A retail outlet sells a seasonal product for $9 per unit. The cost of the produc
ID: 457257 • Letter: A
Question
A retail outlet sells a seasonal product for $9 per unit. The cost of the product is $7 per unit. All units not sold during the regular season are sold for half the retail price in an end-of-season clearance sale. Assume that demand for the product is uniformly distributed between 1 and 10.
a) What’s the recommended order quantity?
b) What is the probability of stockout using your order quantity in part a)?
c) To keep customers happy and returning to the store later, the owner feels that stockout should be avoided if at all possible. What’s your recommended order quantity if the owner is willing to tolerate a 0.15 probability of a stockout?
d) Using your answer to part c), what is the goodwill cost you are assigning to a stockout?
Explanation / Answer
This is an inventory management problem of Single-Period Model.
Cost per unit = $ 7.
Revenue per unit = $ 9.
Salvage value per unit = $ 4.5 (half of $ 9).
Demand for the product is uniformly distributed between 1 and 10.
Excess cost, Ce = Cost per unit – Salvage value per unit = 7 – 4.5 = $ 2.5.
Shortage cost, Cs = Revenue per unit - Cost per unit = 9 – 7 = $ 2.
Service Level, SL = Cs / (Cs + Ce) = 2 / (2 + 2.5) = 2 / 4.5 = 0.444.
a)
Hence, optimal stocking level should satisfy demand 44.4% of the time. For a uniform distribution, this will be at a point equal to minimum demand plus 44.4% of the difference between maximum and minimum demands.
Optimum stocking quantity, So = 1 + 0.444 (10 – 1) = 4.996 5 units.
Recommended order quantity = So = 5 units.
b) Probability of stockout = 1 –SL = 1 - 0.444 = 0.556.
c) Probability of stockout = 0.15.
Service Level, SL = 1 – 0.15 = 0.85.
Optimum stocking quantity, So = 1 + 0.85 (10 – 1) = 8.65 9 units.
Recommended order quantity = So = 9 units.
d) SL = Cs / (Cs + Ce).
0.85 = Cs / (Cs + 0.25).
Solving above equation, we get Cs = $ 14.17.
Goodwill cost corresponding to a probability of stockout of 0.15 = Cs (i.e., shortage cost) = $ 14.17.
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