The paper introduces a model for online parallel machine scheduling, where any single machine is run on the basis of a locally optimal sequencing policy. Jobs choose the machine on which they want to be processed themselves, and in addition, any job owns a piece of private information, namely its indifference cost for waiting one additional unit of timebefore being processed. We study this setting from the perspective of algorithmic mechanism design, and assuming that each job prefers to be completed as early as possible, the utilitarian social choice function minimizes the total weighted completiontimes.We prove that in this setting there exists an online mechanism, running in polynomial time, where rational jobs select their machine in such a way that the resulting schedule is 3.281-competitive with respect to the off-line optimal solution that maximizes social welfare. The mechanism deploys an online payment scheme that induces rational jobs to truthfullyreport their indifference costs, in the sense that it is a myopic best response. Moreover, the payment scheme results in a balanced budget, that is, payments are only made between jobs. We also discuss extensions to mechanisms where truth-telling is even an ex-post weakly dominant strategy, while preserving the competitive ratio.
