Iterative beam search algorithms for the permutation flowshop

We study an iterative beam search algorithm for the permutation flowshop (makespan and flowtime minimization). This algorithm combines branching strategies inspired by recent branch-and-bounds and a guidance strategy inspired by the LR heuristic. It obtains competitive results, reports many new-best-so-far solutions on the VFR benchmark (makespan minimization) and the Taillard benchmark (flowtime minimization) without using any NEH-based branching or iterative-greedy strategy. The source code is available at: https://gitlab.com/librallu/cats-pfsp

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-

An estimation of distribution algorithm for lot-streaming flow shop problems with setup times

Lot-streaming flow shops have important applications in different industries including textile, plastic, chemical, semiconductor and many others. This paper considers an n-job m-machine lot-streaming flow shop scheduling problem with sequence-dependent setup times under both the idling and noidling production cases. The objective is to minimize the maximum completion time or makespan. To solve this important practical problem, a novel estimation of distribution algorithm (EDA) is proposed with a job permutation based representation. In the proposed EDA, an efficient initialization scheme based on the NEH heuristic is presented to construct an initial population with a certain level of quality and diversity. An estimation of a probabilistic model is constructed to direct the algorithm search towards good solutions by taking into account both job permutation and similar blocks of jobs. A simple but effective local search is added to enhance the intensification capability. A diversity controlling mechanism is applied to maintain the diversity of the population. In addition, a speed-up method is presented to reduce the computational effort needed for the local search technique and the NEH-based heuristics. A comparative evaluation is carried out with the best performing algorithms from the literature. The results show that the proposed EDA is very effective in comparison after comprehensive computational and statistical analyses.This research is partially supported by the National Science Foundation of China (60874075, 70871065), and Science Foundation of Shandong Province in China under Grant BS2010DX005, and Postdoctoral Science Foundation of China under Grant 20100480897. Ruben Ruiz is partially funded by the Spanish Ministry of Science and Innovation, under the project "SMPA-Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances" with reference DPI2008-03511/DPI and by the IMPIVA-Institute for the Small and Medium Valencian Enterprise, for the project OSC with references IMIDIC/2008/137, IMIDIC/2009/198 and IMIDIC/2010/175.Pan, Q.; Ruiz García, R. (2012). An estimation of distribution algorithm for lot-streaming flow shop problems with setup times. Omega. 40(2):166-180. https://doi.org/10.1016/j.omega.2011.05.002S16618040

M-machine, no-wait flowshop scheduling with sequence dependent setup times and truncated learning function to minimize the makespan.

Recently, learning effects have been studied as an interesting topic for scheduling problems, however, most researches have considered single or two-machine settings. Moreover, learning factor has been considered for job times instead of setup times and the same learning effect has been used for all machines. This paper studies the m-machine no-wait flowshop scheduling problem considering truncated learning effect in no-wait flowshop environment. In this problem, setup time is a function of job position in the sequence with a learning truncation parameter and each machine has its own learning effect. In this paper, a mixed integer linear programming is proposed for the problem to solve such problem. This problem is NP-hard so an improved genetic algorithm (GA) and a simulated annealing (SA) algorithm are developed to find near optimal solutions. The accuracy and efficiency of the proposed procedures are tested against different criteria on various instances. Numerical experiments approve that SA outperforms in most instances

A robust flexible flow shop problem under processing and release times uncertainty

