Stateline Shipping and Transport Company; Case Problem 4

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The assignment is taken from the text Introduction to Management Science by Bernard W. Taylor 10th edition Stayer University page 273-274. The Manager of the South Atlantic office of the Stateline Shipping and Transport Company is attempting to obtain a huge contact with a potential business partner Polychem, for the collection and removal of their waste products. The potential client has six plants: Kingsport, Danville, Macon, Selma, Columbus, and Allentown where the waste products need to be picked up and then delivered to three disposal site: whitewater, los canos, duras. In this assignment I will assist the manager with developing a model and solving the optimal routes for the effectively removing the waste from each of the six plants to the three disposal sites; Xij is the number of barrels being transported per week from plant i-j to the disposal site; and i=1,2,3,4,5,6 and j=A,B,C. the objective function is to minimize the total transportation cost for all shipment, which is the sum of the individual shipping costs from each of the six plants to each of the three waste disposal sites. Minimize Z= 12x1A+15x1B+17x1C+14x2A+9x2B+10x2c+13x3A+20x3B+11x3C+17x4A+16x4B+19x4C+7x5A+14x5B+12x5C+22x6A+16x6B+18x6C. Then there has to be accountable for the model constraints which is 9 for each plant supply and one of each of the three’s demand waste disposal site; another constraint for the barrels of waste available per week at the three plants able to accommodation. x1A+x1B+x1C=35, x2A+x2B+x2C=26, x3A+x3B+x3C=42, x4A+x4B+x4C=53, x5A+x5B+x5C=29, x6A+x6B+x6C=38

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