Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million.
The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:
Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.
Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility)

-Which of these constraints will ensure that either a low capacity or a high facility capacity facility is built in the European supply region?

Question

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million.
The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:
Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.
Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility)

-Which of these constraints will ensure that either a low capacity or a high facility capacity facility is built in the European supply region?

Quizplus · Accepted Answer

The constraint Y41 + Y42 = 1 ensures that either a low capacity (Y41=1) or high capacity (Y42=1) facility is built in the European supply region. This means that only one of the two facilities can be selected, which guarantees that a decision will be made between the two options. Option B does not ensure that one facility will be selected, as both Y41 and Y42 could be set to zero. Constraints C and D refer to the North American supply region and do not address the question of the appropriate facility size for the European region.

Future Plastics Manufactures Plastic Products for Industrial Use Worldwide