Question: An electronics manufacturer produces circuit boards in Chicago, IL and distributes its products through two regional warehouses in Newark, NJ and Denver, CO. In the current distribution system, the United States is partitioned into two major regions: Eastern and Western. While the Newark warehouse serves the customers in the Eastern region, the Denver warehouse serves the Western region. Typically it takes four weeks to satisfy an order placed by the two warehouses to the manufacturer.

In recent years the company has experienced significant pressure to reduce costs. Therefore, the company is considering centralizing the distribution function at one of the two existing locations. The company would like to maintain the current service level of 94 percent. To perform an analysis, the company has identified a typical product, Product X. The following table provides historical data that includes monthly demand in the two regions for Product X:

Month                     1         2         3          4        5          6

Denver                 200      230      180      220      300      250

Newark                 280      260      320      350      310      300

The ordering cost is $1000 per order while inventory carrying cost is $8 per unit per month. Also, shipping costs from Chicago to Denver and Newark are $12 and $10 per unit, respectively, and the average transportation costs from Denver and Newark to their corresponding customers are both equal to $15 per unit.

However, if Denver becomes the centralized warehouse, the average transportation cost to the Eastern region customers will be $20, while if Newark becomes the centralized warehouse, the average transportation cost to the Western region customers will be $21. Finally, feel free to round your numbers to the nearest integer and use a continuous review inventory system.

Calculate the average and standard deviation of monthly demand at Newark and Denver warehouses.

Calculate the total inventory carrying costs per month under the current decentralized system.Please show all your work

If the company decides to centralize the distribution function, which regional warehouse should be chosen (i.e., Denver or Newark) to minimize the total cost?Why?Please show all your work!