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22BAC-OM Operations Management
Questions:
Walmart Inventory
As a manager at Wal-Mart, you have just realized that the store frequently runs out of Nutella-spread jars. You are suspecting that there might be a problem with the replenishment policy. Thus, you have decided to gather more data.
The demand for Nutella turns out to be normally distributed. The mean demand for one week is 200 jars and the standard deviation for the weekly demand is 30 jars. Wal-Mart’s purchasing cost for Nutella is $4 per jar. The cost of holding one Nutella jar in the inventory is $1 per week. In addition, the store incurs a cost of $25 for placing an order and it takes 2 weeks to receive the order. Wal-Mart is using continuous-time (Q,ROP) policy to replenish its Nutella jar inventory. Based on this, please answer the following questions. Please assume that 1 year = 52 weeks.
a. How many Nutella jars should Wal-Mart order at a time?
b. What should be the reorder point if Wal-Mart wants to provide a 95% service level?
c. How much additional safety stock is needed if the service level is increased from 95% to 99%?
Geoff Gullo owns a small firm that manufactures “Gullo Sunglasses.” He has the opportunity to sell a particular seasonal model to Land’s End. Geoff offers Land’s End two purchasing options:
● Option 1: Geoff offers to set his price at $65 and agrees to credit Land’s End $40 for each unit Land’s End returns to Geoff at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise.
● Option 2: Geoff offers a price of $55 for each unit, but returns are no longer accepted. In this case, Land’s End throws out unsold units at the end of the season.
The season’s demand for this model will be normally distributed with mean of 200 and standard deviation of 125. Land’s End will sell those sunglasses for $100 each. Geoff’s production cost is $25
(a) How many pairs of sunglasses would Land’s End buy under option 1? Option 2?
(b) To help Land’s End choose which option to take, you have run a Crystal Ball simulation For a given quantity of sunglasses purchased, you simulated demand 1,000 times to estimate how many sunglasses would be sold and how many sunglasses would be leftover. Based on this information, which option will Land’s End choose?
|
Probability |
z-value |
Probability |
z-value |
|
0.99 |
2.326 |
0.89 |
1.227 |
|
0.98 |
2.054 |
0.88 |
1.175 |
|
0.97 |
1.881 |
0.87 |
1.126 |
|
0.96 |
1.751 |
0.86 |
1.080 |
|
0.95 |
1.645 |
0.85 |
1.036 |
|
0.94 |
1.555 |
0.84 |
0.994 |
|
0.93 |
1.476 |
0.83 |
0.954 |
|
0.92 |
1.405 |
0.82 |
0.915 |
|
0.91 |
1.341 |
0.81 |
0.878 |
|
0.90 |
1.282 |
0.80 |
0.842 |
22BAC-OM Operations Management
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