1. Proper placement of public service facilities such as schools are essential to efficient urban design,...
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1. Proper placement of public service facilities such as schools are essential to efficient urban design, and you are hired to determine the school locations at a new city. Assume that there are I = 8 districts in this city. In each district i I, there are s many students. According to the preliminary analysis made by the city government, there are J = 6 candidate locations to build schools. The distance between each district i and each candidate location j is given as dij. All students in a district will be assigned to the same school. However, you need to determine to which school (in candidate location j) will the students in district i be assigned. Of course, you must ensure all students are assigned to a school. The cost of building a school in each candidate location depends on the location itself and the number of students that are assigned there. There is a fixed cost of f, to purchase the land. Also, for each student assigned to school j, a cost of c, will be paid to build it (e.g. if the number of students that are assigned to school 5 is 2000, then the total cost of building that school will be fs + 2000 cs). Your total budget is B to build all selected schools. Finally, to come up with a solution that considers social-welfare, your aim is to minimize the maximum distance that needs to be walked by students. Formulate a mathematical model for this problem. 1. Proper placement of public service facilities such as schools are essential to efficient urban design, and you are hired to determine the school locations at a new city. Assume that there are I = 8 districts in this city. In each district i I, there are s many students. According to the preliminary analysis made by the city government, there are J = 6 candidate locations to build schools. The distance between each district i and each candidate location j is given as dij. All students in a district will be assigned to the same school. However, you need to determine to which school (in candidate location j) will the students in district i be assigned. Of course, you must ensure all students are assigned to a school. The cost of building a school in each candidate location depends on the location itself and the number of students that are assigned there. There is a fixed cost of f, to purchase the land. Also, for each student assigned to school j, a cost of c, will be paid to build it (e.g. if the number of students that are assigned to school 5 is 2000, then the total cost of building that school will be fs + 2000 cs). Your total budget is B to build all selected schools. Finally, to come up with a solution that considers social-welfare, your aim is to minimize the maximum distance that needs to be walked by students. Formulate a mathematical model for this problem.
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Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
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