Trade-off between utility and fairness in two-agent single-machine scheduling

We consider the problem arising when two agents, each owning a set of jobs, compete to schedule their jobs on a common processing resource. Each schedule implies a certain utility for each agent and an overall system utility. We are interested in solutions that incorporate some criterion of fairness for the agents and, at the same time, are satisfactory from the viewpoint of system utility. More precisely, we investigate the trade-off between fairness and system utility when both agents want to minimize the total completion time of their respective jobs. We analyze the structure of the set of such trade-off solutions, and propose an exact algorithm for their computation, based on the Lagrangian relaxation of a MILP formulation of the problem. A large set of computational experiments has been carried out to show the viability of the approach. Moreover, the results show that in most cases a solution having a high degree of fairness can be obtained by sacrificing a very limited amount of system utility.