A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation

[EN] The permutation flowshop problem is a classic machine scheduling problem where n jobs must be processed on a set of m machines disposed in series and where each job must visit all machines in the same order. Many production scheduling problems resemble flowshops and hence it has generated much interest and had a big impact in the field, resulting in literally hundreds of heuristic and metaheuristic methods over the last 60 years. However, most methods proposed for makespan minimisation are not properly compared with existing procedures so currently it is not possible to know which are the most efficient methods for the problem regarding the quality of the solutions obtained and the computational effort required. In this paper, we identify and exhaustively compare the best existing heuristics and metaheuristics so the state-of-the-art regarding approximate procedures for this relevant problem is established. (C) 2016 Elsevier B.V. All rights reserved.The authors are sincerely grateful to the anonymous referees, who provide very valuable comments on the earlier version of the paper. This research has been funded by the Spanish Ministry of Science and Innovation, under projects "ADDRESS" (DPI2013-44461-P/DPI) and "SCHEYARD" (DPI2015-65895-R) co-financed by FEDER funds.Fernandez-Viagas, V.; Ruiz García, R.; Framinan, J. (2017). A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation. European Journal of Operational Research. 257(3):707-721. https://doi.org/10.1016/j.ejor.2016.09.055S707721257

Controllable Processing Times in Project and Production Management: Analysing the Trade-Off between Processing Times and the Amount of Resources

The amount of resources assigned to a task highly influences its processing time. Traditionally, different functions have been used in the literature in order to map the processing time of the task with the amount of resources assigned to the task. Obviously, this relation depends on several factors such as the type of resource and/or decision problem under study. Although in the literature there are hundreds of papers using these relations in their models or methods, most of them do not justify the motivation for choosing a specific relation over another one. In some cases, even wrong justifications are given and, hence, infeasible or nonappropriated relations have been applied for the different problems, as we will show in this paper. Thus, our paper intends to fill this gap establishing the conditions where each relation can be applied by analysing the relations between the processing time of a task and the amount of resources assigned to that task commonly employed in the production and project management literature

Generalised accelerations for insertion-based heuristics in permutation flowshop scheduling

The scheduling literature is abundant on approximate methods for permutation flowshop scheduling, as this problem is NP-hard for the majority of objectives usually considered. Among these methods, some of the most efficient ones use an insertion-type of neighbourhood to construct high-quality solutions. It is not then surprising that using accelerations to speed up the computation of the objective function can greatly reduce the running time of these methods, since a good part of their computational effort is spent in the evaluation of the objective function. Undoubtedly, the best-known of these accelerations has been employed for makespan minimisation (commonly denoted as Taillard’s accelerations). These accelerations have been extended to other related problems, but they cannot be employed for the classical permutation flowshop problem if the objective is other than the makespan. In these cases, other types of accelerations have been proposed, but they are not able to achieve a substantial reduction of the computational effort. In this paper, we propose a new speed-up procedure for permutation flowshop scheduling using objectives related to completion times. We first present some theoretical insights based on the concept of critical path. We also provide an efficient way to compute the critical path (indeed Taillard’s accelerations appear as a specific case of these results). The results show that the computational effort is substantially reduced for total completion time, total tardiness, and total earliness and tardiness, thus outperforming the existing accelerations for these problems.This research has been funded by the Spanish Ministry of Science and Innovation, under the project “PROMISE” with reference DPI2016-80750-P

The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm

In this paper, we address the permutation flow shop scheduling problem with sequence-dependent and non-anticipatory setup times. These setups are performed or supervised by multiple servers, which are renewable secondary resources (typically human resources). Despite the real applications of this kind of human supervision and the growing attention paid in the scheduling literature, we are not aware of any previous study on the problem under consideration. To cover this gap, we start theoretically addressing the problem by: proposing three mixed-integer linear programming models to find optimal solutions in the problem; and proposing different decoding procedures to code solutions in approximated procedures. After that, the best decoding procedure is used to propose a new mechanism that generates 896 different dispatching rules, combining different measures, indicators, and sorting criteria. All these dispatching rules are embedded in the traditional NEH algorithm. Finally, an iterated greedy algorithm is proposed to find near-optimal solutions. By doing so, we provide academics and practitioners with efficient methods that can be used to obtain exact solutions of the problem; applied to quickly schedule jobs and react under changes; used for initialisation or embedded in more advanced algorithms; and/or easily updated and implemented in real manufacturing scenarios