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121 Racke und and content: The Darby company manufactures and distributes meters 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 centre was established in Fort Worth, Texas, and later, as business expanded, a second distribution centre 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 centre 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 utilises newer and more efficient equipment as a result manufacturing cost is $0.50 per meter less than at the El Paso plant. Due to the company's rapid growth, not much attention had been paid to the efficiency of its supply chain, but Darby's management decided that it is time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centres is shown in Table 1 The quarterly production capacity is 30,000 meters at the older El Paso plant and 20,000 meters at the San Bernardino plant. Note that no shipments are allowed from the San Bernardino plant to the Fort Worth distribution centre. The company serves nine customer zones from the three distribution centres. The forecast of the number of meters needed in each customer zone for the next quarter is shown in Table 2 The cost per unit of shipping from each distribution centre to each customer zone is given in table 3 Note that some distribution centres cannot serve certain customer zones. These are indicated by dash In its current supply chain demand at the Dallas, San Antonio, Wichita, and Kansas City customer zones is satisfied by shipments from the Fort Worth distribution centre. In a similar manner, the Denver, Salt Lake City, and Phoenix customer zones are served by the Santa Fe distribution centres, and the Los Angeles and San Diego customer zones are served by the Las Vegas distribution centre To determine how many units to ship from each plant, the quarterly customer demand forecasts are aggregated at the distribution centres and a transportation model is used to minimise the cost of shipping from the production plants to the distribution centres Table 1. Shipping cost per unit from production plants to distribution centres ($) Distribution centre Plant Fort Worth Santa Fe Las Vegas El Paso 3.20 2.20 4.20 San Bernardino 1.20 3.90 Table 2. Quarterly demand forecast Customer zone Dallas San Antonio Wichita Kansas City Denver Salt Lake City Phoenix Los Angeles San Diego Demand (metres) 6300 4880 2130 1210 6120 4830 2750 8580 4460 Table 3. Shipping cost from the distribution centres to the customer zones Customer zone Distribution Dallas San Wichita Kansas Denver Salt Phoenix Los San centre Antonio City Lake Angeles Diego City Fort Worth 0.3 2.1 3.1 4.4 6 Santa Fe 5.2 5.4 4.5 6 2.7 4.7 3.4 3.3 2.7 Las Vegas 5.4 3.3 2.1 2.5 2.4 Assessment Tasks For the purpose of improving Darby Company's supply chain, you are asked to develop the Network Model for this problem. (Don't need to write objective function and constraints) (30 marks) 121 Racke und and content: The Darby company manufactures and distributes meters 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 centre was established in Fort Worth, Texas, and later, as business expanded, a second distribution centre 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 centre 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 utilises newer and more efficient equipment as a result manufacturing cost is $0.50 per meter less than at the El Paso plant. Due to the company's rapid growth, not much attention had been paid to the efficiency of its supply chain, but Darby's management decided that it is time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centres is shown in Table 1 The quarterly production capacity is 30,000 meters at the older El Paso plant and 20,000 meters at the San Bernardino plant. Note that no shipments are allowed from the San Bernardino plant to the Fort Worth distribution centre. The company serves nine customer zones from the three distribution centres. The forecast of the number of meters needed in each customer zone for the next quarter is shown in Table 2 The cost per unit of shipping from each distribution centre to each customer zone is given in table 3 Note that some distribution centres cannot serve certain customer zones. These are indicated by dash In its current supply chain demand at the Dallas, San Antonio, Wichita, and Kansas City customer zones is satisfied by shipments from the Fort Worth distribution centre. In a similar manner, the Denver, Salt Lake City, and Phoenix customer zones are served by the Santa Fe distribution centres, and the Los Angeles and San Diego customer zones are served by the Las Vegas distribution centre To determine how many units to ship from each plant, the quarterly customer demand forecasts are aggregated at the distribution centres and a transportation model is used to minimise the cost of shipping from the production plants to the distribution centres Table 1. Shipping cost per unit from production plants to distribution centres ($) Distribution centre Plant Fort Worth Santa Fe Las Vegas El Paso 3.20 2.20 4.20 San Bernardino 1.20 3.90 Table 2. Quarterly demand forecast Customer zone Dallas San Antonio Wichita Kansas City Denver Salt Lake City Phoenix Los Angeles San Diego Demand (metres) 6300 4880 2130 1210 6120 4830 2750 8580 4460 Table 3. Shipping cost from the distribution centres to the customer zones Customer zone Distribution Dallas San Wichita Kansas Denver Salt Phoenix Los San centre Antonio City Lake Angeles Diego City Fort Worth 0.3 2.1 3.1 4.4 6 Santa Fe 5.2 5.4 4.5 6 2.7 4.7 3.4 3.3 2.7 Las Vegas 5.4 3.3 2.1 2.5 2.4 Assessment Tasks For the purpose of improving Darby Company's supply chain, you are asked to develop the Network Model for this problem. (Don't need to write objective function and constraints) (30 marks)