A branch-and-bound algorithm for single machine scheduling with quadratic earliness and tardiness penalties

Kianfar, Kamran; Moslehi, Ghasem

doi:10.1016/j.cor.2012.03.004

Cited by 18 publications

(14 citation statements)

References 30 publications

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“…Two of the studies dealing with quadratic JIT costs were carried out by Hussain and Joshi [22] and Zambrano Rey et al [25], using GA. Other studies were designed for less complex problems such as the flow-shop-like problem [39] or the single machine problem [4,5]. In fact, in a recent study by Demir and Kürşat [10], out of the 23 papers reviewed, none targeted the FJSSP with quadratic earliness and tardiness costs.…”

Section: Relevant Literaturementioning

confidence: 99%

“…JIT scheduling has been studied since the 1990s, but due to the intractable nature of the problem, the main focus has been on single machine problems [4,5], or specific cases of multiple machine problems: job shops with tardiness costs [6], identical parallel machines with earliness and tardiness costs [7], or problems with common due dates with earliness and tardiness penalties [8]. This paper focuses more particularly on flexible job-shop JIT scheduling.…”

Section: Introductionmentioning

confidence: 99%

“…First, a quadratic function represents better the penalties for due date non-compliance, which increase non-linearly [2]. Second, a quadratic penalty function avoids schedules where only a few jobs contribute to the majority of the penalty [5].…”

Section: Introductionmentioning

confidence: 99%

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Solving the flexible job-shop just-in-time scheduling problem with quadratic earliness and tardiness costs

Rey

Bekrar

Trentesaux

et al. 2015

Int J Adv Manuf Technol

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The flexible job-shop scheduling problem is known to be an (Non-deterministic Polynomial-time hard) combinatorial problem and has become a challenge in optimization and manufacturing control. Although flexibility is important in order to respond effectively to higher product variety, shorter lead times, and smaller batch sizes, industrialists also require just-in-time scheduling strategies to increase customer satisfaction. The aim of this paper is to find adequate job release times to meet production demands in relation to specific due dates. Since large deviations in job completion times are undesirable, the scheduling objective for just-in-time production is translated into the minimization of the mean-square due date deviation (MSD), quadratically penalizing inventory (earliness) costs and backlogging (tardiness) costs. Given the computational complexity of the problem, two meta-heuristics are proposed: a genetic algorithm (GA) and particle swarm optimization (PSO), as well as two different approaches to handle job release times. In the GA, job release times are treated as dependent variables, whereas the PSO enables the integration of job release times as independent variables within the particle encoding. These meta-heuristic approaches were compared using three benchmarks, two adapted from the literature and one inspired from a real manufacturing cell. The simulation results show that the GA and PSO attained similar performances, each one with advantages and disadvantages for constrained and unconstrained MSD problems.

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Section: Relevant Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving the flexible job-shop just-in-time scheduling problem with quadratic earliness and tardiness costs

Rey

Bekrar

Trentesaux

et al. 2015

Int J Adv Manuf Technol

View full text Add to dashboard Cite

show abstract

“…e problems of minimizing the quadratic earliness and tardiness have also been considered. In [11][12][13], researchers, under different assumptions, considered the problem in which all quadratic earliness and tardiness penalties are equal, and this problem with symmetric weighted quadratic penalty function was also studied in [14,15], while the asymmetric weighted version of this problem was investigated in [16][17][18]. e relevant scheduling problems with quadratic cost function have also been studied in [19,20].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Single Machine JIT Scheduling with Geometric Processing Times and Due Dates

Luo

2021

Mathematical Problems in Engineering

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In this paper, we investigate a static stochastic single machine JIT scheduling problem in which the jobs’ processing times are stochastically independent and follow geometric distributions whose mean is provided, due dates are geometrically distributed with a common mean, and both the unit penalty of earliness/tardiness and the fixed penalty of earliness/tardiness are deterministic and different. The objective is to minimize the expected total penalties for quadratic earliness, quadratic tardiness, and early and tardy jobs. We prove that the optimal schedule to minimize this problem is V-shaped with respect to the ratio of mean processing time to unit tardiness penalty under the specific condition. Also, we show a special case and two theorems related to this JIT scheduling problem under specific situations where the optimal solutions exist. Finally, based on the V-shaped characteristic, a dynamic programming algorithm is designed to achieve an optimal V-shaped schedule in pseudopolynomial time.

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“…Also, the linear earliness and squared tardiness problem was considered by Schaller [16], Valente [17][18][19], Valente and Schaller [20], and Behnamian and Zandieh [21]. The problem with both quadratic earliness and quadratic tardiness costs was studied by Valente and Alves [22], Valente and Moreira [23], Valente [24], Valente et al [25], Singh et al [26], Kianfar and Moslehi [27], and Vilà and Pereira [28]. A large number of papers have been published on the total weighted tardiness problem.…”

Section: Introductionmentioning

confidence: 99%

Metaheuristics for the single machine weighted quadratic tardiness scheduling problem

Gonçalves

Valente

Schaller

2016

Computers & Operations Research

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This paper considers the single machine scheduling problem with weighted quadratic tardiness costs. Three metaheuristics are presented, namely iterated local search, variable greedy and steady-state genetic algorithm procedures. These address a gap in the existing literature, which includes branch-andbound algorithms (which can provide optimal solutions for small problems only) and dispatching rules (which are efficient and capable of providing adequate solutions for even quite large instances). A simple local search procedure which incorporates problem specific information is also proposed. The computational results show that the proposed metaheuristics clearly outperform the best of the existing procedures. Also, they provide an optimal solution for all (or nearly all, in the case of the variable greedy heuristic) the smaller size problems. The metaheuristics are quite close in what regards solution quality. Nevertheless, the iterated local search method provides the best solution, though at the expense of additional computational time. The exact opposite is true for the variable greedy procedure, while the genetic algorithm is a good all-around performer.

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A branch-and-bound algorithm for single machine scheduling with quadratic earliness and tardiness penalties

Cited by 18 publications

References 30 publications

Solving the flexible job-shop just-in-time scheduling problem with quadratic earliness and tardiness costs

Solving the flexible job-shop just-in-time scheduling problem with quadratic earliness and tardiness costs

Stochastic Single Machine JIT Scheduling with Geometric Processing Times and Due Dates

Metaheuristics for the single machine weighted quadratic tardiness scheduling problem

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