Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

New efficient constructive heuristics for the hybrid flowshop to minimise makespan: A computational evaluation of heuristics

This paper addresses the hybrid flow shop scheduling problem to minimise makespan, a well-known scheduling problem for which many constructive heuristics have been proposed in the literature. Nevertheless, the state of the art is not clear due to partial or non homogeneous comparisons. In this paper, we review these heuristics and perform a comprehensive computational evaluation to determine which are the most efficient ones. A total of 20 heuristics are implemented and compared in this study. In addition, we propose four new heuristics for the problem. Firstly, two memory-based constructive heuristics are proposed, where a sequence is constructed by inserting jobs one by one in a partial sequence. The most promising insertions tested are kept in a list. However, in contrast to the Tabu search, these insertions are repeated in future iterations instead of forbidding them. Secondly, we propose two constructive heuristics based on Johnson’s algorithm for the permutation flowshop scheduling problem. The computational results carried out on an extensive testbed show that the new proposals outperform the existing heuristics.Ministerio de Ciencia e Innovación DPI2016-80750-

NEH-based heuristics for the permutation flowshop scheduling problem to minimize total tardiness

Since Johnson׳s seminal paper in 1954, scheduling jobs in a permutation flowshop has been receiving the attention of hundreds of practitioners and researchers, being one of the most studied topics in the Operations Research literature. Among the different objectives that can be considered, minimising the total tardiness (i.e. the sum of the surplus of the completion time of each job over its due date) is regarded as a key objective for manufacturing companies, as it entails the fulfilment of the due dates committed to customers. Since this problem is known to be NP-hard, most research has focused on proposing approximate procedures to solve it in reasonable computation times. Particularly, several constructive heuristics have been proposed, with NEHedd being the most efficient one, serving also to provide an initial solution for more elaborate approximate procedures. In this paper, we first analyse in detail the decision problem depending on the generation of the due dates of the jobs, and discuss the similarities with different related decision problems. In addition, for the most characteristic tardiness scenario, the analysis shows that a huge number of ties appear during the construction of the solutions done by the NEHedd heuristic, and that wisely breaking the ties greatly influences the quality of the final solution. Since no tie-breaking mechanism has been designed for this heuristic up to now, we propose several mechanisms that are exhaustively tested. The results show that some of them outperform the original NEHedd by about 25% while keeping the same computational requirements.Ministerio de Ciencia e Innovación DPI2010-15573/DPIMinisterio de Ciencia e Innovación DPI2013-44461-P/DP

Efficient heuristics for the parallel blocking flow shop scheduling problem

We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them –especially the IGA– perform considerably better than those algorithms adapted from the DPFSP literature.Peer ReviewedPostprint (author's final draft

Modified Neh Heuristic On Makespan Reduction In Permutation Flow Shop Problems

Permutation flow shop problem (PFSP) is one of the commonly reviewed machine environments in scheduling problems. The order sequence for each process remains unchanged for all machines. Few algorithms have been developed to decide the sequence of n jobs and m machines that can minimize makespan in flow shops. Throughout the past 30 years, the NEH heuristics developed by Nawaz, Enscore and Ham has been commonly regarded as the best heuristic for minimizing the makespan in permutation flow shops. Due to these findings, NEH heuristics is selected as the basis of this study. Modification is done to enhance the objectives of this study, which is makespan and idle time reduction. In this study, a total of 109 flow-shop problems were solved with the number of machines and jobs being set at a range of 4 to 25. 100 problems were carried out using numerical assessments. The process times of the jobs were randomly generated within the range of 1 to 10 using Excel spreadsheets. Whereas the remaining 9 sets of tests were carried out using real world case studies. In each case study, the company involved was provided with a surface mounting technology (SMT) service. It has the capability of planning schedules by adopting the backward scheduling technique. The proposed heuristic, NEH-M will be compared to both the historical production schedule and NEH schedule in order to verify and validate the performance of the proposed idea. The performance of the NEH-M heuristics was computed using the error deviation (ED) formula. The generated results gained through Excel modeling show that the NEH-M heuristics outperforms the historical production schedule in all conditions. On the other hand, when the NEH-M heuristics is compared to the NEH heuristics, the overall performance of makespan reduction is underperforming while the overall performance of idle time reduction is over performing when there are large numbers of machines and jobs

Project scheduling under undertainty – survey and research potentials.

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Efficiency of the solution representations for the hybrid flow shop scheduling problem with makespan objective

In this paper we address the classical hybrid flow shop scheduling problem with makespan objective. As this problem is known to be NP-hard and a very common layout in real-life manufacturing scenarios, many studies have been proposed in the literature to solve it. These contributions use different solution representations of the feasible schedules, each one with its own advantages and disadvantages. Some of them do not guarantee that all feasible semiactive schedules are represented in the space of solutions –thus limiting in principle their effectiveness– but, on the other hand, these simpler solution representations possess clear advantages in terms of having consistent neighbourhoods with well-defined neighbourhood moves. Therefore, there is a trade-off between the solution space reduction and the ability to conduct an efficient search in this reduced solution space. This trade-off is determined by two aspects, i.e. the extent of the solution space reduction, and the quality of the schedules left aside by this solution space reduction. In this paper, we analyse the efficiency of the different solution representations employed in the literature for the problem. More specifically, we first establish the size of the space of semiactive schedules achieved by the different solution representations and, secondly, we address the issue of the quality of the schedules that can be achieved by these representations using the optimal solutions given by several MILP models and complete enumeration. The results obtained may contribute to design more efficient algorithms for the hybrid flow shop scheduling problem.Ministerio de Ciencia e Innovación DPI2016-80750-