The aim of this paper is to present a simheuristic approach that obtains robust solutions for a multi-objective hybrid flow shop problem under uncertain processing and release times. This approach minimizes the expected tardiness and standard deviation of tardiness, as a robustness measure for the stated problem. The simheuristic algorithm hybridizes the NSGA-II with a Monte Carlo Simulation process. Initially, the deterministic scenario was tested on 32 different created small size instances and 32 medium and large benchmarked instances. As a result, the proposed algorithm improved quality of solutions by 1.21% against the MILP model and it also performed better than ERD, NEHedd, and ENS2, while consuming a reasonable computational time. Afterwards, one experimental design was carried out using 10 random instances from the same benchmark as a blocking factor, where four factors of interest were considered. The factors and their respective values are number of generations (50, 100), crossover probability (0.8, 0.9), mutation probability (0.1, 0.2), and population size (60, 100). Results show that the factors instance, mutation probability and number of generations, as well as other interactions between them, have a significant effect in the total tardiness for the deterministic scenario, proving the importance of an appropriate selection of parameters when using genetic algorithms to obtain quality solutions. Then, the performance of the proposed NSGA-II was compared against ERD, NEHedd, and ENS2 methods. Results show that our algorithm improves the quality of the solutions for both objective functions, proving the robustness of our solutions for the HFS problem. Finally, two additional generalized experiments were carried out to analyze the effect of number of jobs (10, 20), number of stages (2, 3), shop condition (0.2, 0.6), probability distribution (uniform, lognormal), and CV (0.05, 0.25, 0.4) on both objective functions. The shop condition, probability distribution and CV were proven to be highly influential on the variability of the results, with the only exception being the coefficient of variation having no statistically significant effect on the total tardiness.The aim of this paper is to present a simheuristic approach that obtains robust solutions for a multi-objective hybrid flow shop problem under uncertain processing and release times. This approach minimizes the expected tardiness and standard deviation of tardiness, as a robustness measure for the stated problem. The simheuristic algorithm hybridizes the NSGA-II with a Monte Carlo Simulation process. Initially, the deterministic scenario was tested on 32 different created small size instances and 32 medium and large benchmarked instances. As a result, the proposed algorithm improved quality of solutions by 1.21% against the MILP model and it also performed better than ERD, NEHedd, and ENS2, while consuming a reasonable computational time. Afterwards, one experimental design was carried out using 10 random instances from the same benchmark as a blocking factor, where four factors of interest were considered. The factors and their respective values are number of generations (50, 100), crossover probability (0.8, 0.9), mutation probability (0.1, 0.2), and population size (60, 100). Results show that the factors instance, mutation probability and number of generations, as well as other interactions between them, have a significant effect in the total tardiness for the deterministic scenario, proving the importance of an appropriate selection of parameters when using genetic algorithms to obtain quality solutions. Then, the performance of the proposed NSGA-II was compared against ERD, NEHedd, and ENS2 methods. Results show that our algorithm improves the quality of the solutions for both objective functions, proving the robustness of our solutions for the HFS problem. Finally, two additional generalized experiments were carried out to analyze the effect of number of jobs (10, 20), number of stages (2, 3), shop condition (0.2, 0.6), probability distribution (uniform, lognormal), and CV (0.05, 0.25, 0.4) on both objective functions. The shop condition, probability distribution and CV were proven to be highly influential on the variability of the results, with the only exception being the coefficient of variation having no statistically significant effect on the total tardiness.Ingeniero (a) IndustrialPregrad

Theoretical and Computational Research in Various Scheduling Models

Nine manuscripts were published in this Special Issue on “Theoretical and Computational Research in Various Scheduling Models, 2021” of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field

BALANCING TRADE-OFFS IN ONE-STAGE PRODUCTION WITH PROCESSING TIME UNCERTAINTY

Stochastic production scheduling faces three challenges, first the inconsistencies among key performance indicators (KPIs), second the trade-offs between the expected return and the risk for a portfolio of KPIs, and third the uncertainty in processing times. Based on two inconsistent KPIs of total completion time (TCT) and variance of completion times (VCT), we propose our trade-off balancing (ToB) heuristic for one-stage production scheduling. Through comprehensive case studies, we show that our ToB heuristic with preference =0.0:0.1:1.0 efficiently and effectively addresses the three challenges. Moreover, our trade-off balancing scheme can be generalized to balance a number of inconsistent KPIs more than two. Daniels and Kouvelis (DK) proposed a scheme to optimize the worst-case scenario for stochastic production scheduling and proposed the endpoint product (EP) and endpoint sum (ES) heuristics to hedge against processing time uncertainty. Using 5 levels of coefficients of variation (CVs) to represent processing time uncertainty, we show that our ToB heuristic is robust as well, and even outperforms the EP and ES heuristics on worst-case scenarios at high levels of processing time uncertainty. Moreover, our ToB heuristic generates undominated solution spaces of KPIs, which not only provides a solid base to set up specification limits for statistical process control (SPC) but also facilitates the application of modern portfolio theory and SPC techniques in the industry

