A product with an annual demand of 900 units has C $34.00 and C $6. The demand e

Question

A product with an annual demand of 900 units has C $34.00 and C $6. The demand extitits some variablity such that the lead-time demand follows normal probability distribution with -25 and o-s. 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 7% probabity of stock-out on any given order cycle? if required, round your answers to the nearest whole number Record point- Safety stock- C. If a manager sets the reorder point at 31, what is the probabilty of a stock out on any oiven order cydle? I required, round your answer to four decimal places P(Stockout/cydle) - d your answer to the nearest whole number Number of Orders - Preious

Explanation / Answer

Annual demand = 900 units

Ordering cost = $ 34

Holding cost = $6

Recommended order quantity = EOQ = Sqrt (( 2* Annual demand * ordering cost)/holding cost)

= sqrt( 2*900*34/6) = 100.995 = 101 units

(B)

Service level = 100 % - probability of stock out required = 100 -7 = 93%

z value corresponding to 93% = 1.48 ( from z table)

Safety stock = Z value * sigma

Given ,

Mean = 25

Sigam = 5

Safety stock = 5* 1.48 = 7.4 = 8 units

Reorder point = Mean + saftey stock = 25 + 8 = 33 units

(C)

Reorder point = 31 units

safety stock = Reorder point - mean = 31 -25 = 6 units

Z level = safety stock / sigma = 6/5 = 1.2

Probability (at Z = 1.2) = 0.3849

Service level (from Z table) = 0.5 + 0.3849 = 0.8849 = 88.5%

P(stock out) = 1-0.8849 = 0.1151 = 11.5%

No. of orders = Annual demand / quantity ordered = 900/101 = 9 orders

  

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