Jackson's semi-preemptive scheduling on a single machine

Extending the Single Machine-Based Relaxation Scheme for the Job Shop Scheduling Problem

“…Similarly, the delivery time q j is such that p kj + q j is equal to the length of the longest path from the O kj node to the sink node in the disjunctive graph. Although the latter problem is strongly N P-hard, its optimal makespan, denoted hereafter by C * 0 (M k ), can be efficiently computed by using effective existing branch-and-bound algorithms [2], [4]. This yields the standard single machine-based lower bound:…”

Efficient Heuristics for Scheduling with Release and Delivery Times

“…For the purpose of a lower bound, preemptive version of the above problems with release and delivery times might be considered and preemptive J-heuristic can then be applied. For relevant studies on a classical job-shop scheduling problem, see, for example, Carlier [5], Carlier and Pinson [6], Brinkkotter and Brucker [3], and more recent works of Gharbi and Labidi [15] and Della Croce and T'kindt [12] and for multiprocessor job-shop scheduling problem with identical machines, see Carlier and Pinson [7]. This approach can also be extended for the case when parallel machines are unrelated [38].…”

Theoretical Expectation versus Practical Performance of Jackson’s Heuristic

“…The heuristic has been successfully used for the obtainment of lower bounds in job-shop scheduling problems. In the classical job-shop scheduling problem the preemptive version of Jackson's heuristic applied for a specially derived single-machine problem immediately gives a lower bound, see, for example, Carlier [9], Carlier and Pinson [19], and Brinkkotter and Brucker [20] and more recent works of Gharbi and Labidi [21] and Croce and T'kindt [22]. Carlier and Pinson [23] have used the extended Jackson's heuristic for the solution of the multiprocessor job-shop problem with identical machines, and it can also be adopted for the case when parallel machines are unrelated (see [24]).…”

“…By going deeper into the structure of Jackson's preemptive schedules, Croce and T'kindt [22] have proposed another (a more "complete") lower bound, which, in practice, also turns out to be more efficient than the above lower bound yielded by an optimal preemptive solution. The lower bound proposed by Gharbi and Labidi [21] is based on the concept of the so-called semipreemptive schedules, derived from the observation that in an optimal nonpreemptive schedule a part of some jobs is to be scheduled within a certain time interval. This yields to the semipreemptive schedules, for which stronger lower bounds can be derived.…”

“…The program for the generation of our instances was constructed under the same development environment as our main program. The job parameters (the release times, the processing times, and the due dates) were generated randomly, somewhat similar as in [9,21], as follows. For job release times and due dates a random number was generated with the rnd() function in Java, with an open range (0, 50 ), where is the number of jobs in each instance.…”