Dell assembles and sells its high end XPS15 laptops throughout the United States. XPS15 is a popular laptop and has received raving reviews from experts and customers.However, in the last couple of months there has been some serious logistics issues resulting in long delays in fulfilling customer orders. Nash Porter, a senior strategist at Dell, has been given the responsibility to figure out how to improve customer service while minimizing total transportation and inventory costs.

Dell divides up its national sales into four regions: East Coast, Midwest, Southwest, and West Coast. Each region is served by a regional sales distribution center. Dell operates three national distribution centers in Florida (serving East Coast and Southwest), Indiana (serving Midwest and West Coast), and Arizona (serving West Coast and Southwest). Dell assembles XPS15 in their main plant in Plano, Texas, and then ships them to the three national distribution centers where they are stored for shipment to the four regional sales distribution centers.The Plano plant has the capacity to produce 55,000 XPS15 per month. The shipments are scheduled for once a month. Dell maintains inventory both at the three national distribution centers as well as the four regional sales distribution centers.

The unit cost of shipping from the plant to national distribution centers or from national distribution centers to the regional distribution centers are given below. Dell also pays a fixed shipping cost, incurred every time a shipment is made of any quantity. Costs are the same for both months.

month. The shipments are scheduled 101 once listribution centers as well as the four regional sales distribution centers. The unit cost of shipping from the plant to national distribution centers or from national distribution enters to the regional distribution centers are given below. Dell also pays a fixed shipping cost, incurred every time a shipment is made of any quantity. Costs are the same for both months From To Unit Shipment Fixed Shipping Cost Cost Plano Indiana 10 5.000 Plano Arizona 8 4.000 Plano Florida 12 4,000 Indiana West Coast 10 3,000 Indiana Midwest 5.000 Arizona West Coast 3,000 Arizona Southwest 3.000 Florida East Coast 5,000 Florida Southwest 4.000 The unit inventory cost at the national distribution centers is $5 per unit per month. Theinventory cost at the regional sales distribution center is $ 10 per unit per month. Nash has asked the marketing department for a forecast of the demand for XPS15 for the four regional sales distribution centers for the next two months. The demand forecasts are shown below: West Coast September 20,000the demand for XPS15 for the four regional sales distribution centers for then nand forecasts are shown below. West Coast September 20,000 West Coast October 20,000 Midwest September 15.000 Midwest October 15.000 Southwest September 10.000 Southwest October 15.000 East Coast September 20.000 East Coast October 25,000 16arketing department also sent Nash estimated inventories at each distril it. Distribution Units Center National Distribution Center Indiana 6.000 Arizona 5.000 Florida 5.000 Regional Distribution Center West Coast 4.000 Midwest 5.000 Southwest 3.000 East Coast 2,000 would like to determine how many XPS15 units to manufacture each m o the distribution centers each month in order to minimize the total trans Currently there is no minimum inventory policy. This helps keep the in not allow for the flexibility to meet unant