A speed-up procedure for the hybrid flow shop scheduling problem

Article number 115903During the last decades, hundreds of approximate algorithms have been proposed in the literature addressing flow-shop-based scheduling problems. In the race for finding the best proposals to solve these problems, speedup procedures to compute objective functions represent a key factor in the efficiency of the algorithms. This is the case of the well-known Taillard’s accelerations proposed for the traditional flow shop with makespan minimisation or several other accelerations proposed for related scheduling problems. Despite the interest in proposing such methods to improve the efficiency of approximate algorithms, to the best of our knowledge, no speed-up procedure has been proposed so far in the hybrid flow shop literature. To tackle this challenge, we propose in this paper a speed-up procedure for makespan minimisation, which can be incorporate in insertion-based neighbourhoods using a complete representation of the solutions. This procedure is embedded in the traditional iterated greedy algorithm. The computational experience shows that even incorporating the proposed speed-up procedure in this simple metaheuristic results in outperforming the best metaheuristic for the problem under consideration.Junta de Andalucía(España) US-1264511Ministerio de Ciencia e Innovación (España) PID2019-108756RB-I0

On insertion tie-breaking rules in heuristics for the permutation flowshop scheduling problem

The most efficient approximate procedures so far for the flowshop scheduling problem with makespan objective – i.e. the NEH heuristic and the iterated greedy algorithm – are based on constructing a sequence by iteratively inserting, one by one, the non-scheduled jobs into all positions of an existing subsequence, and then, among the so obtained subsequences, selecting the one yielding the lowest (partial) makespan. This procedure usually causes a high number of ties (different subsequences with the same best partial makespan) that must be broken via a tie-breaking mechanism. The particular tie-breaking mechanism employed is known to have a great influence in the performance of the NEH, therefore different procedures have been proposed in the literature. However, to the best of our knowledge, no tie-breaking mechanism has been proposed for the iterated greedy. In our paper, we present a new tie-breaking mechanism based on an estimation of the idle times of the different subsequences in order to pick the one with the lowest value of the estimation. The computational experiments carried out show that this mechanism outperforms the existing ones both for the NEH and the iterated greedy for different CPU times. Furthermore, embedding the proposed tie-breaking mechanism into the iterated greedy provides the most efficient heuristic for the problem so far.Ministerio de Ciencia e Innovación DPI2010-15573/DP

A beam-search-based constructive heuristic for the PFSP to minimise total flowtime

In this paper we present a beam-search-based constructive heuristic to solve the permutation flowshop scheduling problem with total flowtime minimisation as objective. This well-known problem is NP-hard, and several heuristics have been developed in the literature. The proposed algorithm is inspired in the logic of the beam search, although it remains a fast constructive heuristic. The results obtained by the proposed algorithm outperform those obtained by other constructive heuristics in the literature for the problem, thus modifying substantially the state-of-the-art of efficient approximate procedures for the problem. In addition, the proposed algorithm even outperforms two of the best metaheuristics for many instances of the problem, using much lesser computation effort. The excellent performance of the proposal is also proved by the fact that the new heuristic found new best upper bounds for 35 of the 120 instances in Taillard’s benchmark.Ministerio de Ciencia e Innovación DPI2013-44461-PMinisterio de Ciencia e Innovación DPI2016-80750-

Reduction of permutation flowshop problems to single machine problems using machine dominance relations

The Permutation Flowshop Scheduling Problem with Makespan objective (PFSP-M) is known to be NP-hard for more than two machines, and literally hundreds of works in the last decades have proposed exact and approximate algorithms to solve it. These works—of computational/experimental nature—show that the PFSP-M is also empirically hard, in the sense that optimal or quasi-optimal sequences statistically represent a very small fraction of the space of feasible solutions, and that there are big differences among the corresponding makespan values. In the vast majority of these works, it has been assumed that (a) processing times are not job- and/or machine-correlated, and (b) all machines are initially available. However, some works have found that the problem turns to be almost trivial (i.e. almost every sequence yields an optimal or quasi-optimal solution) if one of these assumptions is dropped. To the best of our knowledge, no theoretical or experimental explanation has been proposed by this rather peculiar fact. Our hypothesis is that, under certain conditions of machine availability, or correlated processing times, the performance of a given sequence in a flowshop is largely determined by only one stage, thus effectively transforming the flowshop layout into a single machine. Since the single machine scheduling problem with makespan objective is a trivial problem where all feasible sequences are optimal, it would follow that, under these conditions, the equivalent PFSP-M is almost trivial. To address this working hypothesis from a general perspective, we investigate some conditions that allow reducing a permutation flowshop scheduling problem to a single machine scheduling problem, focusing on the two most common objectives in the literature, namely makespan and flowtime. Our work is a combination of theoretical and computational analysis, therefore several properties are derived to prove the conditions for an exact (theoretical) equivalence, together with an extensive computational evaluation to establish an empirical equivalence

