$5\mathrm{.}3$ Golden Spice Inc. was established $20$ years ago in Los Angeles. It imports spice from Southeast Asia in bulk and repackages it for selling to various supermarkets and convenience stores. Its business has grown substantially and the company established regional distribution centers in Philadelphia, Chicago, and Orlando. The markets served by the four distribution centers are roughly equal in size. The monthly demand in each distribution center is independent and follows a normal distribution with a mean of $10,000lb$ and a standard deviation of $6,000lb.$ The total annual inbound and outbound transportation costs are $$220,000$ and $$480,000,$ respectively. The inventory holding cost is $$5$ per lb$/$year$.$ In recent years, due to increased competition, Golden Spice has to increase its CSL to $99\%.$ It was not able to shorten its replenishment lead time, which remains at $4$ months. As a result, the company's inventory holding cost has increased significantly. A supply chain consultant suggested that the company should close its regional distribution center so inventory can be aggregatra in its Los Angeles main distribution center. This will not only redua inventory holding cost but also reduce total inbound transportation cost by $50\%.$ In addition, the annual distribution center operating cost can be reduced by $$300,000.$ To maintain the same level of responsiveness, the consultant suggested using a combination of highway and air for outbound transportation. It was estimated that by doing so the outbound transportation cost will increase by between $140\%$ and $180\%.$ Assuming there is no change in Golden Spice's replenishment policy, should the company close its regional distribution centers?

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