You operate a store that sells sports equipment and you need to place your yearly order for ski jackets. The retail price of a jacket is $600. Your cost is $120 and worst case, you can discount it for $60. You estimate that yearly demand is 200 units with a standard deviation of 60 units. How many should you buy for this season?
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To determine how many ski jackets you should buy for this season, you can use a statistical technique called the Newsvendor Model. This model helps you determine the optimal quantity to order by considering the trade-off between the cost of excess inventory (overstock) and the cost of stockouts (understock).
To apply the Newsvendor Model, you first need to calculate the critical ratio (CR), which is the ratio of the cost of overstock to the sum of the cost of overstock and the cost of understock.
In this case, the cost of overstock is the difference between your cost of $120 and the worst-case discount price of $60, which is $120 - $60 = $60. The cost of understock is the retail price minus your cost, which is $600 - $120 = $480. Therefore, the CR is $60 / ($60 + $480) = 0.1111.
Next, you need to calculate the Z-score, which quantifies the number of standard deviations away from the mean your desired service level corresponds to. A service level is the percentage of demand that you want to satisfy without stockouts. In this case, we'll use a desired service level of 95%, which corresponds to a Z-score of 1.645.
With the Z-score and the standard deviation of demand, you can calculate the safety stock. The safety stock is the buffer quantity you need to have on hand to account for the uncertainty in demand. It is calculated by multiplying the Z-score by the standard deviation. In this case, the safety stock is 1.645 * 60 units = 98.7 units.
Finally, to determine the optimal order quantity, you can use the formula:
Order quantity = expected demand + safety stock.
In this case, the expected demand is 200 units. So the optimal order quantity is 200 + 98.7 = 298.7 units.
However, since you cannot order a fraction of a unit, you should round up the order quantity to the nearest whole number. Therefore, you should order 299 ski jackets for this season.