Scheduling to Maximize the Number of Just-in-Time Jobs: A Survey

Shabtay, Dvir; Steiner, George

doi:10.1007/978-1-4614-1123-9_1

Cited by 9 publications

(10 citation statements)

References 36 publications

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“…We show that, in this setting, the problem of deciding whether all jobs can be scheduled is NP-complete. This solves an open problem posed by Sung and Vlach [13,15]. If the cores do not have to be at the right-end of the intervals, we show that deciding whether all jobs can be scheduled is NP-complete already when all intervals have unit length.…”

Section: Introductionmentioning

confidence: 82%

“…We show that deciding whether there is a complete schedule for this variant is NP-complete. By this we resolve an open problem posed by Sung and Vlach [13,15]. Afterwards, we consider the case where every job has a core at an arbitrary position and show that this variant is NP-complete even if all intervals have unit length.…”

Section: Interval Selection With Shared Coresmentioning

confidence: 88%

“…They showed that the weighted version is NP-hard and presented a dynamic programming algorithm that solves the problem in time O(m · n m+1 ). Settling the complexity of the problem with unit-weight jobs was posed as an open problem [15]; this open problem has also been stated in a recent survey on just-in-time job scheduling [13].…”

Section: Related Workmentioning

confidence: 99%

“…Each row, from top to bottom, is a generalization of the problem in the previous row, starting with IntervalSelection on a single machine, and ending with JISP k . As can be seen from the table, the (general) IntervalSelection, denoted as "no core required" in the table, is closely related to well-known and studied problems: it offers a natural generalization of the setting "with cores" [13,15], and it is an interesting special case of JISP k [4,5,14]. Previous work left a gap in the understanding of the complexity of the problems (the grey areas in the table), which we address and completely close in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Interval Selection with Machine-Dependent Intervals

Böhmová

Disser

Mihaľák

et al. 2013

Lecture Notes in Computer Science

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We study an offline interval scheduling problem where every job has exactly one associated interval on every machine. To schedule a set of jobs, exactly one of the intervals associated with each job must be selected, and the intervals selected on the same machine must not intersect. We show that deciding whether all jobs can be scheduled is NP-complete already in various simple cases. In particular, by showing the NP-completeness for the case when all the intervals associated with the same job end at the same point in time (also known as just-in-time jobs), we solve an open problem posed by Sung and Vlach (J. Sched., 2005). Furthermore, we show NP-completeness for the variant with unit-length intervals where all intervals associated with the same job have a common point, and for the variant with unitlength intervals and three machines. We also study the related problem of maximizing the number of scheduled jobs. We prove that the problem is NP-hard even for two machines and unit-length intervals. We present a 2/3-approximation algorithm for two machines (and intervals of arbitrary lengths).

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Section: Introductionmentioning

confidence: 82%

Section: Interval Selection With Shared Coresmentioning

confidence: 88%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interval Selection with Machine-Dependent Intervals

Böhmová

Disser

Mihaľák

et al. 2013

Lecture Notes in Computer Science

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“…Recently, Shabtay and Steiner [8] published a review of the literature addressing the problem of maximizing the number of just-in-time jobs which demonstrates that this theme has been very little explored. The work presented in [7], which deals with various types of just-in-time scheduling problems, mentions only one paper that considers the number of just-in-time jobs, that is, the survey presented in [8] of single-, parallel-and two-machine flow shop environments.…”

Section: Literature Reviewmentioning

confidence: 99%

Near-Optimal Heuristics for Just-In-Time Jobs Maximization in Flow Shop Scheduling

2018

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The number of just-in-time jobs maximization in a permutation flow shop scheduling problem is considered. A mixed integer linear programming model to represent the problem as well as solution approaches based on enumeration and constructive heuristics were proposed and computationally implemented. Instances with up to 10 jobs and five machines are solved by the mathematical model in an acceptable running time (3.3 min on average) while the enumeration method consumes, on average, 1.5 s. The 10 constructive heuristics proposed show they are practical especially for large-scale instances (up to 100 jobs and 20 machines), with very good-quality results and efficient running times. The best two heuristics obtain near-optimal solutions, with only 0.6% and 0.8% average relative deviations. They prove to be better than adaptations of the NEH heuristic (well-known for providing very good solutions for makespan minimization in flow shop) for the considered problem.

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On the parameterized tractability of the just-in-time flow-shop scheduling problem

Hermelin

Shabtay

Talmon

2019

J Sched

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Since its development in the early 90's, parameterized complexity has been widely used to analyze the tractability of many NP-hard combinatorial optimization problems with respect to various types of problem parameters. While the generic nature of the framework allows the analysis of any combinatorial problem, the main focus along the years was on analyzing graph problems. In this paper we diverge from this trend by studying the parameterized complexity of Just-In-Time (JIT) flow-shop scheduling problems. Our analysis focuses on the case where the number of due dates is considerably smaller than the number of jobs, and can thus be considered as a parameter. We prove that the two-machine problem is W[1]-hard with respect to this parameter, even if all processing times on the second machine are of unit length, while the problem is in XP even for a parameterized number of machines. We then move on to study the tractability of the problem when combining the different number of due dates with either the number of different weights or the number of different processing times on the first machine. We prove that in both cases the problem is fixed-parameter tractable for the two machine case, and is W[1]-hard for three or more machines.

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Scheduling to Maximize the Number of Just-in-Time Jobs: A Survey

Cited by 9 publications

References 36 publications

Interval Selection with Machine-Dependent Intervals

Interval Selection with Machine-Dependent Intervals

Near-Optimal Heuristics for Just-In-Time Jobs Maximization in Flow Shop Scheduling

On the parameterized tractability of the just-in-time flow-shop scheduling problem

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