Estimation of distribution parameters associated with facilities design problems involving forward and backtracking of materials

Khare, Vikas; Khare, Manu; Neema, Mohit

doi:10.1016/0360-8352(88)90038-1

Cited by 15 publications

(3 citation statements)

References 12 publications

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“…However, they considered only the forward movement of material. Khare et al (1988a) extended these methods to consider both forward and backward movement of materials. The expression they proposed for the mean and variance of the material flow cost is shown in their paper.…”

Section: Mathematical Model For the Mofl Problemmentioning

confidence: 99%

A new approach to the multiple objective facility layout problem

Sha

Chen

2001

Integrated Manufacturing Systems

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This paper presents a new approach for combining the quantitative and qualitative objectives to resolve the facility layout problem. In previous studies, there are various approaches to generate solutions for the facility layout problem. Suboptimal solutions need to be considered for large layout problems since optimal algorithms are computationally infeasible. Therefore, it is important to set criteria to measure the quality of various solutions. In this paper, a new measure of solution quality, the probability of superiority, is offered for the determination of the probability that one layout is better than the others. An example is presented to illustrate our proposed approach.

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Section: Mathematical Model For the Mofl Problemmentioning

confidence: 99%

A new approach to the multiple objective facility layout problem

Sha

Chen

2001

Integrated Manufacturing Systems

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“…Recently, Kouvelis et al [23,24], Sarker et al [43], and Nori and Sarker [30] have investigated the optimal and sub-optimal solutions to backtracking problems. However, several other authors deserve the credit for first identifying the existence of backtracking problems in production lines and their rudimentary treatments to solve them [1,21]. Obata [32, pp.…”

Section: Previous Researchmentioning

confidence: 99%

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Sarker¹,

Wilhelm²,

Hogg³

1998

Annals of Operations Research

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The assignment of M unique machines to M locations with the objective of minimizing the total machine-to-machine material transportation cost in a flow line may be formulated as a quadratic assignment problem (QAP). Instead of having M unique machines, if an application involves one or more sets of identical machines, the location problem becomes a tertiary assignment problem (TAP). Solving a large problem of this kind is extremely difficult because of its combinatorial nature. When machine-to-machine flow is fixed, the TAP may be specialized to a QAP for which the unique machine problem is a special case. Obtaining an optimum solution to this problem when M is large is also computationally intractable. However, this problem may be solved by identifying sets of identical machines which may be partitioned into individual, "unique" machines. Properties of a special type of matrix called the amoebic matrix are used in the partitioned problems to provide approximate solutions, which are relabeled to prescribe a solution to the original problem. Results are demonstrated along with suggestions for further research.

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“…Outras aplicações podem ser encontradas em McCormick (1970), Hubert & Schulz. (1976), Heffley (1977), Los (1978), Krackhardt (1988), Khare et al (1988aKhare et al ( , 1988b, Bland & Dawson (1991), Lacksonen & Enscore (1993), Medova (1994), Gouveia & Voß (1995), Bozer & Suk-Chul (1996), Mason & Rönnqvist (1997), Ostrowski & Ruoppila (1997), Ball et al (1998), Haghani & Chen (1998), Kochhar et al (1998), Martin (1998) Desde a sua primeira formulação, o PQA tem atraído a atenção de pesquisadores em todo o mundo, não apenas pela sua importância prática e teórica, mas principalmente pela sua complexidade. Trata-se de um dos mais difíceis problemas de otimização combinatória: instâncias de ordem n > 30 não podem, em geral, ser resolvidas exatamente em tempo computacional aceitável.…”

Section: Introductionunclassified

Uma revisão comentada das abordagens do problema quadrático de alocação

2004

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ResumoO Problema Quadrático de Alocação, PQA, um dos mais difíceis da classe NP-hard, modela diversas aplicações em diferentes áreas como pesquisa operacional, computação paralela e análise estatística de dados discretos. Além disso, problemas conhecidos como o do caixeiro viajante, o da clique maximal, o de particionamento e o de isomorfismo de grafos podem ser formulados como um PQA. Na tentativa de identificar novas propriedades estruturais para este problema, diversas formulações aparecem na literatura. Reunimos tais formulações, destacando suas principais características para classificá-las segundo as técnicas matemáticas nelas adotadas. Finalizamos o artigo avaliando a extensão das contribuições dadas ao problema, quer na elaboração de algoritmos, quer no cálculo de limites inferiores ou na caracterização de classes de exemplares polinomiais ou não, oriundas das diferentes abordagens aqui estudadas.Palavras-chave: problema quadrático de alocação; formulações; otimização combinatória. AbstractThe Quadratic Assignment Problem, QAP, one of the most difficult problems in NP-hard class, models many applications in several areas such as operational research, parallel and distributed computing, and combinatorial data analysis. Besides, other optimization combinatorial problems such as the traveling salesman problem, maximal clique, isomorphism and graph partitioning can be formulated as a QAP. In this paper, we survey some of the most important formulations available, in order to classify them according to their mathematical resources. Finally, we analyze the extension of the contributions brought by the studies of different approaches.

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Estimation of distribution parameters associated with facilities design problems involving forward and backtracking of materials

Cited by 15 publications

References 12 publications

A new approach to the multiple objective facility layout problem

A new approach to the multiple objective facility layout problem

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Uma revisão comentada das abordagens do problema quadrático de alocação

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