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

Deterministic Assembly Scheduling Problems: A Review and Classification of Concurrent-Type Scheduling Models and Solution Procedures

Many activities in industry and services require the scheduling of tasks that can be concurrently executed, the most clear example being perhaps the assembly of products carried out in manufacturing. Although numerous scientific contributions have been produced on this area over the last decades, the wide extension of the problems covered and the lack of a unified approach have lead to a situation where the state of the art in the field is unclear, which in turn hinders new research and makes translating the scientific knowledge into practice difficult. In this paper we propose a unified notation for assembly scheduling models that encompass all concurrent-type scheduling problems. Using this notation, the existing contributions are reviewed and classified into a single framework, so a comprehensive, unified picture of the field is obtained. In addition, a number of conclusions regarding the state of the art in the topic are presented, as well as some opportunities for future research.Ministerio de Ciencia e Innovación español DPI2016-80750-

Heuristics for scheduling a two-stage hybrid flow shop with parallel batching machines: application at a hospital sterilisation plant

The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times, parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements

Minimizing the makespan in a flexible flowshop with sequence dependent setup times, uniform machines, and limited buffers

This research addresses the problem of minimizing the makespan in a flexible flowshop with sequence dependent setup times, uniform machines, and limited buffers. A mathematical model was developed to solve this problem. The problem is NP-Hard in the strong sense and only very small problems could be solved optimally. For exact methods, the computation times are long and not practical even when the problems are relatively small. Two construction heuristics were developed that could find solutions quickly. Also a simulated annealing heuristic was constructed that improved the solutions obtained from the construction heuristics. The combined heuristics could compute a good solution in a short amount of time. The heuristics were tested in three different environments: 3 stages, 4 stages, and 5 stages. To assess the quality of the solutions, a lower bound and two simple heuristics were generated for comparison purposes. The proposed heuristics showed steady improvement over the simple heuristics. When compared to the lower bounds, the heuristics performed well for the smaller environment, but the performance quality decreased as the number of stages increased. The combination of these heuristics defiantly shows promise for solving the problem

An effective iterated greedy algorithm for the mixed no-idle flowshop scheduling problem

In the no-idle flowshop, machines cannot be idle after finishing one job and before starting the next one. Therefore, start times of jobs must be delayed to guarantee this constraint. In practice machines show this behavior as it might be technically unfeasible or uneconomical to stop a machine in between jobs. This has important ramifications in the modern industry including fiber glass processing, foundries, production of integrated circuits and the steel making industry, among others. However, to assume that all machines in the shop have this no-idle constraint is not realistic. To the best of our knowledge, this is the first paper to study the mixed no-idle extension where only some machines have the no-idle constraint. We present a mixed integer programming model for this new problem and the equations to calculate the makespan. We also propose a set of formulas to accelerate the calculation of insertions that is used both in heuristics as well as in the local search procedures. An effective iterated greedy (IG) algorithm is proposed. We use an NEH-based heuristic to construct a high quality initial solution. A local search using the proposed accelerations is employed to emphasize intensification and exploration in the IG. A new destruction and construction procedure is also shown. To evaluate the proposed algorithm, we present several adaptations of other well-known and recent metaheuristics for the problem and conduct a comprehensive set of computational and statistical experiments with a total of 1750 instances. The results show that the proposed IG algorithm outperforms existing methods in the no-idle and in the mixed no-idle scenarios by a significant margin.Quan-Ke Pan is partially supported by the National Science Foundation of China 61174187, Program for New Century Excellent Talents in University (NCET-13-0106), Science Foundation of Liaoning Province in China (2013020016), Basic scientific research foundation of Northeast University under Grant N110208001, Starting foundation of Northeast University under Grant 29321006, and Shandong Province Key Laboratory of Intelligent Information Processing and Network Security (Liaocheng University). Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "RESULT - Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 co-financed by the European Union and FEDER funds and by the Universitat Politecnica de Valencia, for the project MRPIV with reference PAID/2012/202.Pan, Q.; Ruiz García, R. (2014). An effective iterated greedy algorithm for the mixed no-idle flowshop scheduling problem. Omega. 44:41-50. https://doi.org/10.1016/j.omega.2013.10.002S41504

An efficient discrete artificial bee colony algorithm for the blocking flow shop problem with total flowtime minimization

This paper presents a high performing Discrete Artificial Bee Colony algorithm for the blocking flow shop problem with flow time criterion. To develop the proposed algorithm, we considered four strategies for the food source phase and two strategies for each of the three remaining phases (employed bees, onlookers and scouts). One of the strategies tested in the food source phase and one implemented in the employed bees phase are new. Both have been proved to be very effective for the problem at hand. The initialization scheme named HPF2(¿, µ) in particular, which is used to construct the initial food sources, is shown in the computational evaluation to be one of the main procedures that allow the DABC_RCT to obtain good solutions for this problem. To find the best configuration of the algorithm, we used design of experiments (DOE). This technique has been used extensively in the literature to calibrate the parameters of the algorithms but not to select its configuration. Comparing it with other algorithms proposed for this problem in the literature demonstrates the effectiveness and superiority of the DABC_RCTPeer ReviewedPostprint (author’s final draft

Two-Stage Vehicle Routing Problems with Profits and Buffers: Analysis and Metaheuristic Optimization Algorithms

