W$.$ W$.$ Grainger, Inc., is a leading supplier of maintenance, repair, and operating $($MRO$)$ products to businesses and institutions in the United States, Canada, and Mexico, with an expanding presence in Japan, India, China, and Panama. The company works with more than $5,000$ suppliers and runs an extensive website $($www $.$grainger.com$)$ where Grainger offers nearly $1\mathrm{.}5$ million products. The products range from industrial adhesives used in manufacturing, to hand tools, janitorial supplies, lighting equipment, and power tools. When something is needed by one of its customers, it is often needed quickly, so quick service and product availability are key drivers to Grainger$$s success.

Your assignment$*$ involves studying U$.$S$.$ distribution in Grainger$$s supply chain. Grainger works with over $250$ suppliers in the China and Taiwan region. These suppliers produce products to Grainger$$s specifi cations and ship to the United States using ocean freight carriers from four major ports in China and Taiwan. From these ports, product is shipped to U$.$S$.$ entry ports in either Seattle, Washington, or Los Angeles, California. After passing through customs, the $20-$ and $40-$foot containers are shipped by rail to Grainger$$s central distribution center in Kansas City, Kansas. The containers are unloaded and quality is checked in Kansas City. From there, individual items are sent to regional warehouses in nine U$.$S$.$ locations, a Canada site, and Mexico.

Grainger: U$.$S$.$ Distribution

In the United States approximately $40$ percent of the containers enter in Seattle, Washington, and $60$ percent at the Los Angeles, California, port. Containers on arrival at the port cities are inspected by federal agents and then loaded onto rail cars for movement to the Kansas City distribution center. Variable costs for processing at the port are $$7\mathrm{.}00$ per cubic meter $($CBM$)$ in both Los Angeles and Seattle. The rate for shipping the containers to Kansas City is $$0\mathrm{.}0017$ per CBM per mile.

In Kansas City the containers are unloaded and processed through a quality assurance check. This costs $$6\mathrm{.}00$ per CBM processed. A very small percentage of the material is actually sent back to the supplier, but errors in quantity and package size are often found that require accounting adjustments.

Items are stored in the Kansas City distribution center, which serves nine warehouses in the United States. Items are also sent to warehouses in Canada and Mexico, but for the purposes of this study we focus on the United States. The nine warehouses each place orders at the distribution center that contains all the items to be replenished. Kansas City picks each item on the order, consolidates the items onto pallets, and ships the items on $53-$foot trucks destined to each warehouse. Truck freight costs $$0\mathrm{.}0217$ per CBM per mile. The demand forecasts for the items purchased from China$/$Taiwan for next year in cubic meters and shipping distances are given in the following table.

DEMAND $($CBM$)$ DISTANCES

WAREHOUSE AVERAGE MILES FROM KANSAS CITY MILES FROM LOS ANGELES MILES FROM SEATTLE

Kansas City $20,92001,5801,870$

Cleveland $17,1707902,3002,490$

Newark $24,7501,1902,7102,840$

Jacksonville $15,1401,1302,5002,940$

Chicago $22,8804901,9601,970$

Greenville $15,1408902,3902,940$

Memphis $17,1704801,8002,390$

Dallas $22,8804701,4502,140$

Los Angeles $34,3001,58001,160$

Total $190,350$

Although a high percentage of demand was from warehouses either south or east of Kansas City, the question has surfaced concerning the $34,300$ CBM $($approximately $18$ percent of the total volume$)$ that will be shipped to Kansas City and then shipped back to the Los Angeles warehouse. This double$-$transportation could potentially be eliminated if a new distribution center were built in Los Angeles. The idea might be to ship material arriving at the Seattle port by rail to a new Los Angeles distribution center, which would be located at the current location of the Los Angeles warehouse.

It is estimated that the Los Angeles facility could be upgraded at a one$-$time cost of $$1,500,000$ and then operated for $$350,000$ per year. In the new Los Angeles distribution center, containers would be unloaded and processed through a quality assurance check, just as is now done in Kansas City. The variable cost for doing this would be $$7\mathrm{.}00$ per CBM processed, which includes the cost to move the containers from the Los Angeles port to the distribution center.

After the material is processed in Los Angeles, the amount needed to replenish the Los Angeles warehouse $(34,300$ CBM per year on average$)$ would be kept and the rest sent by rail to Kansas City. It would then be directly stocked in the Kansas City distribution center and used to replenish the warehouses. They expect that very little would need to be shipped back to the Los Angeles warehouse after the new system was operating for about six months.

Grainger management feels that it may be possible t