Linear Programming SAP FOundation [PDF]

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Book Problem – Chapter 10 Self Test #4 Team Highlander: Michael Monahan



10/26/11



4.) Arnoff Enterprises manufactures the central processing unit (CPU) for a line of personal computers. The CPUs are manufactured in Seattle, Columbus, and New York and shipped to warehouses in Pittsburgh, Mobile, Denver, Lose Angeles, and Washington, D.C., for further distribution. The following table shows the number of CPUs available at each plant, the number of CPUS required by each warehouse, and the shipping costs (dollars per unit): Warehouse Plant



Pitssburgh Mobile



Denver 5 8 7



Los Angeles 9 30 10



Washington CPUs Available 10 9000 6 4000 4 8000



Seattle Columbus New York CPUs Required



10 2 1



20 10 20



3000



5000



4000



6000



3000



21,000



a. Develop a network representation of this problem. b. Determine the amount of that should be shipped from each plant to each warehouse to minimize the total shipping cost. c. The Pittsburgh warehouse just increased its order by 1000 units, and Arnoff authorized the Columbus plant to increase its production by 1000 units. Will this production increase lead to an increase or decrease in total shipping costs? Solve for the new optimal solution.



Solution:  Network Model:



 Linear Programming Model: !Objective Function; Find the optimal amounts to be shipped between each plant and warehouse to minimize shipping costs !X1 = amount shipped from Seattle to Pitssburgh !X2 = amount shipped from Seattle to Mobile !X3 = amount shipped from Seattle to Denver !X4 = amount shipped from Seattle to Los Angeles !X5 = amount shipped from Seattle to Washington !X6 = amount shipped from Columbus to Pitssburgh !X7 = amount shipped from Columbus to Mobile !X8 = amount shipped from Columbus to Denver !X9 = amount shipped from Columbus to Los Angeles !X10 = amount shipped from Columbus to Washington !X11 = amount shipped from New York to Pitssburgh !X12 = amount shipped from New York to Mobile



!X13 = amount shipped from New York to Denver !X14 = amount shipped from New York to Los Angeles !X15 = amount shipped from New York to Washington;



 Linear Programming Solution: Global optimal solution found. Objective value: Infeasibilities: Total solver iterations:



Seattle to Denver Seattle to Los Angeles Columbus to Mobile New York to Pittsburgh New York to Los Angeles New York to Washington



Units 4000 5000 4000 3000 1000 3000 Total Original



150000.0 0.000000 8



Cost 20,000 45,000 50,000 4,000 10,000 12,000 141,00 150,000 150,000-141,000 = 9,000 in savings