Demand |
Probability |
100 |
0.04 |
120 |
0.07 |
140 |
0.08 |
160 |
0.12 |
180 |
0.16 |
200 |
0.17 |
220 |
0.13 |
240 |
0.09 |
260 |
0.07 |
280 |
0.05 |
300 |
0.02 |
The unit cost of beer is $2 per bottle, the price of beer is $4 per bottle and Richie pays $30 for collecting beers from the distributor every time he gives a new order. He estimates the holding cost as 20% per year.
a) Compute the service level and fill rate when Richie uses an inventory policy (I, S) where I=1 week and S = 220 bottles. Also compute the service level and fill rate when S = 260 bottles.
b) Compute the average size of an order in each case (i.e. when S=220 and when S= 260). In each case, how much inventory does Richie carry in each replenishment cycle on average? Compute the total cost of expected (inventory holding) + (stockout cost) in each case. Which of the two order-up-to levels, S=220 or S=260, makes more sense from a cost minimization perspective? (Hint: Stockout cost = Profit lost) What do you advise Richie to do?
Answer :
Calculate the average demand based on the probability by multiplying probability with demand and totaling at the end.
Demand | Probability | |
100 | 0.04 | 4 |
120 | 0.07 | 8.4 |
140 | 0.08 | 11.2 |
160 | 0.12 | 19.2 |
180 | 0.16 | 28.8 |
200 | 0.17 | 34 |
220 | 0.13 | 28.6 |
240 | 0.09 | 21.6 |
260 | 0.07 | 18.2 |
280 | 0.05 | 14 |
300 | 0.02 | 6 |
0 | 194 |
So average expected demand is 194
Lets calculate service level at S = 220
Service level = | 194/220 | 88.18% |
Lets calculate service level at S = 260
Service level = | 194/260 | 74.62% |
As the average demand 194 is below the stocking levels of 220 and 260, Richie will rarely face stock out issues.
Richie is a bar owner and would like to determine an ordering policy for beers. He...
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