Assume the company operated 250 days per year, expects to use 120,000 units per

Question

Assume the company operated 250 days per year, expects to use 120,000 units per year and uses a perpetual review inventory control system. Assume further they use Banner Freightways which has an average transit time of 3 days with a standard deviation of 2 days, and daily demand is normally distributed with a standard deviation of 50 units. The unit cost continues to be $480. The annual cost of carrying inventory has been recalculated to be 2% per month of the value of the part.

A) Calculate the Economic Order Quantity (EOQ)

B) Calculate the necessary safety stock to cover 98% of the replenishment cycles.

C) Assume North Eastern has an average lead time of 5 days with a 4 day standard deviation. How much lower should its rate be compared to Banner’s in order to offset the service differences between the two carriers?

Explanation / Answer

A)

Annual holding cost = unit price * carrying cost rate = 480*2%*12 = 115.2

Cost to process an order = 80

EOQ = SQRT(2*Annual demand * Ordering cost / Holding cost)

= SQRT(2*120000*80/115.2) = 408

B)

C)

Annual Demand D = 120,000 Days per year Y = 250 Average Daily Demand µ = D/Y 480 Standard Deviation of Daily Demand D = 50 Lead Time (Days) L = 3 Standard Deviation of Lead Time L = 2 Service level = 98% Z-value corresponding to Service Level Z = NORMSINV() 2.05 Safety stock ss = Z(L*D2 + µ2*L2 ) 1,976

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