Mathematical Programming and Heuristics for Scheduling Problems with Early and Tardy Penalties

Ratli, Mustapha; Benmansour, Rachid; Macedo, Rita; Hanafi, Saïd; Wilbaut, Christophe

doi:10.1002/9781118731598.ch8

Cited by 4 publications

(3 citation statements)

References 67 publications

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“…Ratli et al [84] presented a comprehensive list of mathematical models for scheduling jobs on a single machine by minimizing weighted earliness and tardiness. The problem, denoted as 1|| α j E j + β j T j , is relevant in the context of just-in-time production.…”

Section: Scheduling Problemsmentioning

confidence: 99%

Arc Flow Formulations Based on Dynamic Programming: Theoretical Foundations and Applications

de Lima,

Alves,

Clautiaux

et al. 2020

Preprint

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Network flow formulations are among the most successful tools to solve optimization problems. One of such formulations is the arc flow, where variables represent flows on individual arcs of the network. For NP-hard problems, polynomial-sized arc flow models typically provide weak linear relaxations and may have too much symmetry to be efficient in practice. Instead, arc flow models with a pseudo-polynomial size usually provide strong relaxations and are efficient in practice. The interest in pseudo-polynomial arc flow formulations has grown considerably in the last twenty years, in which they have been used to solve many open instances of hard problems. A remarkable advantage of arc flow models is the possibility to solve practical-sized instances directly by a Mixed Integer Linear Programming solver, avoiding the implementation of complex methods based on column generation.In this survey, we present theoretical foundations of pseudo-polynomial arc flow formulations, by showing a relation between their network and Dynamic Programming (DP). This relation allows a better understanding of the strength of these formulations, through a link with models obtained by Dantzig-Wolfe decomposition. The relation with DP also allows a new perspective to relate state-space relaxation methods for DP with arc flow models. We also present a dual point of view to contrast the linear relaxation of arc flow models with that of models based on paths and cycles. To conclude, we review the main solution methods and applications of arc flow models based on DP in several domains such as cutting, packing, scheduling, and routing.

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Section: Scheduling Problemsmentioning

confidence: 99%

Arc Flow Formulations Based on Dynamic Programming: Theoretical Foundations and Applications

de Lima,

Alves,

Clautiaux

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Another survey was later performed by Lauff and Werner (2004) for E-T problems in a multi-machine environment. Recently, Ratli et al (2013) presented an overview on mathematical formulations and heuristics proposed for E-T problems but on a single machine environment. In these three works, the authors only reviewed problems with common due dates for all jobs.…”

Section: An Annotated Bibliography For E-t Problems Related To Those ...mentioning

confidence: 99%

A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems

Kramer

Subramanian

2017

J Sched

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This work proposes a unified heuristic algorithm for a large class of earliness-tardiness (E-T) scheduling problems. We consider single/parallel machine E-T problems that may or may not consider some additional features such as idle time, setup times and release dates. In addition, we also consider those problems whose objective is to minimize either the total (average) weighted completion time or the total (average) weighted flow time, which arise as particular cases when the due dates of all jobs are either set to zero or to their associated release dates, respectively. The developed local search based metaheuristic framework is quite simple, but at the same time relies on sophisticated procedures for efficiently performing local search according to the characteristics of the problem. We present efficient move evaluation approaches for some parallel machine problems that generalize the existing ones for single machine problems. The algorithm was tested in hundreds of instances of several E-T problems and particular cases. The results obtained show that our unified heuristic is capable of producing high quality solutions when compared to the best ones available in the literature that were obtained by specific methods. Moreover, we provide an extensive annotated bibliography on the problems related to those considered in this work, where we not only indicate the approach(es) used in each publication, but we also point out the characteristics of the problem(s) considered. Beyond that, we classify the existing methods in different categories so as to have a better idea of the popularity of each type of solution procedure.

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“…Ratli et al [277] presented a comprehensive list of mathematical models for scheduling jobs on a single machine by minimizing weighted earliness and tardiness. The problem, denoted as 1|| α j E j + β j T j , is relevant in the context of just-in-time production.…”

Section: Scheduling Problemsmentioning

confidence: 99%

Integer programming based methods applied to cutting, packing, and scheduling

Loti de Lima

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Como um adepto do conceito de originação dependente, acredito na contribuição de todos os eventos do universo para a formação deste trabalho. Naturalmente, algumas pessoas me remetem a inuências bastante diretas e gostaria de destacá-las. Em particular, agradeço às pessoas mais importantes para mim: meus pais. Agradeço ao meu orientador, Flávio, que é para mim uma grande inspiração, não só prossional, mas também pessoal.Agradeço ao meu amigo e coorientador Thiago, que me introduziu ao tema desta tese.Agradeço a todos os meus coautores, em particular, ao Manuel Iori e ao José Valério de Carvalho, que contribuíram de uma forma imensa para minha formação como pesquisador.Agradeço a todos que me deram algum suporte ou passaram pela minha vida ao longo dos anos. Finalmente, agradeço à FAPESP, pelo apoio nanceiro (processo 2017/11831-1). ResumoEsta tese foca em otimização combinatória, um dos grandes campos em otimização. Esse campo consiste de problemas de decisão, nos quais é dado um conjunto discreto potencialmente enorme de soluções possíveis e deve-se encontrar uma única solução que otimize uma dada função objetivo. Esses problemas têm um grande número de aplicações no mundo real, principalmente em logística industrial e em cadeia de suprimentos.Primeiro, estudamos formulações de uxo em redes que podem ser aplicadas a problemas gerais de otimização combinatória. Apresentamos um survey discutindo as fundamentações teóricas e as principais aplicações bem-sucedidas dos chamados modelos de uxo em arcos pseudo-polinomiais. Em seguida, propomos novos métodos exatos para resolver tais modelos, envolvendo geração de colunas, regras de branching especializadas e estratégias de xação de variáveis. Aplicamos os métodos de solução propostos a problemas bem estudados da literatura de corte, empacotamento e escalonamento, incluindo, por exemplo, os clássicos bin packing problem e cutting stock problem. Nossos experimentos computacionais mostram a ecácia dos métodos propostos, resolvendo na otimalidade um grande número de instâncias benchmark em aberto, de vários problemas.A segunda parte desta tese dá atenção especial à área de corte e empacotamento bidimensional, que está entre as áreas mais estudadas em otimização combinatória. Apresentamos uma revisão das referências mais relevantes que surgiram nas últimas duas décadas e propomos uma biblioteca online para organizar sistematicamente os materiais mais relevantes sobre tais problemas. Essas contribuições podem facilitar pesquisas futuras na área ativa de corte e empacotamento bidimensional.Nossa última contribuição diz respeito a um problema do mundo real surgido de uma empresa italiana de produção de carne. O problema é composto por um grande conjunto de decisões complexas, envolvendo a alocação diária de mão de obra e o escalonamento de pedidos na empresa. Para resolver esse problema, propomos uma heurística construtiva de três fases, implementada em um framework multi-start. Nosso algoritmo supera em média as decisões tomadas pela estratégia anterior da empresa.

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Mathematical Programming and Heuristics for Scheduling Problems with Early and Tardy Penalties

Cited by 4 publications

References 67 publications

Arc Flow Formulations Based on Dynamic Programming: Theoretical Foundations and Applications

Arc Flow Formulations Based on Dynamic Programming: Theoretical Foundations and Applications

A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems

Integer programming based methods applied to cutting, packing, and scheduling

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