Formulation problems
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The three kibbutzim belonging to the Southern Confederation have agreed that every kibbutz will plant the same proportion of its available irrigable land. However, any combination of the crops may be grown at any of the kibbutzim. The job facing the Coordinating Technical Office is to plan how many acres to devote to each crop at the respective kibbutzim while satisfying the above restrictions. The objective is to maximize the total net return to the Southern Confederation as a whole. Define the decision variables and formulate the problem. (Transportation) A corporation manufactures fertilizer and currently has quantities available at three depots. There are 600 bags available at depot 1, 500 bags available at depot 2 and 400 bags at depot 3. Orders have been placed by three distribution centers. 300 bags are required at center A; 700 bags at center B and 500 bags at center C. The table below shows the cost per bag, in dollars, of shipping fertilizer from each depot to each distribution center.
Define the decision variables and formulate the problem. (Transportation) The Easy Drive Car Rental Agency needs 500 new cars in its Nashville operation and 300 new cars in Jacksonville and it currently has 400 new cars in both Atlanta and Birmingham. It costs $30 to move a car from Atlanta to Nashville, $70 to move a car from Atlanta to Jacksonville, $40 from Birmingham to Nashville and $60 from Birmingham to Jacksonville. The agency wants to determine how many cars should be transported from the agencies in Atlanta and Birmingham to the agencies in Nashville and Jacksonville in order to meet demand while minimizing the transport costs. (Transportation) A manufacturer of television sets has two plants and two distribution centers. For the coming week, distribution center A requires 300 sets, and center B 250 sets. At most, 275 sets will be available at plant 1 and at most 325 sets will be available at plant 2. Television sets can be shipped from either plant to either distribution center. However, unit shipping costs differ along the four routes. It costs $10 per set for shipments from plant 1 to center A, $12 per set for shipments from plant 1 to center B, $14 per set for shipments from plant 2 to center A and $11 per set for shipments from plant 2 to center B. Demand at the two centers is to be fully met. Define the decision variables and formulate the problem (* MS-WS-2’de ve 347-WS-2’de var) (Transportation) Don Yale, president of Hardrock Concrete Company has plants in three locations and is currently wondering on three major construction projects, located ad different sites. The shipping cost per truckload of concrete, plant capacities and project requirements are provided in the accompanying table
(Transportation). Oranges are grown, picked and then stored in warehouses in Tampa, Miami and Fresno. These warehouses supply oranges to markets in New York, Phildelphia, Chicago and Boston. The following table shows the shipping costs per truckload (in hundreds of dollars), supply and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago:
Formulate this problem as a linear programming model (Transportation) During the war in Iraq, large amounts of military material and supplies had to be shipped daily from supply depots in the US to bases in the Middle East. The critical factor in the movement of these supplies was speed. The following table shows the number of plane loads of supplies available each day from each of six supply depots and the number of daily loads demanded at each of five bases. (Each planeload is approximately equal in tonnage.) Also included are the transprort hours per plane, including loading and fueling, actual flight time and unloading and refueling.
Determine the optimal daily flight Schedule that will minimize total transport time (Transshipment). Walsh’s Fruit Company contracts with growers in Ohio, Pennsylvania and New York to produce grapes. The grapes are processed into juice at the farms and stored in refrigerated vats. Then the juice is shipped to two plants, where it is processed into bottled grape juice and frozen concentrate. The juice and concentrate are then transported to three food warehouses/ distribution centers. The transportation costs per ton from the farms to the plants and from the plants to the distributors and the supply at the farms and demand at the distribution centers are summarized in the following tables Plant__Farm'> Plant
Distribution Center
Formulate the problem (Transportation) A sports apparel company has received an order for a college basketball team’s national championship T-shirt. T-shirts are produced in 3 plants. The shirts are shipped fromthe factories to the 3 distribution centers. Following are the production and transportation costs ($/shirt) from the T-shirt factories to the distribution centers, plus the supply of T-shirts at the factories and demand for the shirts at the distribution centers. Production costs:
Distribution costs:
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