, with a mean of 20,000 and a standard
deviation of 10,000. Each jacket sells for $60 and costs $30 to produce. Any leftover
jackets at the end of the season are sold for $25 at the year-end clearance sale. Holding
jackets until the year-end sale adds another $5 to their cost. A recent recruit has
suggested shipping leftover jackets to South America for sale in the winter there rather
than running a clearance. Each jacket will fetch a price of $35 in South
America, and all jackets sent there are likely to sell. Shipping costs add $5 to the cost of
any jacket sold in South America. Would you recommend the South American option?
How will this decision affect production decisions at Champion? How will it affect
profitability? On average, how many jackets will Champion ship to South America each
season?
CR – 12/3/2020 10:04 AM Page 1 13-4.xlsx – 13.4
Exercise 13-4: Champion
Inputs Current Policy South America Option
Anticipated demand 20000 20000
Standard deviation 10000 10000
Unit costs 30 30
Sales price 60 60
Disposal value 25 =E23-E24
Inventory holding costs 5 5
South America sale price 35
Shipping costs 5
Salvage value =C21-C22 =E21-E22
Cost of understocking =C20-C19 =E20-E19
Cost of overstocking =C19-C27 =E19-E27
Outputs
Optimal cycle service level =C28/(C28+C29) =E28/(E28+E29)
Optimal production size =NORMINV(C32,C17,C18) =NORMINV(E32,E17,E18)
Expected profits
=(C20-C27)*C17*NORMDIST((C33-C17)/C18,0,1,1)-(C20-C27)*C18*NORMDIST((C33-C17)/C18,0,1,0)-C33*C29*NORMDIST(C33,C17,C18,1)+C33*C28*(1-NORMDIST(C33,C17,C18,1))
=(E20-E27)*E17*NORMDIST((E33-E17)/E18,0,1,1)-(E20-E27)*E18*NORMDIST((E33-E17)/E18,0,1,0)-E33*E29*NORMDIST(E33,E17,E18,1)+E33*E28*(1-NORMDIST(E33,E17,E18,1))
Expected overstock
=(C33-C17)*NORMDIST((C33-C17)/C18,0,1,1)+C18*NORMDIST((C33-C17)/C18,0,1,0)
=(E33-E17)*NORMDIST((E33-E17)/E18,0,1,1)+E18*NORMDIST((E33-E17)/E18,0,1,0)
Champion manufactures winter fleece jackets for sale in the United States. Demand for jackets during the season is normally distributed, with a mean of 20,000 and a standard deviation
of 10,000. Each jacket sells for $60 and costs $30 to produce. Any leftover jackets at the end of the season are sold for $25 at the year-end clearance sale. Holding jackets until the year-
end sale adds another $5 to their cost. A recent recruit has suggested shipping leftover jackets to South America for sale in the winter there rather than running a clearance. Each jacket
will fetch a price of $35 in South America, and all jackets sent there are likely to sell. Shipping costs add $5 to the cost of any jacket sold in South America. Would you recommend the
South American option? How will this decision affect production decisions at Champion? How will it affect profitability? On average, how many jackets will Champion ship to South
America each season?