22. Tax Preparers, Inc. works 250 days per year. The com- pany uses adding machi

Question

22. Tax Preparers, Inc. works 250 days per year. The com- pany uses adding machine tape at a rate of eight rolls per day. Usage is believed to be normally distributed with a standard deviation of three rolls during lead time. The cost of ordering the tape is $10, and holding costs are $0.30 per roll per year. Lead time is two days. (a) Calculate the economic order quantity. (b) What reorder point will provide an order-cycle (c) How much safety stock must the company hold to (d) What reorder point is needed to provide an order- (e) How much safety stock must the company hold to service level of 97 percent? have a 97 percent order-cycle service level? cycle service level of 99 percent? have a 99 percent order-cycle service level?

Explanation / Answer

Daily demand, d = 8

Annual demand, A = 8*250 = 2000

Holding cost, h = 0.3 per unit per year

Ordering cost, k = 10

a) Economic order quantity, Q = SQRT(2*A*k/h)

= SQRT(2*2000*10/0.3)

= 365

b) For 97 percent service level, z-statistic = NORMSINV(.97) = 1.88

Lead time L = 2 days

Std dev of lead time demand, s = 3

Reorder point = dL + z*s = 8*2+1.88*3 = 21.64

c) Safety stock for 97 percent service level = z*s = 1.88*3 = 5.64

d) z-stat for 99 percent sl = NORMSINV(.99) = 2.33

Reorder point = 8*2+2.33*3 = 23

e) Safety stock for 99 percent sl = 2.33*3 = 7

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