Polychem wants Stateline to pick up and transport waste products from its six plants to three waste disposal sites. The chemical wastes that will be hauled can be hazardous to humans and the environment if they leak. A number of towns and communities in the region where the plants are located prohibit hazardous materials from being shipped through their municipal limits. Shipments must be handled carefully and transported at reduced speeds and traverse circuitous routes. Calculations for cost of shipping a barrel from each of the six plants to each of the three disposal sites is:
WASTE DISPOSAL SITE
Plant Whitewater Los Canos Duras
Kingsport $12 $15 $17
Danville 14 9 10
Macon 13 20 11
Selma 17 16 19
Columbus 7 14 12
Allentown 22 16 18
The plants generate the following amounts of waste products each week:
PLANT WASTE PER WEEK (bbl)
The three waste sites of Whitewater, Los Canos and Duras can accommodate a maximum of 65, 80, and 105 barrels per week respectively.
The manager is considering using each of the plants and waste disposal site as intermediate shipping points. Trucks would be able to drop a load at a plant or disposal site to be picked up and carried to the final destination by another truck and vice versa. Stateline would not incur any handling costs because Polychem has agreed to take care of all local handling of the waste materials at the plants and the waste disposal sites. The only cost Stateline incurs is the actual transportation cost. The manager wants to consider the possibility that it may be cheaper to drop and pick up loads at intermediate points rather than ship them directly. The estimated shipping costs per barrel between each of the six plants is:
PLANT Kingsport Danville Macon Selma Columbus Allentown
Kingsport $____ $6 $4 $9 $7 $8
Danville $6 _____ 11 10 12 7
Macon $5 11 _____ 3 7 15
Selma $9 10 3 ____ 3 16
Columbus $7 12 7 3 ____ 14
Allentown $8 7 15 16 14 ____
the estimated shipping cost per barrel between each of the three waste disposal sites is:
WASTE DISPOSAL SITE WHITEWATER LOS CANOS DURAS
Whitewater $______ $12 $10
Los Canos $12 $___ $15
Duras $10 $15 $___
The manager wants to determine the shipping routes that will minimize Stateline’s total cost in order to develop a contract proposal to submit to Polychem for waste disposal. She wants to know if it would be cheaper to ship directly from the plants to the waste site or if she should drop and pick up some loads at the various plants and waste sites. Develop a model to assist the manager and solve the model to determine the optimal routes.
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