Scheduling Groups of Jobs on a Single Machine

Webster, Scott; Baker, Kenneth R.

doi:10.1287/opre.43.4.692

Cited by 322 publications

(109 citation statements)

References 22 publications

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“…Following the notation of [7], these problems are denoted respectively by 1|s-batch, r i |F , 1|p-batch, b < n, r i |F (bounded case) and 1|p-batch, r i |F (unbounded case). We refer to [1], [6], [7], [14], [16], [17], [19] for extended reviews on pure batch scheduling problems and on extensions (e.g. scheduling group of jobs with group-dependent setup times, jobs requiring several machines throughout their execution, etc.).…”

Section: Introductionmentioning

confidence: 99%

Batching identical jobs

Baptiste¹

2000

Mathematical Methods of Operations Research (ZOR)

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We study the problems of scheduling jobs, with different release dates and equal processing times, on two types of batching machines. All jobs of the same batch start and are completed simultaneously. On a serial batching machine, the length of a batch equals the sum of the processing times of its jobs and, when a new batch starts, a constant setup time s occurs. On a parallel batching machine, there are at most b jobs per batch and the length of a batch is the largest processing time of its jobs. We show that in both environments, for a large class of so called "ordered" objective functions, the problems are polynomially solvable by dynamic programming. This allows us to derive that the problems where the objective is to minimize the weighted number of late jobs, or the weighted flow time, or the total tardiness, or the maximal tardiness are polynomial. In other words, we show that 1|p-batch, b < n, r i , p i = p|F and 1|s-batch, r i , p i = p|F , are polynomial for F ∈ { w i U i , w i C i , T i , T max }. The complexity status of these problems was unknown before.

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Section: Introductionmentioning

confidence: 99%

Batching identical jobs

Baptiste¹

2000

Mathematical Methods of Operations Research (ZOR)

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“…In the former model, the jobs in a batch are processed in serial, and thus the processing time of a batch is equal to the sum of the processing times of the jobs in that batch. In the latter model, the jobs in a batch are processed in parallel, and thus the processing time of a batch is equal to the longest processing time of the jobs in that batch [5].…”

Section: Introductionmentioning

confidence: 99%

A Linear Time Exact Algorithm for Scheduling Unit-processing-time-jobs with Sizes 1 or k

Xin¹,

Mu²,

Mou³

2017

Proceedings of the 2017 2nd International Conference on Materials Science, Machinery and Energy Engineering (MSMEE 2017)

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Abstract. The problem of scheduling jobs with sizes on batch machines is considered. Each machine can process several jobs as a batch simultaneously as long as the total size of these jobs does not exceed the capacity of the machine. The processing time of a batch is defined to be the longest processing time of the jobs in the batch. The goal is to minimize makespan, i.e., the maximum job completion time. It has been known to be strongly NP-hard. A linear time exact algorithm is presented for a special case where all the jobs have processing times 1 and sizes 1 or k (k is not fixed).

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“…Ahn and Hyun (1990), Bruno and Sethi (1977), Mason and Anderson (1991), and Monma and Potts (1989) propose algorithms for minimizing total weighted flowtime on a single machine with family setup times. We refer to Webster and Baker (1995) and Liaee and Emmons (1997) for a review of scheduling literature on family scheduling problems. Further we note here that sequence-dependent setup times tend to make solutions difficult to find.…”

Section: Introductionmentioning

confidence: 99%

Family sequencing and cooperation

Grundel

Çiftçi²,

Borm

et al. 2013

European Journal of Operational Research

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This paper analyzes a single-machine scheduling problem with family setup times both from an optimization and a cost allocation perspective. In a so-called family sequencing situation jobs are processed on a single machine, there is an initial processing order on the jobs, and every job within a family has an identical cost function that depends linearly on its completion time. Moreover, a job does not require a setup when preceded by another job from the same family while a family specific setup time is required when a job follows a member of some other family.Explicitly taking into account admissibility restrictions due to the presence of the initial order, we show that for any subgroup of jobs there is an optimal order, such that all jobs of the same family are processed consecutively. To analyze the allocation problem of the maximal cost savings of the whole group of jobs, we define and analyze a so-called corresponding cooperative family sequencing game which explicitly takes into account the maximal cost savings for any coalition of jobs. Using nonstandard techniques we prove that each family sequencing game has a non-empty core by showing that a particular marginal vector belongs to the core. Finally, we specifically analyze the case in which the initial order is family ordered.

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Scheduling Groups of Jobs on a Single Machine

Cited by 322 publications

References 22 publications

Batching identical jobs

Batching identical jobs

A Linear Time Exact Algorithm for Scheduling Unit-processing-time-jobs with Sizes 1 or k

Family sequencing and cooperation

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