The annual demand for sugar at a local soft drink company is normally distribute

Question

The annual demand for sugar at a local soft drink company is normally distributed with a mean of 800 tons and a standard deviation of 25 tons. The sugar sells for $500 each ton, and the annual inventory holding cost rate is 10%. Ordering costs are $5 per order. The delivery time for sugar is 5 working days. Assume that there are 250 working days in a year.

1.Determine the optimal order quantity.

2.What size of safety stock should the company keep at a service-level of 90%?

3.Suppose they keep 8 extra tons in inventory as a safety stock. What is the service-level obtained?

4.Evaluate the fill rate( B beta )for a safety stock of 5 tons.

5.What is the expected number of units short per year?

6.Compare the level of safety stock for each policy a alpha=B beta=0.95.

Explanation / Answer

Annual demand, D = 800 tons

Daily demand, d = 800/250 = 3.2 ton

SD of daily demand, = 25/250 = 1.58

Ordering cost, S = $ 5

Holding cost, H = 500*10% = $ 50

Lead time, L = 5 days

1) Optimal order quantity = (2DS/H) = (2*800*5/50) = 12.65 tons

2) For 90% service level, z = NORMSINV(.90) = 1.28

Safety stock = zL = 1.28*1.58*5 = 4.53 tons

3) With 8 extra tons, safety stock = 4.53+8 = 12.53

z = 12.53/(1.585) = 3.55

Service level = NORMSDIST(3.55) = 0.9998 or 99.98 %

4) For safety stock of 5 tons, z = 5/(1.585) = 1.415

Corresponding value of L(z) = .0355

Fill rate = 1 - L(z)*/d = 0.9825 or 98.25 %

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