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

Hermelin, Danny; Shabtay, Dvir; Talmon, Nimrod

doi:10.1007/s10951-019-00617-7

Cited by 14 publications

(11 citation statements)

References 29 publications

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“…Single machine scheduling where two agents compete to schedule their private jobs is investigated by Hermelin et al [22]. There are few other result [23,24,27,44] focused on identifying tractable scenarios for various scheduling paradigms (such as flow-shop scheduling or e.g. structural limitations of the job-machine assignment).…”

Section: Configuration Lpmentioning

confidence: 99%

Scheduling Kernels via Configuration LP

Knop¹,

Koutecký²

2020

Preprint

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Makespan minimization (on parallel identical or unrelated machines) is arguably the most natural and studied scheduling problem. A common approach in practical algorithm design is to reduce the size of a given instance by a fast preprocessing step while being able to recover key information even after this reduction. This notion is formally studied as kernelization (or simply, kernel) -a polynomial time procedure which yields an equivalent instance whose size is bounded in terms of some given parameter. It follows from known results that makespan minimization parameterized by the longest job processing time pmax has a kernelization yielding a reduced instance whose size is exponential in pmax. Can this be reduced to polynomial in pmax?We answer this affirmatively not only for makespan minimization, but also for the (more complicated) objective of minimizing the weighted sum of completion times, also in the setting of unrelated machines when the number of machine kinds is a parameter.Our algorithm first solves the Configuration LP and based on its solution constructs a solution of an intermediate problem, called huge N -fold integer programming. This solution is further reduced in size by a series of steps, until its encoding length is polynomial in the parameters. Then, we show that huge N -fold IP is in NP, which implies that there is a polynomial reduction back to our scheduling problem, yielding a kernel.Our technique is highly novel in the context of kernelization, and our structural theorem about the Configuration LP is of independent interest. Moreover, we show a polynomial kernel for huge N -fold IP conditional on whether the so-called separation subproblem can be solved in polynomial time. Considering that integer programming does not admit polynomial kernels except for quite restricted cases, our "conditional kernel" provides new insight.

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Section: Configuration Lpmentioning

confidence: 99%

Scheduling Kernels via Configuration LP

Knop¹,

Koutecký²

2020

Preprint

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“…Parameterized complexity studies of NP-hard scheduling problems gained more and more interest over the recent years[4,9,12,22]; we contribute to this field with several of our results.…”

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confidence: 83%

Equitable Scheduling on a Single Machine

Heeger¹,

Hermelin²,

Mertzios³

et al. 2020

Preprint

Self Cite

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We introduce a natural but seemingly yet unstudied generalization of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. Our generalization lies in simultaneously considering several instances of the problem at once. In particular, we have n clients over a period of m days, where each client has a single job with its own processing time and deadline per day. Our goal is to provide a schedule for each of the m days, so that each client is guaranteed to have their job meet its deadline in at least k ≤ m days. This corresponds to an equitable schedule where each client is guaranteed a minimal level of service throughout the period of m days. We provide a thorough analysis of the computational complexity of three main variants of this problem, identifying both efficient algorithms and worst-case intractability results. * Supported by DFG Research Training Group 2434 "Facets of Complexity". † Supported by the EPSRC grant EP/P020372/1. ‡ Supported by the DFG, project MATE (NI 369/17). 1 For instance, in 2018, ACM started its new conference series on "Fairness, Accountability, and Transparency (FAT)".

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“…The discrete manufacturing system in this paper uses the Flow-Shop scheduling [22] mode for processing; that is, the machine groups on the production line execute the different processes to complete the production order of the products, the processing procedure of the product types is the same, and they are processed only once in each machine group on the production line. The Flow-Shop scheduling model is a simplified model of many actual pipeline production scheduling problems, and it is also a typical non-deterministic polynomial hard (NP-hard) problem.…”

Section: Mathematical Model Of the Manufacturing Systemmentioning

confidence: 99%

Integrated Control Policy for a Multiple Machines and Multiple Product Types Manufacturing System Production Process with Uncertain Fault

You

Guo

et al. 2020

Processes

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The optimization of production cost has always been a key issue in manufacturing systems; for the single product type manufacturing systems, lots of research studies have proved the validity of the hedging point control policy in production cost control. However, due to the complexity of the multiple machines and multiple product types manufacturing systems with uncertain fault, it is difficult to achieve a good control effect only by using the hedging point control policy. To optimize the total production cost under constantly changing demands, an integrated control policy that combines the prioritized hedging point (PHP) control policy with the production capacity planning during production is proposed, and the decision variables are obtained by a particle swarm optimization (PSO) algorithm. The simulation experiments show the effectiveness of the proposed integrated control policy in production cost control for the multiple machines and multiple product types manufacturing system.

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

Cited by 14 publications

References 29 publications

Scheduling Kernels via Configuration LP

Scheduling Kernels via Configuration LP

Equitable Scheduling on a Single Machine

Integrated Control Policy for a Multiple Machines and Multiple Product Types Manufacturing System Production Process with Uncertain Fault

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