Consider a paint retailer who sells 100 different colors of paints. Assume that

Question

Consider a paint retailer who sells 100 different colors of paints. Assume that weekly demand for each color is independent and is normally distributed with a mean of 40 and a standard deviation of 20. The replenishment lead time from the paint factory is two weeks and the retailer aims for a CSL=0.95.

(1) How much safety stock in total will the retailer have to hold if paint is mixed at the factory and held in inventory at the retailer as individual colors?

(2) How much safety stock in total will the retailer have to hold if the retailer holds base paint (supplied by the paint factory) and mixes colors on demand?

Explanation / Answer

Mean weekly demand, m = 40

Std dev of weekly demand, s = 20

Lead time, L = 2 weeks

z value for CSL 0.95 = NORMSINV(0.95) = 1.645

(1) Safety stock of each individual color = z*s*L = 1.645*20*2 = 46.52

Total safety stock of 100 colors = 100*46.52 = 4652

(2) Aggregate mean demand, = 40*100 = 4000 per week

SD of aggregate demand, s = 20100 = 200   (because the demand of each color is independent)

Safety stock of base paint = 1.645*2002 = 465

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