A note on parallel-machine scheduling with controllable processing times and job-dependent learning effects

Lin, Shan-Shan

doi:10.1051/ro/2021030

Cited by 5 publications

(4 citation statements)

References 41 publications

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“…In future research, we can extend it to multi-machine problems such as parallel machines or flow shop settings. It is also interesting to extend the model to the single-machine group scheduling problem with general shortened job processing times, due-date assignment (see [29]) or positional-dependent learning effects (see [2,4,13]).…”

Section: Discussionmentioning

confidence: 99%

Single machine group scheduling problem with makespan objective and a proportional linear shortening

et al. 2022

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This paper considers a group scheduling problem with shorten (i.e., a proportional linear shortening) job processing times and ready times on a single machine. If the jobs are in the same group, they have independent and constant ready times. The setup time of a group is independent constant setup time between each group. The goal is to determine the optimal group sequence and the job sequence within the groups such that the makespan (i.e., the maximum completion time) is minimized. For the general case of the problem, an initial heuristic algorithm (an upper bound) and some lower bounds are proposed, and then a branch-and-bound algorithm can be developed to solve the problem.

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Section: Discussionmentioning

confidence: 99%

Single machine group scheduling problem with makespan objective and a proportional linear shortening

et al. 2022

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“…We will show that C j (σ) ≤ C i (σ ′ ). Taking the difference between (20) and (22), it is obtained that…”

Section: The Nondecreasing Function F(x Y) On Xmentioning

confidence: 99%

“…e distinctive proof technique is developed based on the adding-term operation, the subtracting-term operation, and the Lagrange mean value theorem. Lin [20] studied job-dependent learning effect and controllable processing time on the unrelated parallel machine. e three objective functions are considered, including the weighted sum of total completion time, total load, and total compression cost.…”

Section: Introductionmentioning

confidence: 99%

Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

Shen¹,

Yu-ke

Liu

2021

Discrete Dynamics in Nature and Society

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This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.

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“…They proposed an integer non-linear programming model and a dynamic programming model, which can be executed in pseudo-polynomial time. While Lin [13] addressed the parallel-machine scheduling with controllable processing times and job-dependent learning effects, the objective function is to minimize the weighted sum of total completion time, total compression cost, and total load. They showed that the problem can be solved in O(n m+2 ) time, where n (resp.…”

Section: Introductionmentioning

confidence: 99%

Study on Scheduling Problems with Learning Effects and Past Sequence Delivery Times

He,

Zhao,

et al. 2023

Mathematics

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In this paper, we study a single-machine green scheduling problem with learning effects and past-sequence-dependent delivery times. The problem can be properly applied to tackle green manufacturing where production and delivery time are variable and highly subject to process-reengineering. Our goal is to determine the optimal sequence such that total weighted completion time and maximum tardiness are minimized. For the general case, we provide the analysis procedure of lower bound, and also propose the heuristic and branch-and-bound algorithms. Furthermore, computational experiments are conducted to demonstrate the effectiveness of our algorithms.

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A note on parallel-machine scheduling with controllable processing times and job-dependent learning effects

Cited by 5 publications

References 41 publications

Single machine group scheduling problem with makespan objective and a proportional linear shortening

Single machine group scheduling problem with makespan objective and a proportional linear shortening

Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

Study on Scheduling Problems with Learning Effects and Past Sequence Delivery Times

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