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

Abstract

a b s t r a c tThis 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.

Just-in-time preemptive single machine problem with costs of earliness/tardiness, interruption and work-in-process

“…The WIP costs are based on the differences among the start and completion times of the jobs. This model presented two main advantages over an existing model HS presented by Hendel and Sourd (2005).…”

“…Also they discussed for several dominance rules and the particular case of the scheduling problem around a common due date. Furthermore, presented the lower bound for the timing algorithm and explained that a local search algorithm based on their new timing algorithm is sooner than a local search algorithm, which uses the timing algorithm presented by Hendel and Sourd (2005). Khorshidian et al (2011) presented a new mathematical model in the expansion of the classical single machine E/T scheduling problem where preemption is allowed and idle time is also considered.…”

“…In the classical one-machine problem with earliness-tardiness where preemption is allowed, each job has two due dates instead of one; one of them deals with the starting time and the other with completion time of jobs (Bülbül et al, 2007;Sourd & Kedad-Sidhoum, 2008;Hendel et al, 2009). Hendel et al (2009) investigated a new single machine scheduling problem with earliness and tardiness to capture the JIT philosophy, where the earliness costs depend on the start times of the jobs and tardiness costs depend on completion times.…”

“…Hendel et al (2009) investigated a new single machine scheduling problem with earliness and tardiness to capture the JIT philosophy, where the earliness costs depend on the start times of the jobs and tardiness costs depend on completion times. They applied an efficient representation of dominant schedules and introduced a polynomial algorithm to compute the best schedule for a given representation.…”

A genetic algorithm for preemptive scheduling of a single machine

“…Bülbül et al (2007) investigated a single machine earliness/tardiness scheduling problem with general weights, ready times and due dates and the method is based on a time-indexed preemptive relaxation of the problem. Hendel et al (2009) studied the concept of preemption in scheduling, with earliness and tardiness penalties where the earliness costs was dependent on the start times of the jobs. They proposed an efficient representation of dominant schedules to measure the most appropriate schedule for a given representation.…”