(Solved Homework): A highly perishable dairy product is ordered daily at a particular super market…

A highly perishable dairy product is ordered daily at a particular super market. The product, which costs $1.19 per unit, sells for $1.65 per unit. If units are unsold at the end of the day, the supplier will accept returns for a refund of $1 per unit. Daily demand is assumed to be normally distributed with a mean of 150 units and a standard deviation of 30 units.

a. What daily order quantity would you recommend to the super market?

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b. What is the probability that the super market will sell out of the item? It may be questioned why the supplier has chosen to offer almost a full refund for the product.

c. How many units would the super market order if the supplier offered only $0.25 as a refund? Or no refund, $0?

d. How would the supplier’s and retailer’s profits change as the refund changes from $1 to $0.25 to $0? (use specific numbers to fuel your answer here and assume a supplier production cost of $0. The numbers used can by hypothetical. The interest is in seeing what direction profits move in as the refund amount changes) Which refund amount would you recommend for the supplier?

Expert Answer

m Mean demand 150
s Std dev 30
C Cost 1.19
v Salvage value 1
P Selling price 1.65
Co Overage cost 0.19 (c-v)
Cu Underage cost 0.46 (p-c)
Cr Critical ratio 0.707692 Cu/(Co+Cu) Ans B
Q Quanitity 166.3997 (norminv(C,m,s)) Ans A
m Mean demand 150
s Std dev 30
C Cost 1.19
v Salvage value 0.25
P Selling price 1.65
Co Overage cost 0.94 (c-v)
Cu Underage cost 0.46 (p-c)
Cr Critical ratio 0.328571 Cu/(Co+Cu)
Q Quanitity 29.47181 (norminv(C,m,s)) Ans c
m Mean demand 150
s Std dev 30
C Cost 1.19
v Salvage value 0
P Selling price 1.65
Co Overage cost 1.19 (c-v)
Cu Underage cost 0.46 (p-c)
Cr Critical ratio 0.27879 Cu/(Co+Cu)
Q Quanitity 29.30213 (norminv(C,m,s)) Ans C


Salvage 1 0.25 0
Q 166.40 29.5 29.30
Margin Supplier 0.19 0.94 1.19
Margin Retailer 0.46 0.46 0.46
Profit supllier 31.62 27.70 34.87
Profit retailer 76.54 13.56 13.48

For supplier return should be at 0, as the profit for supplier is highest in this scenario

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