Exercise 13-2: Green Thumb
Inputs Problem 1 Improved Forecasting
Anticipated demand 100 100
Standard deviation 40 15
Unit costs $150 $150
Sales price $200 $200
Disposal value $50 $50
Inventory holding costs $20 $20
Salvage value $30 $30
Cost of understocking $50 $50
Cost of overstocking $120 $120
Outputs Improvements
Optimal cycle service level 0.2941 0.2941 0.0000
Optimal order size 78.34 91.88 13.53
Expected profits $2,657 $4,121 $1,464
Expected overstock 7.41 2.78 -4.63
Expected understock 29.07 10.90 -18.17
The general manager at Green Thumb decides to conduct extensive market research for its new product.
At the end of the market research, the manager estimates demand to be normally distributed, with a mean
of μ= 100 and a standard deviation of σ= 15. How should Green Thumb alter its production plans in
Exercise 1 as a result of the market research? How much increase in profit is it likely to observe? How
does the improved forecast affect the demand lost by Green
Thumb because of understocking? Use cost and price information from Exercise 1.
CR – 12/3/2020 10:04 AM Page 1 13-2.xlsx – 13.2
Exercise 13-2: Green Thumb
Inputs Problem 1 Improved Forecasting
Anticipated demand 100 100
Standard deviation 40 15
Unit costs 150 150
Sales price 200 200
Disposal value 50 50
Inventory holding costs 20 20
Salvage value =C21-C22 =E21-E22
Cost of understocking =C20-C19 =E20-E19
Cost of overstocking =C19-C25 =E19-E25
Outputs Improvements
Optimal cycle service level =C26/(C26+C27) =E26/(E26+E27) =E30-C30
Optimal order size =NORMINV(C30,C17,C18) =NORMINV(E30,E17,E18) =E31-C31
Expected profits
=(C20-C25)*C17*NORMDIST((C31-C17)/C18,0,1,1)-(C20-C25)*C18*NORMDIST((C31-C17)/C18,0,1,1)-C31*C27*NORMDIST(C31,C17,C18,1)+C31*C26*(1-NORMDIST(C31,C17,C18,1))
=(E20-E25)*E17*NORMDIST((E31-E17)/E18,0,1,1)-(E20-E25)*E18*NORMDIST((E31-E17)/E18,0,1,1)-E31*E27*NORMDIST(E31,E17,E18,1)+E31*E26*(1-NORMDIST(E31,E17,E18,1))
=E33-C33
Expected overstock
=(C31-C17)*NORMDIST((C31-C17)/C18,0,1,1)+C18*NORMDIST((C31-C17)/C18,0,1,0)
=(E31-E17)*NORMDIST((E31-E17)/E18,0,1,1)+E18*NORMDIST((E31-E17)/E18,0,1,0)
=E35-C35
Expected understock
=(C17-C31)*(1-NORMDIST((C31-C17)/C18,0,1,1))+C18*NORMDIST((C31-C17)/C18,0,1,0)
=(E17-E31)*(1-NORMDIST((E31-E17)/E18,0,1,1))+E18*NORMDIST((E31-E17)/E18,0,1,0)
=E36-C36
The general manager at Green Thumb decides to conduct extensive market research for its new product. At the end of the market research, the manager estimates demand to be normally distributed, with a mean
of μ= 100 and a standard deviation of σ= 15. How should Green Thumb alter its production plans in Exercise 1 as a result of the market research? How much increase in profit is it likely to observe? How does
the improved forecast affect the demand lost by Green Thumb because of understocking? Use cost and price information from Exercise 1.