Equitable Assignment Rules

P. W. Glynn and J.L. Sanders

Technical Report, Mathematics Research Center, University of Wisconsin, Madison (1984)

This paper investigates the formalization of an important class of management decision problems. The problems considered are those of making equitable workload assignments to personnel. The paper proposes a series of intuitively appealing assignemnt rules, including random assignment, fixed assignment, block rotation and rules that reverse inequities caused by the last period's assignments. It is shown that in the two-person case none of these rules satisfies the simple criterion that cumulative differences of workload assignments among personnel become and remain small. Differences in the properties of these rules are investigated under threee additional but less strenuous criteria. It is shown that a new assignment rule called the counter-current rule does satisfy the criterion stated above; further, it is shown that it is an optimal rule under a fairly weak set of requirements. The extension of the results from the two-person case to the n-person case to the n-person case is discussed briefly and some initial results are presented.