The cost per unit of shipping from each distribution center to each customer zone is given...

    

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The cost per unit of shipping from each distribution center to each customer zone is given in the following table. Note that some distribution centers do not serve certain customer zones because the costs would be prohibitive. Customer zone DC Dal SA Wich KC Den SLC Pho LA SD FW 0.30 2.10 3.10 4.40 6.00 SF 5.20 5.40 4.50 6.00 2.70 4.70 LV - 5.40 3.30 3.40 3.30 2.40 2.10 2.70 2.50 In the current distribution system, demand at the Dallas, San Antonio, Wichita, 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 center, and the Los Angeles and San Diego cus- tomer zones are served by the Las Vegas distribution center. The El Paso plant supplies the Ft. Worth and Santa Fe distribution centers, while the Sacramento plant supplies the Las Vegas distribution center. You have been called in to make recommendations for improving the distribution system, and, in particular, to address the following issues. a. First, consider the problem of creating the minimum-cost production and distribution plan without the current distribution center limitations. In other words, customer zones would not necessarily be assigned to unique distribution centers, and distribution centers would not necessarily be assigned to unique plants. Write a LP formulation that determines the minimum- cost distribution plan with this added flexibility. Clearly describe all variables, objective, and constraints. b. Implement and solve your LP using Excel solver. c. Now, consider the problem of finding the minimum-cost production and distribution plan with the company's current restrictions regarding which distribution centers can serve which plants and customer zones. What changes would you need to make to your LP? d. Implement and solve the new LP using Excel solver. Make sure that the Excel file that you submit contains both the original LP and new LP in separate sheets. The cost per unit of shipping from each distribution center to each customer zone is given in the following table. Note that some distribution centers do not serve certain customer zones because the costs would be prohibitive. Customer zone DC Dal SA Wich KC Den SLC Pho LA SD FW 0.30 2.10 3.10 4.40 6.00 SF 5.20 5.40 4.50 6.00 2.70 4.70 LV - 5.40 3.30 3.40 3.30 2.40 2.10 2.70 2.50 In the current distribution system, demand at the Dallas, San Antonio, Wichita, 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 center, and the Los Angeles and San Diego cus- tomer zones are served by the Las Vegas distribution center. The El Paso plant supplies the Ft. Worth and Santa Fe distribution centers, while the Sacramento plant supplies the Las Vegas distribution center. You have been called in to make recommendations for improving the distribution system, and, in particular, to address the following issues. a. First, consider the problem of creating the minimum-cost production and distribution plan without the current distribution center limitations. In other words, customer zones would not necessarily be assigned to unique distribution centers, and distribution centers would not necessarily be assigned to unique plants. Write a LP formulation that determines the minimum- cost distribution plan with this added flexibility. Clearly describe all variables, objective, and constraints. b. Implement and solve your LP using Excel solver. c. Now, consider the problem of finding the minimum-cost production and distribution plan with the company's current restrictions regarding which distribution centers can serve which plants and customer zones. What changes would you need to make to your LP? d. Implement and solve the new LP using Excel solver. Make sure that the Excel file that you submit contains both the original LP and new LP in separate sheets.

Answer rating: 100% (QA)

a Let the decision variable xij represent the amount of product shipped from distribution center i t... View the full answer