The Apportionment Problem

One of the first equity problems that arises in the distribution of resources is the apportionment problem. It is concerned with distributing available personnel or other resources in “integral parts” to different subdivisions or tasks. One may be distributing seats in a legislature among different political constituencies, allocating the number of available teachers for a high school or college to the different departments, or determining the number of ships to be assigned to the different fleets in the Navy given certain priorities and goals. In practice this problem frequently arises even before one considers the classical assignment problem that is concerned with the existence of feasible and efficient assignments of resources to various units, such as assigning particular individuals to certain jobs. Several different methods for solving the apportionment problem as well as many of the relevant properties of the various methods will be presented in this chapter, along with examples that indicate a few of the more obvious applications.

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