A Branch-and-Bound Algorithm to Minimize the Makespan in a Flowshop with Blocking

Abstract

This work addresses the minimization of the makespan criterion for the flowshop problem with blocking. In this environment there are no buffers between successive machines, and therefore intermediate queues of jobs waiting in the system for their next operations are not allowed. We propose a lower bound which exploits the occurrence of blocking. A branch-and-bound algorithm that uses this lower bound is described and its efficiency is evaluated on several problems. Results of computational experiments are reported.

Scheduling The Flow Shop With Blocking Problem With The Chaos-Induced Discrete Self Organising Migrating Algorithm

“…where C Ron is the referenced makespan provided by Ronconi (2005), and C DSOM AC is the makespan found by the DSOMA C algorithm. Furthermore, average percentage relative difference (APRD), maximum percentage relative difference (MaxPRD), minimum percentage relative difference (MinPRD) and the standard deviation (SD) of PRD are calculated.…”

<b>Evaluation of heuristics for a branch and bound algorithm to minimize the makespan in a flowshop with blocking

“…During the past 40 years, the scheduling problem with the objective of minimizing the makespan in flowshop environment with blocking constraint has been studied by many researchers such as Companys & Mateo (2005); Ronconi (2005); Ronconi & Armentano (2001). This problem, which is described as Fm|block|Cmax according to Pinedo (2008), consists of scheduling n jobs that must be processed by m machines always with the same flow.…”

“…They solved eight problems unsolved by other methods. Ronconi (2005) developed an algorithm that exploits the occurrence of blocking in order to minimize the makespan time. Computational experiments proved that the proposed lower bound works better than the lower bound from Ronconi & Armentano (2001).…”

“…In this work, the efficiency of the use of an initial solution to the Branch and Bound algorithm was evaluated by comparison of the algorithms. The branch and bound algorithm used, as well as the lower bound, was proposed by Ronconi (2005). Four heuristic methods (MM, PF, wPF, and PW) were tested using a 180 problems data.…”

“…Neste trabalho, a eficiência da utilização de uma solução inicial para o algoritmo branch e bound foi avaliada com a comparação dos algoritmos. O algoritmo branch e bound utilizado, bem como o limitante inferior foram propostos por Ronconi (2005). Cinco métodos heurísticos foram avaliados (MM, PF, wPF e PW) utilizando um conjunto de problemas teste composto de 180 problemas.…”