A fractional 0–1 program for task assignment with respect to preferences. (May 2019) - Güngör, Murat
Highlights: This is a new application of fractional 0–1 programming. Satisfaction is defined appropriately as a ratio of two linear functions. A simpler solution approach is proposed for a similar problem in the literature. The numeric study shows the usefulness of the integer-programming-based heuristic. Abstract: We consider a task assignment problem with respect to preferences. The objective is to maximize total weighted satisfaction while maintaining a fair distribution. The problem's mathematical model turns out to be a multiple-ratio, constrained, fractional 0–1 program since satisfaction is defined as a ratio of two linear functions. We discuss the computational complexity of the problem, give three equivalent mixed-integer linear formulations, and propose a naive heuristic the usefulness of which is demonstrated by a numeric study. This paper not only provides a new application of fractional 0–1 programming, but it also suggests an alternative solution approach for a similar problem dealt in the literature before with nonlinear nonconvex methods.