Scheduling jobs with equal processing times on a single machine: minimizing maximum lateness and makespan

Lazarev, Alexander A.; Arkhipov, Dmitry I.; Werner, Frank

doi:10.1007/s11590-016-1003-y

Cited by 10 publications

(3 citation statements)

References 5 publications

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“…Special cases of the problem have been analyzed in recent years. For example, Lazarev et al [2] considered the problem with only a single machine and identical processing times for all jobs.…”

Section: Fundamental Models For Production Schedulingmentioning

confidence: 99%

Modeling and Solving an Extended Parallel Resource Scheduling Problem in the Automotive Industry

Kulcsár-Forrai¹,

Kulcsár²

2017

ACTA POLYTECH HUNG

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This paper presents an extended model for solving time-varying resourceconstrained scheduling problems. The motivation for our research comes from the automotive industry. The problem is to create fine schedules for a complex manufacturing system to satisfy diverse customer demands. The detailed characteristics of the analyzed scheduling problem and the developed solving approach are described in this paper. To consider the impact of the assistant processes that are connected to the manufacturing primary processes, we elaborated a problem-transformation procedure and a new extended scheduling model that can manage time-varying availability constraints of parallel resources, unit processing times, job-dependent release times and due dates. This paper also presents slack-oriented and JIT-oriented algorithms that can solve the resourceconstrained scheduling problems. The research results have been successfully applied and tested in practice.

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Section: Fundamental Models For Production Schedulingmentioning

confidence: 99%

Modeling and Solving an Extended Parallel Resource Scheduling Problem in the Automotive Industry

Kulcsár-Forrai¹,

Kulcsár²

2017

ACTA POLYTECH HUNG

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“…In [18], the idea of the dual approach is considered in detail, but there is no sufficient experimental study of the effectiveness of this approach. Lazarev et al [20] considered the problem of minimizing maximum lateness and the makespan in the case of equal processing times and proposed a polynomial time approach for finding the Pareto-optimal set of feasible solutions. They presented two approaches, the efficiency of which depends on the number of jobs and the accuracy of the input-output parameters.…”

Section: Introductionmentioning

confidence: 99%

On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty

Lazarev¹,

Pravdivets²,

Werner

2020

Mathematics

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In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs.

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“…The above paper considers the corresponding bi-criteria scheduling problem and finds the Pareto-optimal set of feasible solutions. Lazarev [20] and Lazarev et al [21] have proposed a polynomial time solution finding the Pareto-optimal set for two special cases of our bi-criteria problem with specially-ordered job parameters and equal-length jobs, respectively. An exact enumerative algorithm for the no idle time problem with the objective to minimize maximum job lateness was proposed by Carlier et al [22], whereas the practical importance of the solutions with no idle time intervals was emphasized by Chrétienne [23].…”

Section: Introductionmentioning

confidence: 99%

Scheduling a Single Machine with Primary and Secondary Objectives

Vakhania

2018

Algorithms

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We study a scheduling problem in which jobs with release times and due dates are to be processed on a single machine. With the primary objective to minimize the maximum job lateness, the problem is strongly NP-hard. We describe a general algorithmic scheme to minimize the maximum job lateness, with the secondary objective to minimize the maximum job completion time. The problem of finding the Pareto-optimal set of feasible solutions with these two objective criteria is strongly NP-hard. We give the dominance properties and conditions when the Pareto-optimal set can be formed in polynomial time. These properties, together with our general framework, provide the theoretical background, so that the basic framework can be expanded to (exponential-time) implicit enumeration algorithms and polynomial-time approximation algorithms (generating the Pareto sub-optimal frontier with a fair balance between the two objectives). Some available in the literature experimental results confirm the practical efficiency of the proposed framework.

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Scheduling jobs with equal processing times on a single machine: minimizing maximum lateness and makespan

Cited by 10 publications

References 5 publications

Modeling and Solving an Extended Parallel Resource Scheduling Problem in the Automotive Industry

Modeling and Solving an Extended Parallel Resource Scheduling Problem in the Automotive Industry

On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty

Scheduling a Single Machine with Primary and Secondary Objectives

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