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Bicycle Retailer (Centralized Inventory) GreatLake Bicycle is a high-end bike store in Chicago. It has two...

Bicycle Retailer (Centralized Inventory)

GreatLake Bicycle is a high-end bike store in Chicago. It has two shops, one in Museum Park, the other is in River North. The cycle service level is set to be 95% in both shops. The weekly demand in Museum Park shop is normally distributed with a mean of 50 and a standard deviation of 25. The weekly demand in River North is normally distributed with a mean of 70 and a standard deviation of 20. Whenever a shop makes a replenishment order, it takes 3 weeks for the bike to arrive at each shop.

(a) If the two shops manager their inventory separately, what is the safety stock in each store? What is the total safety stock?

(b) If GreatLake Bicycle rents a room in downtown Chicago as a central warehouse, serving both shops, what is the safety stock in the central warehouse? The replenishment lead time is still 3 weeks, it takes no time to deliver a bicycle from the central warehouse to the retail shop. Assuming demands are independent.

(c) What if the demands in the two shops are negatively correlated with the correlation coefficient of -0.5? Keep all the other conditions in (b)?

(d) What if the demands in the two shops are perfectly positively correlated? Perfect positive correlation means the correlation coefficient is +0.5.

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Answer #1

(a) What is the safety stock in each store?

SS of River North = 100

SS of Museum Park = 125

(b) If GreatLake Bicycle rents a room on IIT DTC campus as a central warehouse, serving both shops, what is the safety stock in the central warehouse? The replenishment lead time is still 3 weeks, it takes no time to deliver a bicycle from the central warehouse to the retail shop. Assuming demands are independent.

SS = 113

(c) What if the demands in the two shops are negatively correlated with the correlation coefficient of -0.5? Keep all the other conditions in (b)?

SS = +10

(d) What if the demands in the two shops are perfectly positively correlated? Perfect positive correlation means the correlation coefficient is +0.5.

SS = +18

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