A regional automotive dealership

A regional automotive dealership has 3 showrooms in 3 locations from which it sells hydrogen-powered passenger vehicles. Demands at these locations are normally distributed (relevant parameters are shown in the table below) and are uncorrelated. Currently, each retail location carries its own cycle and safety stocks, serving its customer base independently, with a company-wide 99% cycle service level policy, which dictates that no customer demand go unsatisfied and every backlog is eventually satisfied at a cost of $500/car. For uniformity, each location uses a periodic review inventory control system with a review period of 30 days. The dealership remains open 365 days in a year. The delivery lead time from the manufacturer of these cars is 12 days. It costs $2,000/year to hold an automobile in inventory at its car lots at these 3 locations. Management is considering implementing an inter-location, lateral transshipment policy, under which a demand shortfall at any location will be satisfied through a same day delivery from either of the other two locations (if the product is available). The cost of such a lateral local shipment is expected to be $200 per car. Can this proposed policy be economically justified? What are the expected annual cost savings, if any, resulting from this policy? If this lateral transshipment policy is adopted, is it advisable to reduce the dealership’s cycle service to 95%, from a cost standpoint? 

Annual Demand (units) 

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Location       Mean       Std. Deviation 

1                    2000           500

2                    5000           1000

3                    3000            900

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