The Darby Company manufactures and distributes meter used to measure electric power consumption.

The Darby Company manufactures and distributes meter used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base throughout Texas. A distribution center was established in Ft. Worth, Texas later, as business expanded to the north, a second distribution center was established in Santa Fe, New Mexico.The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada, and Utah. With the growth of the West Coast business, the Darby Company opened a third distribution center in Las Vegas and just two years ago opened a second production plant in San Bernardino, California.Manufacturing costs differ between the company's production plants. The cost of each meter produced at the El Paso plant is $10.50. The San Bernardino plant utilizes new and more efficient; as a result, manufacturing costs are $.50 per meter less than at the El Paso plant.The company's rapid growth meant that not much attention was paid to the efficiency of the distribution system. Darby's management decided it is now time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centers is shown in Table 1 below.Table 1Shipping cost per unit ($) from prod. plants to distribution centers                        Distribution CenterPlant         Ft Worth    Sante Fe    Las VegasEl Paso        3.20         2.20        4.20San Bernardino ---          3.90        1.20The quarterly production capacity is 30,000 meters at the older ElPaso plant and 20,000 meters at the San Bernardino plant. Note that no shipments are allowed from the San Bernardino plant to the Ft. Worth distribution center.The company serves nine customer zones from the three distribution centers. The forecast of the number of meters needed in each customer zone for the next quarter is shown in Table 2.Table 2: Quarterly Demand ForecastCustomer Zone  Demand (meters)Dallas            6300San Antonio       4880Wichitia          2130Kansas City       1210Denver            6120Salt Lake City    4830Phoenix           2750Los Angeles       8580San Diego         4460 The cost per unit of shipping from each distribution center to each customer zone is given in Table 3. Note that some of the distribution centers cannot serve certain customer zones.Table 3: Shipping cost from distribution centers to customer zones ($)                                  Customer Zone                  San              Kansas      Salt Lake          Dallas  Antonio  Wichita  City  Denver  City   Phoenix  LA  SD Ft Wor     0.3    2.1       3.1     4.4   6.0     --      --    --   --Sante Fe   5.2    5.4       4.5     6.0   2.7     4.7     3.4  3.3 2.7 Las Vegas  --      --       --       --   5.4     3.3     2.   2.1 2.5 In the current distribution system, demand at the Dallas, San Antonio, Wichitia, and Kansas City customer zones is satisfied by shipments from the Ft. Worth distribution center. In a similar manner, the Denver, Salt Lake City, and Phoenix customer zones are served by the Santa Fe distribution, and the Los Angeles and San Diego customer zones are served by the Las Vegas distribution center. To determine how many units to ship from each plant, the quarterly customer demand forecasts are aggregated at the distribution centers and a transportation model is used to minimize the cost of shipping from the production plants to the distribution centers.Question for overall problem1. If the company does not change its current distribution strategy, what will its manufacturing and distribution costs be for the following quarter?2. Suppose that the company is willing to consider dropping the distribution center limitations; that is, customer could be served by any of the distribution centers for which costs are available. Can costs be reduced? By how much?3. The company wants to explore the possibility of satisfying some for the customer demand directly from the production plants. Inparticular, the shipping cost is $.30 per unit from San Bernardino to Los Angeles and $.70 from San Bernardino to San Diego. The cost for direct shipments from El Paso to San Antonio is $3.50 per unit. Can distribution costs be further reduced by considering these direct plant customer shipments?4. Over the next five years. Darby is anticipating moderate growth (5000 meters) to the North and West. Would you recommend that they consider plant expansion at this time?The problem should be worked out on ExcelThe Darby Company manufactures and distributes meter used to measureelectric power consumption. The company started with a small productionplant in El Paso and gradually built a customer base throughout Texas.A distribution center was established in Ft. Worth, Texas later, asbusiness expanded to the north, a second distribution center wasestablished in Santa Fe, New Mexico.The El Paso plant was expanded when the company began marketingits meters in Arizona, California, Nevada, and Utah. With the growth ofthe West Coast business, the Darby Company opened a third distributioncenter in Las Vegas and just two years ago opened a second productionplant in San Bernardino, California.Manufacturing costs differ between the company's production plants.The cost of each meter produced at the El Paso plant is $10.50. TheSan Bernardino plant utilizes new and more efficient; as a result,manufacturing costs are $.50 per meter less than at the El Paso plant.The company's rapid growth meant that not much attention was paid tothe efficiency of the distribution system. Darby's management decidedit is now time to address this issue. The cost of shipping a meterfrom each of the two plants to each of the three distribution centers isshown in Table 1 below.Table 1Shipping cost per unit ($) from prod. plants to distribution centersDistribution CenterLas Vegas4.201.20The quarterly production capacity is 30,000 meters at the older ElPasoplant and 20,000 meters at the San Bernardino plant. Note that noshipments are allowed from the San Bernardino plant to the Ft. Worthdistribution center.The company serves nine customer zones from the three distributioncenters. The forecast of the number of meters needed in each customerzone for the next quarter is shown in Table 2.Table 2: Quarterly Demand ForecastCustomer Zone Demand (meters)630048802130121061204830275085804460The cost per unit of shipping from each distribution center to eachcustomer zone is given in Table 3. Note that some of the distributioncenters cannot serve certain customer zones.Table 3: Shipping cost from distribution centers to customer zones ($)Customer ZoneSalt LakePhoenix LA SD--3.4 3.3 2.72.1 2.5In the current distribution system, demand at the Dallas, San Antonio,Wichitia, and Kansas City customer zones is satisfied by shipments fromthe Ft. Worth distribution center. In a similar manner, the Denver,Salt Lake City, and Phoenix customer zones are served by the Santa Fedistribution, and the Los Angeles and San Diego customer zones areserved by the Las Vegas distribution center. To determine how many unitsto ship from each plant, the quarterly customer demand forecasts areaggregated at the distribution centers and a transportation model isused to minimize the cost of shipping from the production plants to thedistribution centers.Question for overall problem1. If the company does not change its current distribution strategy,what will its manufacturing and distribution costs be for the followingquarter?2. Suppose that the company is willing to consider dropping thedistribution center limitations; that is, customer could be served byany of the distributon centers for which costs are available. Can costsbe reduced? By how much?3. The company wants to explore the possibility of satisfying some forthe customer demand directly from the production plants. Inparticular, the shipping cost is $.30 per unit from San Bernardion toLos Angeles and $.70 from San Bernardion to San Diego. The cost fordirect shipments from El Paso to San Antonio is $3.50 per unit. Candistribution costs be frther reduced by considering these direct plantcustomer shipments?4. Over the next five years. Darby is anticipating moderate growth(5000 meters) to the North and West. Would you recommend that theyconsdier plant expansion at this time?