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-

Heuristics for the distributed blocking Ffow shop scheduling problem

Postprint (published version

Native metaheuristics for non-permutation flowshop scheduling

The most general flowshop scheduling problem is also addressed in the literature as non-permutation flowshop (NPFS). Current processors are able to cope with the combinatorial complexity of (n!)exp m. NPFS scheduling by metaheuristics. After briefly discussing the requirements for a manufacturing layout to be designed and modeled as non-permutation flowshop, a disjunctive graph (digraph) approach is used to build native solutions. The implementation of an Ant Colony Optimization (ACO) algorithm has been described in detail; it has been shown how the biologically inspired mechanisms produce eligible schedules, as opposed to most metaheuristics approaches, which improve permutation solutions. ACO algorithms are an example of native non-permutation (NNP) solutions of the flowshop scheduling problem, opening a new perspective on building purely native approaches. The proposed NNP-ACO has been assessed over existing native approaches improving most makespan upper bounds of the benchmark problems from Demirkol et al. (1998)

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

A review and classification of heuristics for permutation flow-shop scheduling with makespan objective

Makespan minimization in permutation flow-shop scheduling is an operations research topic that has been intensively addressed during the last 40 years. Since the problem is known to be NP-hard for more than two machines, most of the research effort has been devoted to the development of heuristic procedures in order to provide good approximate solutions to the problem. However, little attention has been devoted to establish a common framework for these heuristics so that they can be effectively combined or extended. In this paper, we review and classify the main contributions regarding this topic and discuss future research issues.Ministerio de Ciencia y Tecnología DPI-2001-311

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