A school boundaries problem. A school district has been undergoing rapid population changes. Some of its areas are depopulating of school age children in the elementary levels. Other areas arc gaining elementary-school-age children quite rapidly. As a consequence. some schools arc overcrowded and others have too many desks and rooms. The district office has established one new school in an area that had been rural hut has grown quickly with new houses and young families.

The district has been divided into small areas or neighborhoods. The distance via the street network between each neighborhood and each elementary school is known. School buses are in use to transport the children who do not walk or who have other transport. Nonetheless, to prevent excessive time on the bus, the planning office has set an upper limit of 2.5 miles for school assignments. That is, no pupil is to be assigned to a school more than 2.5 miles from the centroid of their neighborhood.

In addition, pupils whose neighborhood is within 0.25 miles are expected to walk to school or obtain their own transportation. ( When we were young. let me tell you ... ). Each of the elementary schools. indexed by j. has a capacity of hi. Each neighborhood. indexed by i. is anticipated to have an average through time of as pupils. The distance between neighborhood i and school j is du. The goal of the planning office is to assign pupils to schools to minimize the transport burden as measured in pupils multi-plied by miles traveled on the bus from neighborhood to school.

The circuitous route of the school bus is not counted here, only the most direct distance from neighborhood to school. Although the goal is least-pupil-transport burden, it is also required that each school be at least at 60% of its capacity. Your challenge is to capture these several restrictions, in addition to the usual requirements of a transportation problem.

To review, children within 0.25 miles of their school will not be transported. No one can be assigned to a school more than 2.5 miles away, and schools must be at 60% of capacity. You will want to modify the matrix of distances to accomplish the first two of these additional restrictions. How would you examine the impact of the new school that has been built relative to these requirements?