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

A bounded-search iterated greedy algorithm for the distributed permutation flowshop scheduling problem

As the interest of practitioners and researchers in scheduling in a multi-factory environment is growing, there is an increasing need to provide efficient algorithms for this type of decision problems, characterised by simultaneously addressing the assignment of jobs to different factories/workshops and their subsequent scheduling. Here we address the so-called distributed permutation flowshop scheduling problem, in which a set of jobs has to be scheduled over a number of identical factories, each one with its machines arranged as a flowshop. Several heuristics have been designed for this problem, although there is no direct comparison among them. In this paper, we propose a new heuristic which exploits the specific structure of the problem. The computational experience carried out on a well-known testbed shows that the proposed heuristic outperforms existing state-of-the-art heuristics, being able to obtain better upper bounds for more than one quarter of the problems in the testbed.Ministerio de Ciencia e Innovación DPI2010-15573/DP

The permutation flowshop scheduling problem: analysis, solution procedures and problem extensions

During the past twenty five years, following the massive use of internet and the EU single Market, European manufacturing companies struggle in a more competitive market, where firms from different countries must fight for common customers. As a consequence, prices of the products have decreased and the efficiency in the production processes of the companies have become more and more important. Nowadays, this fact is also increasing due to the competition from companies in developing countries whose labour cost is substantially lower. Therefore, production management is a key element for companies to survive. Production management involves decision making over several issues such as master scheduling, material requirements planning, capacity planning, manufacturing scheduling, ... Among these decisions, manufacturing scheduling plays an essential role on resource productivity and customer service. Its role is also increasing in many service industries as transportation, computer and communications industries, which are moving towards manufacture-to-order and virtual environments. Manufacturing scheduling deals with the determination of the jobs which are processed for each resource in each instant of time, i.e. establishes the schedules of the resources along the horizon under consideration. In order to determine the best schedule for the shop floor, both the specific constraints and the goal of the shop have to be considered. In these environments, the difficulty of the scheduling problem increases and becomes NP-hard even for the most simple scheduling problems, being extremely complex for real manufacturing scenarios. Additionally, scheduling decisions should be made in short time intervals requiring a rapid response time, due to several aspects such as the lifetime of a schedule, the delay in the suppliers, arrivals of new jobs to be processed, rescheduling due to failures while processing a job, .... All these issues strongly stress the need to find fast and efficient solution procedures (i.e. heuristics and metaheuristics) for solving manufacturing scheduling problems. In practice, several processing layouts have been adopted by companies to manufacture their products. Among them, the Permutation Flowshop Scheduling Problem (PFSP in the following), which is the problem addressed in this Thesis, stands out as the most relevant, being one of the most studied problems in Operations Research. There are several reasons for this fact: On the one hand, the flow shop layout is the common configuration in many real manufacturing scenarios, as it presents several advantages over more general job shop configuration, and, in addition, many job shops are indeed a flow shop for most of the jobs. On the other hand, many models and solution procedures for different constraints and layouts have their origins in the flowshop scheduling problem, which increases the importance to find efficient algorithms for this scheduling problem. Despite the huge number of research conducted on the PFSP, we believe that there is room for improving the current state of the art in the topic by: 1. deepening the understanding of the problem with respect to their input parameters, 2. devising new approximate solution procedures for the common employed objectives, and 3. addressing problem extensions to capture more realistic situations. To carry out this goal, the following general research objectives are identified: 1. To review the PFSP literature for the most common objectives, i.e. makespan, total completion time and due-date-based objectives (total tardiness, and total earliness and tardiness). 2. To analyse the influence of the processing times and due dates of the jobs on the PFSP. 3. To provide schedulers with faster and more efficient heuristics and metaheuristics to solve the PFSP for makespan, total completion time, total tardiness, and total earliness and tardiness minimisation. 4. To demonstrate the efficiency and good performance of the solution procedures developed in Goal 3. 5. To extend the proposals in Goal 3 to some constrained PFSP based on real manufacturing environments. To achieve these objectives, the Thesis have been structured in five parts as follows: - Part I is divided into two chapters. In Chapter 1.1, we introduce this Thesis and discuss its main contributions. In Chapter 2, the problem under consideration is stated. The measures to compare approximated algorithms are discussed in Chapter 3. There, the benchmarks used to evaluated the algorithms are introduced and an alternative indicator is proposed to overcome some problems detected using the traditional ones. - In Part II, we analyse the problem in detail along three chapters. Dealing with Objective 1, the main contributions in the literature are review for the most-common objective functions in Chapter 4. Additionally, in Chapter 5, we extensively study the behaviour of the problem depending on the configuration of the shops, i.e. processing times and due dates of the jobs (see Goal 2). - In Part III, we propose new novelties efficient algorithms to solve the PFSP under several objectives. The procedures, constructive and improvement heuristics and metaheuristics, exploit the specific structure of the problem to both reduce the computational times of them and improve the quality of the solutions. Additionally, they are validated in extensive computational evaluations, comparing them with the state-of-the-art algorithms under the same conditions. More specifically, this part is divided in four chapters and addresses the general research objectives GO3 and GO4. Firstly, a new tie-breaking mechanism to minimise makespan, which can be incorporated in the two most efficient algorithms for the problem, is proposed in Chapter 6. In Chapter 7, two efficient constructive heuristics are proposed to minimise total flowtime. Several tie-breaking mechanisms are proposed and compared to minimise total tardiness in Chapter 8. Finally, four procedures to minimise total earliness and tardiness are proposed in Chapter 9. - In Part IV, focused in more real manufacturing environment, new constraints are added to the traditional problem as well as different consideration and interaction between factories are taken into account. The proposed environments are solved using efficient approximate methods taken into consideration ideas of the traditional PFSP. More specifically, an iterated non-population algorithm to minimise makespan subject to a maximum tardiness is proposed in Chapter 10. In the Chapter 11, we add the blocking constraints to the traditional PFSP. These constraints take into consideration limited buffers between the machines. This problem, of permutation nature, is solved by means of an efficient beam-search-based constructive heuristic trying to minimise the total completion time. In Chapter 12, we consider the parallel flowshop scheduling problem also denoted as distributed PFSP where several identical flowshop or even flowshop factories are available in parallel to assign the jobs. The problem is solved using a bounded-search iterated greedy algorithm - Finally, in Part V, the conclusions of this research and future research lines are discussed.Premio Extraordinario de Doctorado U

