1. Evaluate Brown’s proposal that he should use the holding cost for one unit for the two-week period as the cost of average in the newsvendor model. Calculate this average cost for the Great White SKU.
The holding cost for one unit for two-week period = Cost of average
Holding cost = 25%
Cost/unit = $20
Annual holding cost = 25% of $20 = 0.25 * 20
Annual holding cost = $5 per unit
25 bi-weeks in a year
Cost of Average = $5/25 = $0.2/unit for two-week period.
2. Evaluate Brown’s proposal that he should use the margin on one unit (=retail price – wholesale price) as the cost of underage.
Cost of underage = margin on one unit
Retail price = $21
Wholesale price = $20
Cost of underage = $21 – $20
Cost of Underage = $1
3. Calculate the critical fractile based on the underage and average costs given 1 and 2 above. This gives the optimal in-stock rate for those costs. The corresponding optimal order-up-to point is the smallest order-up-to point that has an in-stock rate equal to or higher than the critical fractile. Use your table of order-up-to points and in-stock rates to find the optimal order-up-to point based on your calculated critical fractile.
Critical Fractile = (cost of underage)/(cost of average + cost of underage)
= 1/(0.2 + 1)
Critical Fractile = 0.8333
Optimal Stock Rate = 83.33%
Using Excel sheet for different order up to point = 59 to 63 (Stock rate = 84% > 83.33%)
| Decision Variable | |
| Order up to Point | 59 |
| Total Results | |
| Total Demand | 2012 |
| Total Sales | 1905 |
| Average Inventory | 39.10 |
| Total Lost Sales (units) | 107 |
| Total Gross Profit | $1,905 |
| Total Inventory Holding Cost | $391.02 |
| Net Profit | $1,514 |
| In-Stock Rate | 84% |
| Fill Rate | 94.7% |
| Decision Variable | |
| Order up to Point | 60 |
| Total Results | |
| Total Demand | 2012 |
| Total Sales | 1913 |
| Average Inventory | 40.07 |
| Total Lost Sales (units) | 99 |
| Total Gross Profit | $1,913 |
| Total Inventory Holding Cost | $400.74 |
| Net Profit | $1,512 |
| In-Stock Rate | 84% |
| Fill Rate | 95.1% |
| Decision Variable | |
| Order up to Point | 61 |
| Total Results | |
| Total Demand | 2012 |
| Total Sales | 1921 |
| Average Inventory | 41.05 |
| Total Lost Sales (units) | 91 |
| Total Gross Profit | $1,927 |
| Total Inventory Holding Cost | $410.49 |
| Net Profit | $1,511 |
| In-Stock Rate | 84% |
| Fill Rate | 95.5% |
| Decision Variable | |
| Order up to Point | 62 |
| Total Results | |
| Total Demand | 2012 |
| Total Sales | 1929 |
| Average Inventory | 42.03 |
| Total Lost Sales (units) | 83 |
| Total Gross Profit | $1,929 |
| Total Inventory Holding Cost | $420.26 |
| Net Profit | $1,509 |
| In-Stock Rate | 84% |
| Fill Rate | 95.9% |
| Decision Variable | |
| Order up to Point | 63 |
| Total Results | |
| Total Demand | 2012 |
| Total Sales | 1937 |
| Average Inventory | 43 |
| Total Lost Sales (units) | 75 |
| Total Gross Profit | $1,937 |
| Total Inventory Holding Cost | $430.05 |
| Net Profit | $1,507 |
| In-Stock Rate | 84% |
| Fill Rate | 96.3% |
Optimal order up to point (average) = (59+60+61+62+63)/5
Optimal order up to point = 61
Question：
4. The number calculated from 3 does not match the order-up-to point determined in #1 (a-v). Brown wonders if his cost of underage depends on his order-up-to point. Evaluate Brown’s thought that if his order-up-to point is high enough, the cost of underage is close to his margin minus the holding cost, but as his order-up-to point gets lower and lower the cost of underage should get closer to just the margin.
5. Based on 4, the margin calculated in 2 is the maximum value of the cost of underage. Calculate the minimum value of the cost of underage and the corresponding order-up-to point. What is the maximum difference in net profits over the range of order-up-to points from the order point calculated in 3 to the order-up-to point calculated here?
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