This thesis considers the Two-Stage Vehicle Routing Problem (VRP) with Profits and Buffers, which generalizes various optimization problems that are relevant for practical applications, such as the Two-Machine Flow Shop with Buffers and the Orienteering Problem. Two optimization problems are considered for the Two-Stage VRP with Profits and Buffers, namely the minimization of total time while respecting a profit constraint and the maximization of total profit under a budget constraint. The former generalizes the makespan minimization problem for the Two-Machine Flow Shop with Buffers, whereas the latter is comparable to the problem of maximizing score in the Orienteering Problem. For the three problems, a theoretical analysis is performed regarding computational complexity, existence of optimal permutation schedules (where all vehicles traverse the same nodes in the same order) and potential gaps in attainable solution quality between permutation schedules and non-permutation schedules. The obtained theoretical results are visualized in a table that gives an overview of various subproblems belonging to the Two-Stage VRP with Profits and Buffers, their theoretical properties and how they are connected. For the Two-Machine Flow Shop with Buffers and the Orienteering Problem, two metaheuristics 2BF-ILS and VNSOP are presented that obtain favorable results in computational experiments when compared to other state-of-the-art algorithms. For the Two-Stage VRP with Profits and Buffers, an algorithmic framework for Iterative Search Algorithms with Variable Neighborhoods (ISAVaN) is proposed that generalizes aspects from 2BF-ILS as well as VNSOP. Various algorithms derived from that framework are evaluated in an experimental study. The evaluation methodology used for all computational experiments in this thesis takes the performance during the run time into account and demonstrates that algorithms for structurally different problems, which are encompassed by the Two-Stage VRP with Profits and Buffers, can be evaluated with similar methods. The results show that the most suitable choice for the components in these algorithms is dependent on the properties of the problem and the considered evaluation criteria. However, a number of similarities to algorithms that perform well for the Two-Machine Flow Shop with Buffers and the Orienteering Problem can be identified. The framework unifies these characteristics, providing a spectrum of algorithms that can be adapted to the specifics of the considered Vehicle Routing Problem.:1 Introduction 2 Background 2.1 Problem Motivation 2.2 Formal Definition of the Two-Stage VRP with Profits and Buffers 2.3 Review of Literature on Related Vehicle Routing Problems 2.3.1 Two-Stage Vehicle Routing Problems 2.3.2 Vehicle Routing Problems with Profits 2.3.3 Vehicle Routing Problems with Capacity- or Resource-based Restrictions 2.4 Preliminary Remarks on Subsequent Chapters 3 The Two-Machine Flow Shop Problem with Buffers 3.1 Review of Literature on Flow Shop Problems with Buffers 3.1.1 Algorithms and Metaheuristics for Flow Shops with Buffers 3.1.2 Two-Machine Flow Shop Problems with Buffers 3.1.3 Blocking Flow Shops 3.1.4 Non-Permutation Schedules 3.1.5 Other Extensions and Variations of Flow Shop Problems 3.2 Theoretical Properties 3.2.1 Computational Complexity 3.2.2 The Existence of Optimal Permutation Schedules 3.2.3 The Gap Between Permutation Schedules an Non-Permutation 3.3 A Modification of the NEH Heuristic 3.4 An Iterated Local Search for the Two-Machine Flow Shop Problem with Buffers 3.5 Computational Evaluation 3.5.1 Algorithms for Comparison 3.5.2 Generation of Problem Instances 3.5.3 Parameter Values 3.5.4 Comparison of 2BF-ILS with other Metaheuristics 3.5.5 Comparison of 2BF-OPT with NEH 3.6 Summary 4 The Orienteering Problem 4.1 Review of Literature on Orienteering Problems 4.2 Theoretical Properties 4.3 A Variable Neighborhood Search for the Orienteering Problem 4.4 Computational Evaluation 4.4.1 Measurement of Algorithm Performance 4.4.2 Choice of Algorithms for Comparison 4.4.3 Problem Instances 4.4.4 Parameter Values 4.4.5 Experimental Setup 4.4.6 Comparison of VNSOP with other Metaheuristics 4.5 Summary 5 The Two-Stage Vehicle Routing Problem with Profits and Buffers 5.1 Theoretical Properties of the Two-Stage VRP with Profits and Buffers 5.1.1 Computational Complexity of the General Problem 5.1.2 Existence of Permutation Schedules in the Set of Optimal Solutions 5.1.3 The Gap Between Permutation Schedules an Non-Permutation Schedules 5.1.4 Remarks on Restricted Cases 5.1.5 Overview of Theoretical Results 5.2 A Metaheuristic Framework for the Two-Stage VRP with Profits and Buffers 5.3 Experimental Results 5.3.1 Problem Instances 5.3.2 Experimental Results for O_{max R, Cmax≤B} 5.3.3 Experimental Results for O_{min Cmax, R≥Q} 5.4 Summary Bibliography List of Figures List of Tables List of Algorithm

An Effective Hybrid Genetic Algorithm for Hybrid Flow Shops with Sequence Dependent Setup Times and Processor Blocking

Hybrid flow-shop or flexible flow shop problems have remained subject of intensive research over several years. Hybrid flow-shop problems overcome one of the limitations of the classical flow-shop model by allowing parallel processors at each stage of task processing. In many papers the assumptions are generally made that there is unlimited storage available between stages and the setup times are neglected or considered independent from sequences of jobs. In this paper we study the hybrid flow shop problems with sequence dependent setup times and processor blocking. We present an effective hybrid genetic algorithm with some state-of-the-art procedures for these NP-hard problems to minimize total completion time or makespan. We established a benchmark to draw an analogy between the performance of our algorithm and RKGA. The obtaining results clearly show the superiority performance of our algorithm