The one-machine just-in-time scheduling problem with preemption

This paper investigates the notion of preemption in scheduling, with earliness and tardiness penalties. Starting from the observation that the classical cost model where penalties only depend on completion times does not capture the just-in-time philosophy, we introduce a new model where the earliness costs depend on the start times of the jobs. To solve this problem, we propose an efficient representation of dominant schedules, and a polynomial algorithm to compute the best schedule for a given representation. Both a local search algorithm and a branch-and-bound procedure are then derived. Experiments finally show that the gap between our upper bound and the optimum is very small.