Exact and heuristic algorithms for scheduling on two identical machines with early work maximization

Abstract Early work criterion is a new-proposed objective in the scheduling field, in which the early parts of jobs processed before their due dates are aimed to be maximized. In this paper, we consider such a criterion for scheduling on two identical machines. For the simplified model with a common due date of all jobs, we show that the classical LPT (Largest Processing Time first) heuristic is an approximation algorithm with the worst case ratio 10 9 . For the general model with arbitrary due dates, we propose a branch-and-bound algorithm equipped with several truncation rules, upper and lower bounds techniques, as well as dominance rules to solve small scale instances, while a genetic algorithm to solve big instances. Finally, the efficiencies of the proposed algorithms are validated by the numerical experiments, in which we show that the branch-and-bound algorithm can find the exact solutions within a reasonable time-consumption when an instance is small, and the genetic algorithm is an efficient approach when the problem instance turns to big.

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