A firm uses a one-week periodic review inventory system. A two-day lead time is

Question

A firm uses a one-week periodic review inventory system. A two-day lead time is needed for any order, and the firm is willing to tolerate an average of one stockout per year. a. Using the firm’s service guideline, what is the probability of a stockout associated ??????????with each replenishment decision? b. What is the replenishment level if demand during the review period plus lead-time period is normally distributed with a mean of 60 units and a standard deviation of 12 units? c. What is the replenishment level if demand during the review period plus lead-time period is uniformly distributed between 35 and 85 units?

Explanation / Answer

a) For a one week review period, considering 52 weeks in a year, Probability of stockout = 1 stockout / 52 weeks = 1.92 %

b) For 1.92% stockout probability, service level = 1 - 1.92% = 98.08 %

z = NORMSINV(0.9808) = 2.07

Replenishment level = demand during the review period plus lead-time + z * Standard deviation

= 60 + 2.07*12

= 85

c)

Replenishment level = lower limit of demand during the review period plus lead-time + service level * difference of maximum and minimum demand

= 35 + 0.9808*(85-35)

= 84

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