The owner of a certain pork store uses (Q, R) model to manage its inventory. The

Question

The owner of a certain pork store uses (Q, R) model to manage its inventory. The owner hopes that the proportion of the cycles with stock-out cannot be larger than 10%. Fixed cost of replenishmem is $15 per order. The holding cost is $18 per pound per day. The mean and variance of the demand per week is 100 and 25, respectively. The lead time is three weeks (seven days per week). Find the Q and R so that the desired service level can be achieved. Find the safety stock based on the given service level. Due to the space limitation of warehouse, and the safety stock can only be set as 8. How to update the original target of the service level? Suppose the owner is also interested in another service level focusing on the proportion of the demand that can be met by the stock without backordering, using the result of R obtained in part to find such service level. Suppose the owner would like to determine its reordering point so that the proportion of demands that are met from stock without backordering can be 95%, what is the reordering point? Suppose the owner would like to achieve both the target in part e) and the original target (.i.e., the target you used in )), what will be the reorder point?

Explanation / Answer

a) Q = (2*100*15/1.8/7)^0.5 = 15.43,

ROP = dL + ss = 100*3 + 1.28*25*3^0.5 = 355.5, here 1.28 is the Z-value corresponding to 90% service level.

b) = Safety stock = 1.28*25*3^0.5 = 55.5,

c), With safety stofk = 8, service level will be determined by Z-value. Z-value = 8/25/3^0.5 = 0.184752. Probability function corresponding to this Z-value = 57.5%.

d)

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