An Algorithm for Developing Gerrymandered School Zone Boundaries

Southeastern Geographer Vol. 23, No. 1, May 1983. pp. 26-34 AN ALGORITHM FOR DEVELOPING GERRYMANDERED SCHOOL ZONE BOUNDARIES Cyrus B. Dawsey, III Racial segregation in the public education system has been a significant problem confronting American society during the second half ofthe twentieth century. Beginning with Brown vs. Board ofEducation in 1954, federal courts have repeatedly rendered decisions mandating the elimination of racially identifiable units. (2) Where schools have achieved racial balance, travel distances have increased and forced many children into unfamiliar and unfriendly neighborhoods. Consequently, the pressure on school officials to minimize the costs and inconveniences associated with busing has been great. Several researchers have applied linear programming models, standard tools for allocating demand to service centers, to the school desegregation problem. (2) The incorporation of a network algorithm and the use of dummy cells in a school-tract matrix are examples ofmodifications which have been used to refine the procedure for assigning students while maintaining a proper racial balance. (3) The general approach has been to minimize an objective function: m n m ? Min Z = S S du bu + S S du Wu(1) i=l j=li = l j=l subject to (for all values ofj): m B1 = S bu(2) 1=1 m W1 = S wu(3) i = l m m Bj/Wj = S B1/ S W1 + toi(4) i=li=l Dr. Dawsey is Associate Professor of Geography at Auburn University in Auburn , AL 36830. Vol. XXIII, No. 1 27 where Z = total distance, m = a number of residential areas, ? = number of schools, d^ = distance from residential area i to school j, b¡j = blacks from residential area i allocated to school j, w¡¡ = whites from residential area i allocated to school j, B¡ = total blacks at residential area i, Bj = total blacks allocated to school j, W¡ = total whites allocated in school j, and toi = a tolerance factor. Application of an appropriate algorithm such as the "Northwest corner solution" results in the assignment of students to schools in a manner which minimizes the total travel distance. (4) Black and white populations are considered as two separate groups, and allocation from residential areas to schools is made independently within each group. The procedure usually produces two distinct school zone maps, one for whites and the other for blacks. (5) Because the solutions differ for the two groups, many neighborhoods assigned to one school on the first map are assigned to another school on the second. In these areas students of different races residing next to each other are forced to attend different schools. Gerrymandering is another method used for delineating school boundaries. (6) Rather than drawn in a way which occasionally assigns white and black students from one residential area to different schools, boundaries between zones are made applicable to all races. A single set of lines is produced in a manner which ensures the proper mixture within each zone. Though gerrymandering seems to be widely used in small communities and frequently applied in larger ones, the development of formal allocational procedures has lagged. (7) This professional neglect does not seem justified. The development of unambiguous zone boundaries, regardless of race, would prevent some of the inequities associated with the present busing in many cities where blacks travel far greater distances. Furthermore, some preservation of the community school ideal would be possible. Students might not attend the nearest school, but all in the neighborhood would go to the same school. Gerrymandering imposes an added restriction: all students within a residential area must be assigned to the same school. The objective function of equation (1) is minimized subject to the constraints of equations (2), (3), and (4), and the additional (for all values of j): by + w(J = B1 + W1(5) b,j/w, = B1AV,(6) 28Southeastern Geographer PURPOSE AND ALGORITHM. The purpose of this study was to test the hypothesis that a computer program, developed by the author, would produce a gerrymandered school zone boundary map for which the total student travel distance would be less than for the map being used in a real school system. Zone contiguity and busing distance would also be compared. The computer procedure involved swapping allocated residential areas...