Problem 10-31 (Algorithmic) A product with an annual demand of 700 units has co-

Question

Problem 10-31 (Algorithmic) A product with an annual demand of 700 units has co-$32.00 and Ch-$7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with 25 and ? 5. Note: Use Appendix B to identify the areas for the standard normal distribution. a. What is the recommended order quantity? Round your answer to the nearest whole number. b, what are the reorder point and safety stock if the firm desires at most a 5% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number. Record point- Safety stock- . 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) How many times would you expect a stock-out during the year if this reorder point were used? Round your answer to the nearest whole number. Number of Orders -

Explanation / Answer

Q = 80 units

Corresponding Z value = NORMSINV ( 0.95 ) = 1.6448

Standard deviation of demand during lead time = 5 units

Therefore , safety stock = Z value x standard deviation of demand during lead time = 1.6448 x 5 = 8.224 ( 8 rounded to nearest whole number )

Reorder point = Mean lead time demand + safety stock = 25 + 8 = 33

REORDER POINT = 33

SAFETY STOCK = 8

31 = Mean demand during lead time + Safety stock

Or, 31 = 25 + Safety stock

Or , Safety stock = 31 – 25 = 6

Or, Z value x Standard deviation of demand during lead time = 6

Or, Z x 5 = 6

Or, Z = 6/5 = 1.2

Corresponding probability for Z = 1.2 as derived from standard normal distribution table = 0.88493

Therefore , in stock probability = 0.88493

Thus, stockout probability = 1 – 0.88493 = 0.11507

Total number of orders to be placed in a year = Annual demand / EOQ ( as in answer #a) = 700/80

Number of stockouts in a year

= Total number of orders to be placed in a year x stockout probability

= 700/80 x 0.11507

= 1.006 ( 1 rounded to nearest whole number )

PROBABILITY OF STOCKOUT IN ANY GIVEN CYCLE = 0.11507

NUMBER OF ORDERS DURING WHICH STOCK OUT IS EXPECTED IN A YEAR = 1

Q = 80 units

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