Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect

Sun, Xinyu; Geng, Xin-Na; Wang, Ji‐Bo; Liu, Feng

doi:10.1080/00207543.2018.1510559

Cited by 31 publications

(11 citation statements)

References 28 publications

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“…In terms of the processing time of a job is a bounded linear function or convex function of the amount of the resource allocated to the processing of it, this kind of problems is divided into two categories: scheduling with linear resource‐dependent processing times and scheduling with convex resource‐dependent processing times. The body of literature on this topic is vast, and we refer the reader to the recent studies of Shabtay and Steiner (2007a)), Sun, Geng, Wang, and Liu (2019), Tadumadze, Boysen, Emde, and Weidinger (2019), and Yang, Lai, and Yang (2014), and the survey by Shabtay and Steiner (2007b). Since our paper focuses on scheduling with linear resource‐dependent processing times, in what follows we review some related studies following this line of research.…”

Section: Literature Reviewmentioning

confidence: 99%

Two‐agent scheduling with linear resource‐dependent processing times

Wang

Qiu

et al. 2020

Naval Research Logistics

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This paper considers a two‐agent scheduling problem with linear resource‐dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is NP‐hard in the ordinary sense, and there does not exist a polynomial‐time approximation algorithm with performance ratio unless P=NP; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.

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Section: Literature Reviewmentioning

confidence: 99%

Two‐agent scheduling with linear resource‐dependent processing times

Wang

Qiu

et al. 2020

Naval Research Logistics

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“…References [53] and [54] included uncertain setup times and due date constraints to two-machine NWFSPs, respectively. Reference [55] introduced convex resource-dependent processing times, and, more recently, [56,57] integrated the convex resource allocation and common flow allowance, respectively, into the two-machine NWFSPs considering the learning effect. NWFSP with more than two machines is more realistic, hence, has received wider recognition in the academic literature.…”

Section: Literature Reviewmentioning

confidence: 99%

Improved Beam Search for Optimizing No-Wait Flowshops With Release Times

et al. 2020

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Production management of perishable goods is highly complex and requires well-informed decisions in corresponding stages. In such production environments, scheduling problems with time constraints are of high relevance to ensure the timely flow of the work-in-process material and goods. This study introduces the no-wait flowshop scheduling problem with release times (NWFSP-RT) to help advance decision support systems in the food production industry. For this purpose, an original mixed-integer linear programming (MILP) formulation is proposed for minimizing the makespan. Since Beam Search (BS) algorithm has been successfully applied to solve various scheduling problems, a BS algorithm, and an improved variant, the local search-based Beam Search (BSLS) algorithms are developed to solve the NWFSP-RT problem. Extensive numerical analysis is conducted to analyze the performance of the algorithms in solving this highly intractable extension of the scheduling problems. We showed that BSLS effectively avoids early convergence and local optimality while dismissing non-promising search directions within a partial enumeration solution approach. The statistical analysis confirmed that the improved BS algorithm performs better in terms of solution quality. Applications of the developed heuristic are worthwhile research topics to pursue in solving other complex optimization problems. INDEX TERMS Flowshop scheduling, no-wait, release time, Beam Search.

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“…Generally, each of the due-dates is defined as the sum of its processing time and a job-independent constant. Significant papers considering different SLK objective functions include: [4,12,14,22,30,31,33,35,37,40].…”

Section: Numerical Example 331mentioning

confidence: 99%

A unified approach for single machine scheduling with position-dependent workloads and positional penalties

Mor

2020

SN Appl. Sci.

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In this paper, we provide unified methods for solving scheduling problems with convex resource allocation, concentrating on objective functions that can be expressed as a scalar product of the actual processing times vector and a job-independent and position-dependent penalties vector. We assume general position-dependent workloads, i.e., the workloads are not restricted to be either monotone functions of the job positions or to specific functions. The first unified method focuses on minimizing a scheduling measure subject to a constraint on the resource consumption, whereas the second addresses the complementary problem of minimizing the consumed resource given an upper bound on the scheduling measure. For each unified approach, we provide a methodical analysis and consequently provide a O n 3 solution algorithm. Furthermore, to demonstrate the unified schemes, we solve several scheduling measures that involve earliness and tardiness penalties.

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Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect

Cited by 31 publications

References 28 publications

Two‐agent scheduling with linear resource‐dependent processing times

Two‐agent scheduling with linear resource‐dependent processing times

Improved Beam Search for Optimizing No-Wait Flowshops With Release Times

A unified approach for single machine scheduling with position-dependent workloads and positional penalties

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