Management at Building Supplies, LLC., is considering entering a new market. Thr

Question

Management at Building Supplies, LLC., is considering entering a new market. Three potential sites have been selected to build cement plants but it may build only one or two plants. The cement produced at the plants will be shipped to three distribution centers in the city. The following table gives the weekly capacities and fixed operating costs of the proposed plants, the unit variable shipping costs from each potential plant to each distribution center, and the weekly demands of the distribution centers. The capacities and demands are in tons Shipping Cost to Distribution Center Capacity lOperatin 2 Cost 300 280 320 12000 11000 14000 4 4 Demand 2100 1700 1900 You are required to formulate an integer programming model to determine at which sites plants should be built and the quantity to ship from each plant to each distribution center. The objective is to minimize the total of weekly fixed operating costs and variable transportation costs. The correct definitions of the decision variables are y-quantity shipped along the road from plant ito distribution center j 0, ifx, -0, i.e., if the road from plant i to distribution center j is not used 1 ifx>0, i.e., if the road from plant i to distribution center j is used y-quantity shipped along the road from plant i to distribution center j 0, if a plant is not built at site i 1, if a plant is built at site i y-variable cost of shipping a unit along the arc from potential plant /to distribution center j fixed cost of the road along the arc from potential plant i to distribution center j ariable cost of shipping a unit along the arc from potential plant i to distribution center j y -fixed cost of operating the plant at site i none of the above

Explanation / Answer

Decision variables are those variable whose values are adjusted so as to obtain the most optimal outcome. Here, we need to decide whether a plant is to be set up at a site and if a plant is set up, what quantity needs to be transported from that plant.

Answer: Option 2, xij denotes the quantity shipped from i to j and y denotes whether a plant is set up at a site or not.

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