Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine

Kong, Min; Liu, Xinbao; Pei, Jun; Zhou, Zhiping; Pardalos, Pãnos M.

doi:10.1007/s11590-019-01389-x

Cited by 18 publications

(6 citation statements)

References 33 publications

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“…The source radioactivity is continuously decaying and the source radioactivity at time t satisfies A t = A 0 ⋅ e − t , the treatment duration p i needs to satisfy the following formula to meet the given dose d i in the treatment plan, ∫ 2 shows that J i starts being processed at time t 1 and the processing time of J i is the sum of setup time s and treatment duration p i , where the treatment duration p i is determined by the patient dose and source radioactivity. It should be noted that radiotherapy treatment should be arranged in working time and in practice, working hours of a day in the hospital we investigate are 8:00-12:00 and 13:30-17:30 Wang et al (2018a, b, c) p Kong et al (2019) p j (t) = b j t Liu et al (2018…”

Section: Problem Descriptionmentioning

confidence: 98%

“…Pei et al (2015Pei et al ( , 2018Pei et al ( , 2019a ) studied serial-batching scheduling problems with deteriorating jobs or learning effect and designed intelligent algorithms with superior performance for each specific problem. Furthermore, there are many advanced methods designed for problems with this phenomenon in recent years, such as Wang et al (2018a, b, c), Wang et al (2018a, b, c), Kong et al (2019), Liu et al (2018), Lu et al (2018) and so on. Note that in most studies considering the deteriorating effect in industry, such effect is not continuously changing with time and only considered at the start time point of the process.…”

Section: Machine Scheduling With Deteriorating Jobsmentioning

confidence: 99%

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A column generation approach for patient scheduling with setup time and deteriorating treatment duration

et al. 2021

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Nowadays most cancer patients are treated by radiotherapy. The treatment duration of patients will grow longer over time because of the half-life decaying effect of the radioactive source, which can be regarded as a continuous non-linear deteriorating effect. How to sequence the treatment of the patients before the radioactivity is reduced to the lowest available intensity is an important and complex problem. Meanwhile, the treatment sequence of cancer patients should not only be based on the waiting time but also on the severity of their illness. Therefore, the dual factors which reflect the severity of patients' illness as well as waiting time should be considered. The dual factors are denoted as the treatment value of patients in this paper and we determine patients in the waiting list to be selected, assigned and sorted for treatment, so as to maximize the overall treatment value of all patients. We also consider the setup time for each time of treatment, which cannot be ignored in reality. The original problem model is difficult to solve directly, so we reformulate the original problem to a set covering problem and it is solved by a column generation approach we develop. The master problem of selecting plans for treatment blocks and subproblems of generating plans are solved by GUROBI and dynamic programming, respectively. Numerical experiments are conducted to demonstrate the efficiency of the proposed column generation approach.

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Section: Problem Descriptionmentioning

confidence: 98%

Section: Machine Scheduling With Deteriorating Jobsmentioning

confidence: 99%

A column generation approach for patient scheduling with setup time and deteriorating treatment duration

et al. 2021

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“…Picking line ID 6-10 has medium-scale initial unit picking time in range (11,20). Picking line ID 11-15 has a large initial unit picking time in range (21,30). Within each group, there are different scale values of other parameters.…”

Section: Fatigue Analysismentioning

confidence: 99%

“…Based on the involved machines, current research about batch scheduling is reviewed from two main categories: single machine batch scheduling [24][25][26][27] and batch scheduling on multiple machines. Batch scheduling involved with multiple machines includes two sides: parallel batch machines [28][29][30][31][32] and flow shop batching and scheduling problems [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

A Heuristic Solution Approach to Order Batching and Sequencing for Manual Picking and Packing Lines considering Fatiguing Effect

Feng

2021

Scientific Programming

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In this research, we study an extended version of the joint order batching and scheduling optimization for manual vegetable order picking and packing lines with consideration of workers’ fatiguing effect. This problem is faced by many B2C fresh produce grocers in China on a daily basis which could severely decrease overall workflow efficiency in distribution center and customer satisfaction. In this order batching and sequencing problem, the setup time for processing each batch is volume-dependent and similarity dependent, as less ergonomic motion is needed in replenishing and picking similar orders. In addition, each worker’s fatiguing effect, usually caused by late shift and repetitive operation, which affects order processing times, is assumed to follow a general form of logistic growth with respect to the start time of order processing. We develop a heuristic approach to solve the resultant NP-hard problem for minimization of the total completion time. For order batching, a revised similarity index takes into account not only the number of common items in any two orders but also the proportion of these items based on the vegetable order feature. To sequence batches, the genetic algorithm is adapted and improved with proposed several efficient initialization and precedence rules. Within each batch, a revised nondecreasing item quantity algorithm is used. The performance of the proposed heuristic solution approach is evaluated using numerical instances generated from practical warehouse operations of our partnering B2C grocer. The efficiency of the proposed heuristic approach is demonstrated.

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“…Hermelin et al (2019) analyzed the parameterized tractability of single-machine scheduling involving rejection and makespan minimization. Kong et al (2019) proposed dynamic programming algorithm (H-DP) to tackle the problem of bounded parallel-batching single-machine scheduling involving non-identical job sizes, deteriorating jobs, setup time and job rejection, and also to minimize the sum of the make span and total penalty. Yavari et al (2019) proposed 2 meta-heuristic algorithms containing SPGA and N-SPGA for solving the OAS problem or rejection in a two-stage assembly environment and maximized the sum of revenues minus the total weighted tardiness.…”

Section: Introductionmentioning

confidence: 99%

Modeling and solution methods for hybrid flow shop scheduling problem with job rejection

et al. 2021

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This paper addresses the hybrid flow shop scheduling problem by considering job rejection to minimize the sum of the total tardiness cost of the scheduled jobs and total cost of the rejected jobs as a single-objective problem. A mixed-integer linear programming model is proposed to solve small-sized problems within an acceptable computational time. Also, this paper exhibits two innovative heuristic algorithms, which are presented to discover fast solutions for the problem along with five meta-heuristics are adapted to solve large-sized problems in the model. Another contribution of this paper is to illustrate the different encoding and decoding methods adapted to algorithms, which are capable of obtaining a feasible schedule and furthermore, to guarantee the efficiency of the solutions based on the schedule. The results obtained from the computational study demonstrate the mathematical model and proposed algorithms effectiveness. Additionally, this paper studies the efficacy of job rejection noting the scheduling for a real-world hybrid flow shop in the tile industry production system. As well as, in this paper, the problem is viewed from a bi-objective problem perspective, so that the tardiness costs of the scheduled jobs and rejection costs of rejected jobs as two objectives are minimized simultaneously to obtain the Pareto solutions. We analyze relationship between the results of the single-objective and bi-objective approaches on small and large-sized problems.

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Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine

Cited by 18 publications

References 33 publications

A column generation approach for patient scheduling with setup time and deteriorating treatment duration

A column generation approach for patient scheduling with setup time and deteriorating treatment duration

A Heuristic Solution Approach to Order Batching and Sequencing for Manual Picking and Packing Lines considering Fatiguing Effect

Modeling and solution methods for hybrid flow shop scheduling problem with job rejection

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