The Hudson Systems company has a product that must be shipped from a production facility, then...
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The Hudson Systems company has a product that must be shipped from a production facility, then to a warehouse, and then to a retail store. The product is manufactured in either Atlanta (with production capacity of 800), Boston (with a production capacity of 500), or Chicago (with a production capacity of 700). From the production facilities, the product is then shipped to a warehouse to be stored. These warehouses are located in Edison and Fargo. Lastly, from the warehouse, the product goes to a retail store in either Houston (with demand of 900), Indianapolis (with a demand of 500), or Jacksonville (with a demand of 500). The table below shows the costs (in dollars) of shipping the product Ediso Fargo Houston Indianapoli Jacksonvill n S Atlanta 6 4 Boston 1 8 Chicag 3. 1 Edison Fargo 6 3 4 2 3 8 Determine how the product should be shipped from the production facilities to the warehouses, and then from the warehouses to the retail stores in order to minimize cost You may use your notes and then Excel or SAS to do this problem. But not the internet (other than SAS) or other people. Production Facilities Supply Atlanta 800 Boston 500 Chicago 700 Retail Stores Demand Warehouses Houston 900 Edison Fargo Indianapolis 500 Jacksonville 500 The objective equation is: Cost 6*x[1.4]+4*x[1,5]+1*x[2.4]+8*x[2.5]+3*x[3,4]+1*x[3.5]+6*x[4.1]+3*x[4,2]+4*x(4.3}+2*x[5.1]+3*x15. 21+8'x[5.3] With the constraints: Supply in ATL: x[1.4]+x[1.5] =500 Warehouse in Edison: x[1.4]+x[2,4]+x[3,4]-x[4.1]-[4.2]-[4,3]=0 Warehouse in Fargo: x[1.5]+x[2.5]+x[3.5]-x[5.1]-x[5.2]-x[5.3]=0 In SAS, this is my code: proc optmodel; var xi in 1..5, jin 1..5)>=0; min C = 6*x[1.4]+4*x[1,5]+1*x[2.4]+8*x[2.5]+3*x[3,4]+1*x(3,5]+6*x[4.1]+3*x(4.2]+4*x[4.3]+2*x[5.1]+3*x(5, 21+8*x[5.3]; con SupplyATL: x[1.4]+x[1.5] con DemandIndi: x[4,2]+x(5,2]>=500; con Demand Jacksonville: x[4.3]+x[5.3]>=500; con WarehouseEdison: x[1.4]+x[2,4]+x[3,4]-x[4.1]-x[4.2]-[4,3]=0; con WarehouseFargo: x[1,5]+x[2.5]+x[3.5]-x(5,1)-x[5.2]-x[5.3]=0; solve; print x And that produces this result: x 1 2 3 4 5 1 000 0 700 2 00 0 500 0 3 0 0 0 0 700 4 0 0 500 00 00 5 900 500 0 What this means is the company should ship: 700 from Atlanta to Fargo 500 from Boston to Edison 700 from Chicago to Fargo And then 700 from Edison to Jacksonville 900 from Fargo to Houston 500 from Fargo to Indianapolis The Hudson Systems company has a product that must be shipped from a production facility, then to a warehouse, and then to a retail store. The product is manufactured in either Atlanta (with production capacity of 800), Boston (with a production capacity of 500), or Chicago (with a production capacity of 700). From the production facilities, the product is then shipped to a warehouse to be stored. These warehouses are located in Edison and Fargo. Lastly, from the warehouse, the product goes to a retail store in either Houston (with demand of 900), Indianapolis (with a demand of 500), or Jacksonville (with a demand of 500). The table below shows the costs (in dollars) of shipping the product Ediso Fargo Houston Indianapoli Jacksonvill n S Atlanta 6 4 Boston 1 8 Chicag 3. 1 Edison Fargo 6 3 4 2 3 8 Determine how the product should be shipped from the production facilities to the warehouses, and then from the warehouses to the retail stores in order to minimize cost You may use your notes and then Excel or SAS to do this problem. But not the internet (other than SAS) or other people. Production Facilities Supply Atlanta 800 Boston 500 Chicago 700 Retail Stores Demand Warehouses Houston 900 Edison Fargo Indianapolis 500 Jacksonville 500 The objective equation is: Cost 6*x[1.4]+4*x[1,5]+1*x[2.4]+8*x[2.5]+3*x[3,4]+1*x[3.5]+6*x[4.1]+3*x[4,2]+4*x(4.3}+2*x[5.1]+3*x15. 21+8'x[5.3] With the constraints: Supply in ATL: x[1.4]+x[1.5] =500 Warehouse in Edison: x[1.4]+x[2,4]+x[3,4]-x[4.1]-[4.2]-[4,3]=0 Warehouse in Fargo: x[1.5]+x[2.5]+x[3.5]-x[5.1]-x[5.2]-x[5.3]=0 In SAS, this is my code: proc optmodel; var xi in 1..5, jin 1..5)>=0; min C = 6*x[1.4]+4*x[1,5]+1*x[2.4]+8*x[2.5]+3*x[3,4]+1*x(3,5]+6*x[4.1]+3*x(4.2]+4*x[4.3]+2*x[5.1]+3*x(5, 21+8*x[5.3]; con SupplyATL: x[1.4]+x[1.5] con DemandIndi: x[4,2]+x(5,2]>=500; con Demand Jacksonville: x[4.3]+x[5.3]>=500; con WarehouseEdison: x[1.4]+x[2,4]+x[3,4]-x[4.1]-x[4.2]-[4,3]=0; con WarehouseFargo: x[1,5]+x[2.5]+x[3.5]-x(5,1)-x[5.2]-x[5.3]=0; solve; print x And that produces this result: x 1 2 3 4 5 1 000 0 700 2 00 0 500 0 3 0 0 0 0 700 4 0 0 500 00 00 5 900 500 0 What this means is the company should ship: 700 from Atlanta to Fargo 500 from Boston to Edison 700 from Chicago to Fargo And then 700 from Edison to Jacksonville 900 from Fargo to Houston 500 from Fargo to Indianapolis
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Related Book For
Practical Management Science
ISBN: 978-1305250901
5th edition
Authors: Wayne L. Winston, Christian Albright
Posted Date:
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