Problem 10-31 (Algorithmic) A product with an annual demand of 900 units has c,-

Question

Problem 10-31 (Algorithmic) A product with an annual demand of 900 units has c,-$34.00 and Ch-$6Th e demand exhibits some variability such that the lead-time demand follows a normal obability distribution with -25 and -5. Note: Use Appendix 8 to identify the areas for the standard normal distribution. a. What is the recommended order quantity? Round your answer to the nearest whole number. 0"-| 1011 b. what are the reorder point and safety stock if the firm desires at most a 7% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number. Record point - safety stock 35 c. If a manager sets the reorder point at 31, what is the probability of a stock-out on any given order cycle? If required, round your answer to four decimal places P(Stockout/cycle) - 11.5 How many times would you expect stock-out during the year if this reorder poi nt were used? Round your answer to the nearest whole number. Number of Orders -

Explanation / Answer

(a)
Recommended order quantity = Economic order quantity (EOQ)

EOQ = sqrt(2.D.Co/Ch) = sqrt(2*900*34/6) = 101

(b)

7% stockout probability in a cycle = 93% service level

Z = NORMSINV(93%) = 1.475 (since the Appendix B has not been added, I use excel formula for finding Z)

Safety Stock = Z x = 1.475 x 5 = 7.38 or 7 (rounded off)

Reorder point = average lead time demand + safety stock = 25+7= 32 (depending on rounding off rule of safety stock)

(c)

ROP = 31
So, Safety stock = 31 - 25 = 6
or, Z x = 6 or Z = 6/5 = 1.2
CSL = NORMSDIST(1.2) = 88.5%

P(Stockout per cycle) = 100% - 88.5% = 11.5%

No. of times stockouts will be there = No. of orders x 11.5%
= (900/101) x 11.5% = 1.02 or 1 (rounded off)

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