Question

1) Fun Colors Inc. is a firm selling supplies for home improvement and decorating projects. At their founding in 1920, they chose to compete in the market by ensuring high product availability and variety. To support this strategy, they decided to keep 1-gallon cans of 75 different colors in the store with sufficient inventory that they would be able to meet customer demand for any color 98% of the time. A marketing study had shown that the demand for each color was more or less the same and independent of each other. The weekly demand forecast per color followed a normal distribution with a mean of 100 cans/week and a standard deviation of 40. The store ordered each colors from the factory located in Cincinnati, and the delivery time was around 2 weeks. Fun Colors paid $3.50/can.

a) How much safety stock of each color was required to support Fun Colors planned availability? (10 points)

b) Cost of capital for Fun Colors is 20% per year. What was Fun Colors’ annual holding cost for safety stock across all colors?

c) Shortly after Fun Colors entered the market, the industry’s technology changed tremendously. The competition was now implementing a new technology that enabled instant in-store customization of a color from one base-tone paint. To match the competition, Fun Colors examined switching to this new method of customization. To implement it, they would need to lease the mixing equipment. They would then stock a single base tone. (The dyes for coloring the base were produced locally and would only require a trivially small amount of in-store inventory.) The base paint would cost $3.50/gallon. Since the delivery for the base color would again be from Cincinnati, the lead-time would be 2 weeks.

There is a single vendor leasing the mixing equipment. What is the maximum Fun Colors should be willing to pay per month to lease the new machine?

Answer 1

Safety stock SS = z*σ*sqrt(L)

Here, z = 2.05 for 98% service level, σ = 40 per color and L = 2 weeks

Safety stock of each color = 2.05*40*sqrt(2) = 115.9 or 116 cans

Safety stock required for each color is 116 cans

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Cost of cans P = 3.50. Cost of capital is 20%. This means the holding cost H = 20% of 3.5 or 0.7

Holding cost for safety stock = SS*H = 116*0.7 = 81.2 per color

Total holding cost for safety stock per year = 81.2*75 = 6090

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If all the colors are now can be produced by the base color the aggregated standard deviation of demand is 40*sqrt(75) = 346.4 cans

This means the new safety stock = 2.05*346.4*sqrt(2) = 1004.26 cans or 1005 cans

This means the total holding cost for safety stock per year is 0.7*1005 = 703.5

This is a saving of 6090-703.5 = 5386.5

As long as they do not pay more than 5386.5 per year on leasing the equipment, they will be gaining with the new plan.

Maximum Fun Colors should be willing to pay per month is 5386.5/12 = 448.8