Abstract

The classical flexible flowshop ($\mathit{FFc}$) environment consists of $c$-stages in series with $m$-machines in parallel at each stage, where each job has to undergo a particular series of actions. In this paper we consider a similar, yet different, and still a challenging real-life setting, that, to the best of our knowledge, has not been studied to date. We assume that there are $\ell$-sets in parallel in which each of the sets is an $m$-machine proportionate flowshop. In this new setting, each job can be processed on each one of the sets, but once a set is chosen, the job must be processed on all of its machines, in first-in-first-out method. We study several fundamental scheduling measures such as makespan, maximum tardiness with common due-date, total tardiness with common due-date, and total load. Moreover, we consider optional job-rejection and focus on minimising the total completion time. All problems are shown to be NP-hard, and pseudo-polynomial dynamic programming (DP) solution algorithms and Simulated Annealing (SA) metaheuristics are provided. The efficiency of all our proposed algorithms is validated through an extensive numerical study.

摘要

经典的柔性流水线（$\mathit{FFC}$) 环境包括$C$- 阶段串联$米$- 在每个阶段并行的机器，每个工作都必须经历一系列特定的动作。在本文中，我们考虑了一个相似但不同但仍然具有挑战性的现实生活环境，据我们所知，迄今为止尚未研究过。我们假设有$\ell$-并行集合，其中每个集合都是一个$米$-机器比例流水线。在这个新设置中，每个作业都可以在每个集合上处理，但是一旦选择了一个集合，该作业必须在其所有机器上以先进先出的方式处理。我们研究了几种基本的调度措施，例如制造时间、共同到期日的最大迟到、共同到期日的总迟到和总负荷。此外，我们考虑了可选的拒绝工作，并专注于最小化总完成时间。所有问题都被证明是 NP-hard，并且提供了伪多项式动态规划 (DP) 求解算法和模拟退火 (SA) 元启发式算法。我们提出的所有算法的效率都通过广泛的数值研究得到验证。