Approximation algorithms for the parallel flow shop problem

Abstract

We consider the N P-hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems:assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnson's rule. For m = 2, we present a 3 2 -approximation algorithm, and for m = 3, we present a 12 7 -approximation algorithm. Both these algorithms run in O(n log n) time. These are the first approximation algorithms with fixed worst-case performance guarantees for the parallel flow shop problem.

Frontiers in Algorithmics

“…Given a complete (permutation) genome R and an incomplete scaffold S, fill the missing genes in R − S into S to have S such that the genomic distance (or DCJ distance [26]) between R and S is minimized. It was shown that this problem can be solved in polynomial time.…”

“…A random CSP model, called Model RB, is defined by Xu and Li [23], which has an increasing domain size and exhibits exact phase transition phenomena. Many hard instances with planted solutions can be generated via Model RB [24,26], to be successfully used as benchmarks in various algorithmic competitions and in many research papers, such as the annual CSP solver competitions, the annual Pseudo-Boolean (0-1 Integer Programming) solver competitions, the annual MAX-SAT solver competitions, and the annual SAT solver competitions, etc. [24].…”

“…In the past, the hardness of model RB is theoretically shown by exponential lower bounds on the length of resolution [25], and some analysis on the evolution of its solution space [27,28], besides many experimental results [26]. Some structural parameters of constraint hypergraphs are also analyzed to show hardness of Model RB with respective to the structural decomposition methods, such as hinge width [15], decycling number [12], treewidth [22], and hypertree width [16].…”

Programación de Máquinas Paralelas no Relacionadas con Tiempos de Montaje dependientes de la Secuencia y Entrada Dinámica usando Algoritmos Genéticos

“…Aunque es frecuente en la literatura el tratamiento de este tipo de problema partiendo del supuesto de que las máquinas paralelas son idénticas como puede verse en trabajos recientes como los de Salazar-Hornig & Medina (2013), Gicquel et al (2012), Zhang & van de Velde (2012), Carpov et al (2012) y Kis & Kovacs (2012) entre otros; en la realidad de las empresas es más común encontrar máquinas paralelas no relacionadas, por razones de evolución tecnológica en el tiempo o por decisión de la compañía para tener equipos adecuados a las necesidades de producción de diferentes líneas de productos.…”

“…Salazar-Hornig & Medina (2013) utilizaron un algoritmo genético para minimizar el makespan suponiendo máquinas paralelas idénticas. Zhang & Van de Velde (2012) propusieron un algoritmo de aproximación, Driessel & Monch (2011) y James & Almada-Lobo (2011) aplicaron búsqueda en vecindario variable, Lin et al (2011) resolvieron un problema de paralelismo con un algoritmo voraz; mientras Chang & Chen (2011) adaptaron algoritmos genéticos. Ribas-Vila et al (2009) estudiaron un conjunto de heurísticas teniendo a la vez el criterio de minimizar el tiempo medio de fabricación y la tardanza.…”