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

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-

Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments

In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing research coping with optimization problems in uncertain environment aims at finding a single sufficiently robust solution so that random noise and unpredictable circumstances would have the least possible detrimental effect on the quality of the solution. The measures of robustness are usually based on various kinds of empirically designed averaging techniques. In contrast to the previous work, our algorithm aims at finding a collection of robust schedules that allow for a more informative decision making. The notion of robustness is measured quantitatively in terms of the classical mathematical notion of a norm on a vector space. We provide a theoretical insight into the relationship between the properties of the probability distribution over the uncertain delivery times and the robustness quality of the schedules produced by the algorithm after a polynomial runtime in terms of approximation ratios

Solving a flow shop scheduling problem with missing operations in an Industry 4.0 production environment

Industry 4.0 is a modern approach that aims at enhancing the connectivity between the different stages of the production process and the requirements of consumers. This paper addresses a relevant problem for both Industry 4.0 and flow shop literature: the missing operations flow shop scheduling problem. In general, in order to reduce the computational effort required to solve flow shop scheduling problems only permutation schedules (PFS) are considered, i.e., the same job sequence is used for all the machines involved. However, considering only PFS is not a constraint that is based on the real-world conditions of the industrial environments, and it is only a simplification strategy used frequently in the literature. Moreover, non-permutation (NPFS) orderings may be used for most of the real flow shop systems, i.e., different job schedules can be used for different machines in the production line, since NPFS solutions usually outperform the PFS ones. In this work, a novel mathematical formulation to minimize total tardiness and a resolution method, which considers both PFS and (the more computationally expensive) NPFS solutions, are presented to solve the flow shop scheduling problem with missing operations. The solution approach has two stages. First, a Genetic Algorithm, which only considers PFS solutions, is applied to solve the scheduling problem. The resulting solution is then improved in the second stage by means of a Simulated Annealing algorithm that expands the search space by considering NPFS solutions. The experimental tests were performed on a set of instances considering varying proportions of missing operations, as it is usual in the Industry 4.0 production environment. The results show that NPFS solutions clearly outperform PFS solutions for this problem.Fil: Rossit, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Toncovich, Adrián Andrés. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Rossit, Diego Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Nesmachnow, Sergio. Facultad de Ingeniería; Urugua

Variant-oriented Planning Models for Parts/Products Grouping, Sequencing and Operations

This research aims at developing novel methods for utilizing the commonality between part/product variants to make modern manufacturing systems more flexible, adaptable, and agile for dealing with less volume per variant and minimizing total changes in the setup between variants. Four models are developed for use in four important domains of manufacturing systems: production sequencing, product family formation, production flow, and products operations sequences retrieval. In all these domains, capitalizing on commonality between the part/product variants has a pivotal role. For production sequencing; a new policy based on setup similarity between product variants is proposed and its results are compared with a developed mathematical model in a permutation flow shop. The results show the proposed algorithm is capable of finding solutions in less than 0.02 seconds with an average error of 1.2%. For product family formation; a novel operation flow based similarity coefficient is developed for variants having networked structures and integrated with two other similarity coefficients, operation and volume similarity, to provide a more comprehensive similarity coefficient. Grouping variants based on the proposed integrated similarity coefficient improves changeover time and utilization of the system. A sequencing method, as a secondary application of this approach, is also developed. For production flow; a new mixed integer programing (MIP) model is developed to assign operations of a family of product variants to candidate machines and also to select the best place for each machine among the candidate locations. The final sequence of performing operations for each variant having networked structures is also determined. The objective is to minimize the total backtracking distance leading to an improvement in total throughput of the system (7.79% in the case study of three engine blocks). For operations sequences retrieval; two mathematical models and an algorithm are developed to construct a master operation sequence from the information of the existing variants belonging to a family of parts/products. This master operation sequence is used to develop the operation sequences for new variants which are sufficiently similar to existing variants. Using the proposed algorithm decreases time of developing the operations sequences of new variants to the seconds

Scheduling strategies for the furniture industry

Technological developments and more demanding production standards have constantly been pushing the envelope, changing the perception of what is possible and desired in manufacturing processes. Such improvements are often made at marginal cost, yet have the potential to significantly benefit performance, enabling a strong competitive advantage. In this case study, a factory in the furniture industry is considered, where there are vast improvement opportunities and an increase in flexibility is needed. Furthermore, this problem can be best approximated by the flow shop model and the most critical characteristic is sequence-dependent setup times. To address this problem, an iterated greedy with local search meta-heuristic is implemented, which will be responsible for scheduling production orders in the way that best suits makespan and, consequently, productivity. Additionally, OptQuest, the optimiser functionally built into the Flexsim simulating software was also tested against the meta-heuristic and, still through simulation, a local rule was implemented, which allowed each workstation to define its own sequence of jobs, to minimise setup times. Lastly, the best performing of the previous methods was also compared to the original heuristic that had previously been specifically created for this problem. Through testing, it was found that the iterated greedy with local search meta-heuristic was able to generate solutions that had a much better makespan value than the ones produced by OptQuest, while the local rule was not able to provide significant improvement. Then, the meta-heuristic was compared to the original heuristic and, although the newly implemented algorithm did not consider all characteristics of the problem, productivity far outperformed that of the original technique