Table 1: Lead Time Distribution a. Suppose that the reorder point is 12. Based o

Question

Table 1: Lead Time Distribution

a. Suppose that the reorder point is 12. Based on the lead time demand distribution shown on Table 1, what is the probability that stockout would not occur?

b. Suppose that the reorder point is 10 and order quantity is 30. Based on the lead time demand distribution shown on the table above, what is the ll rate?

c.  Suppose that the demand during lead time follows a normal distribution N(50,20). In order to maintain a service level (Type I)= 80%, what would be our reorder point?

d. Suppose the mean absolute deviation of the forecast errors is 10. Calculate the safety stock to achieve 80% type I service level target.

Explanation / Answer

(a)

Probability that stockout would not occur = Probability that the lead time demand is more than the ROP

= P(D > 12) = 20%

(b)

Fill Rate = 1 - (Expected Shortage per cycle, ESC / Q)

ESC with ROP being 10 = (12 - 10) x 0.3 + (14 - 10) x 0.2 = 1.4

Fill rate = 1 - (1.4 / 30) = 95.33%

(c)

Z = NORMSDIST(80%) = 0.788

Mean = 50, SD = 20

ROP = Average lead time demand + Safety Stock = 50 + Z x 20 = 50 + 0.788*20 = 65.76 or 66

(d)

Note that for large samples, the MAD provides a good estimate of the standard deviation (more formally, the MAD becomes a consistent estimator of the population standard deviation)

So, take SD = 10

Safety stock = Z x SD = 0.788 x 10 = 7.88 or 8

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