A Greedy Heuristic for a Nonlinear Generalized Assignment Problem
In this paper, we examine a nonlinear Generalized Assignment Problem. In particular,
we wish to minimize the sum of the cost of assigning jobs to machines plus the sum of a nonlinear
function of a linear function of the assignments made to each machine. We propose a greedy
heurstic based on a set of dual multipliers associated with the optimal solution to the relaxation
of the problem that allows a job to be split among machines. We develop properties of the solution
returned by the greedy heurstic. We analyze the performance of the greedy heuristic under a probabilistic model
for several types of functions, including piecewise linear functions, concave functions, and polynomial functions.