======== A distributor is planning to calculate the optimal service level given the following information. Based on past data, sales response rate…

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A distributor is planning to calculate the optimal service level given the following information. Based on past data, sales response rate is 0.12% change in revenue for a 1% change in the service level (fill rate). Trading margin is $18 per item, inventory carrying cost is 24% per year, annual sales through the warehouse is 120,000 items. Cost of each item is $75, demand standard deviation is 300 items for a week, and the lead time is 4 weeks.

a. Calculate ΔP 

ΔP =    Trading Margin x Sales Response Rate x Annual Sales

            =$18 x 0.12% x120,000

            =$2,592

® Therefore, Delta_P (ΔP) is $2592

b. Calculate ΔC 

ΔC =   Annual Carrying cost x Standard Product Cost X Demand Standard Deviation x lead – time x ΔZ

            = 24% x $75 x 300 x 4 x ΔZ

            = 21600ΔZ

® Therefore, Delta_C (ΔC) is 21600ΔZ

c. Calculate ΔZ 

Set ΔP = ΔC

ΔZ = (ΔP / ΔC)

            = 2592 / 21600

            = 0.12

® Therefore, ΔZ is 0.12

d. Determine the optimal service level 

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