Efficient heuristics for the hybrid flow shop scheduling problem with missing operations

In this paper, we address the hybrid flowshop scheduling problem for makespan minimisation. More specifically, we are interested in the special case where there are missing operations, i.e. some stages are skipped, a condition inspired in a realistic problem found in a plastic manufacturer. The main contribution of our paper is twofold. On the one hand we carry out a computational analysis to study the hardness of the hybrid flowshop scheduling problem with missing operations as compared to the classical hybrid flowshop problem. On the other hand, we propose a set of heuristics that captures some special features of the missing operations and compare these algorithms with already existing heuristics for the classical hybrid flowshop, and for the hybrid flowshop problem with missing operations. The extensive computational experience carried out shows that our proposal outperforms existing methods for the problem, indicating that it is possible to improve the makespan by interacting with the jobs with missing operations.Ministerio de Ciencia e Innovación DPI2016-80750-

A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimize total flowtime

This paper focuses on the blocking flow shop scheduling problem with the objective of total flowtime minimisation. This problem assumes that there are no buffers between machines and, due to its application to many manufacturing sectors, it is receiving a growing attention by researchers during the last years. Since the problem is NP-hard, a large number of heuristics have been proposed to provide good solutions with reasonable computational times. In this paper, we conduct a comprehensive evaluation of the available heuristics for the problem and for related problems, resulting in the implementation and testing of a total of 35 heuristics. Furthermore, we propose an efficient constructive heuristic which successfully combines a pool of partial sequences in parallel, using a beam-search-based approach. The computational experiments show the excellent performance of the proposed heuristic as compared to the best-so-far algorithms for the problem, both in terms of quality of the solutions and of computational requirements. In fact, despite being a relative fast constructive heuristic, new best upper bounds have been found for more than 27% of Taillard’s instances.Ministerio de Ciencia e Innovación DPI2013-44461-P/DP

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-