question archive A retail store in Hanes Mall purchases computer software from a distributor for resale
A retail store in Hanes Mall purchases computer software from a distributor for resale
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A retail store in Hanes Mall purchases computer software from a distributor for resale. For an upcoming promotion, the retailer needs to determine the best order size for a one-time purchase. One of the products is a word processing program that will have a special sale price of $350. The retailer estimates the following demand schedule:
Demand Probability
50 0.1
55 0.2
60 0.2
65 0.3
70 0.15
75 0.05
Consider the following change made by the distributor. In order to reduce its risk, the distributor would refund $200 back to the store for only 80% of the returned items. For the remaining 20% of the returned items, the restocking charge is 40%, that is, the distributor would only return $150 to the store. Re solve the question to find the new optimal order quantity for the retailer and the new expected optimal profit.
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Answer:
Cost of the item, C = 200/0.8 = $250
Price of the software, P = $350
Expected salvage value for the returns, s = 200*fraction of returns getting $200 + 150*Fraction of returns getting $150
= 200*0.8 + 150*0.2 = $190
Therefore, Cost of underage, Cu = P - C = 350 - 250 = $100
Cost of overage, Co = C - s = 250 - 190 = $ 60
Critical Ratio, CR = Cu/(Cu + Co)
CR = 100/( 100 + 60) = 0.625
Cumulative probability for a demand 'x' = sum of probability of all the demands which are less than or equal to 'x'
Now, the optimal order quantity will be the least demand for which the cumulative probability, F(x) > = CR . We can see this happening for Demand = 65. Hence, the optimal order quantity = 65
Revenue = Minimum (Order Quantity, Demand)*P + Max(Order Quantity - Demand, 0)*s
Cost = (Order Quantity)*C
Profit = Revenue - Cost
Expected Profit = Profit * Corresponding Probability
New expected Optimal Profit = $5,780
PFA