Analysis of no-wait flow shop scheduling problems and solving with hybrid scatter search method

Beklemesiz Akış Tipi Çizelgeleme (BATÇ), pratik uygulamalarından dolayı kapsamlı bir araştırma alanıdır. BATÇ problemlerinde işler, makinelerde kesintisiz olarak işlem görmek zorundadır. Bir işin tüm makinelerde işlenme süresi boyunca, makineler bekleyebilir fakat işler kesintisiz olarak işlenmelidir. Amaç ise makinelerin boşta bekleme süresini en aza indirmektir. BATÇ problemlerinin çoğunluğunda toplam gecikmenin ve maksimum tamamlanma zamanının minimizasyonu olmak üzere, iki performans ölçüsü göz önünde bulundurulur. Literatürde, son yirmi beş yılda BATÇ ile ilgili yapılan çalışmalar analiz edilmiştir. BATÇ problemlerinin çözümü ile ilgili geliştirilen kesin ve yaklaşık çözüm veren yöntemler incelenmiştir. Literatürde 1 ve 2 makineli problemler için optimum çözüm veren matematiksel yöntemler bulunurken, 3 ve daha fazla makineli problemler için standart zamanda optimum çözüm veren bir yöntem bulunmamaktadır. Kabul edilebilir bir süre içerisinde m makine içeren problemlere optimum ya da optimuma yakın çözümler üretebilmek için sezgisel ve meta sezgisel yöntemler geliştirilmektedir. Bu çalışmada, BATÇ problemlerinin çözümü için Hibrit Dağınık Arama (HDA) yöntemi önerilmiştir. Önerilen yöntem, literatürde iyi bilinen kıyaslama problemleri yardımı ile test edilmiştir. Elde edilen sonuçlar, Hibrit Uyarlanabilir Öğrenme Yaklaşım (HUÖY) algoritması ve Hibrit Karınca Kolonileri Optimizasyon (HKKO) algoritması ile kıyaslanmıştır. Amaç fonksiyonu olarak maksimum tamamlanma zamanının minimizasyonu seçilmiştir. Elde edilen çözüm sonuçları, önerilen HDA yönteminin BATÇ problemlerinin çözümünde etkili olduğunu göstermiştir.No-wait flow shop (NWFS) is extensively research area due to its practical applications. In NWFS, jobs are processed in machines without interruption. During the schedule period, machines can wait, but jobs cannot wait. The aim is to minimize the idle time for machines. The majority of NWFS, two performance measures are consid-ered: minimization of total delay and minimization of the makespan. The researches on the NWFS in the last twenty-five years have been analysed from the literature. The methods developed for the solution of the NWFS, which give exact and approximate solutions, have been examined. While there are mathematical methods that give optimum solutions for 1 and 2 machine problems in the literature, there is no method that provides optimum solutions in standard time for problems with 3 or more machines. The difference methods are developed in order to produce optimum or near-optimum solutions to m-machine problems in an acceptable time. A Hybrid Scatter Search Method (HSSM) is proposed for solving the NWFS. The developed HSSM tested with the well-known benchmarking instances in the literature. The results obtained were compared with the Hybrid Adaptive Learning Approach algorithm and the Hybrid Ant Colonies Optimization algorithm. The objective function is makespan minimization. According to solutions, the proposed HSSM is an effective metaheuristic to solve NWFS

Heuristics and metaheuristics for heavily constrained hybrid flowshop problems

Due to the current trends in business as the necessity to have a large catalogue of products, orders that increase in frequency but not in size, globalisation and a market that is increasingly competitive, the production sector faces an ever harder economical environment. All this raises the need for production scheduling with maximum efficiency and effectiveness. The first scientific publications on production scheduling appeared more than half a century ago. However, many authors have recognised a gap between the literature and the industrial problems. Most of the research concentrates on optimisation problems that are actually a very simplified version of reality. This allows for the use of sophisticated approaches and guarantees in many cases that optimal solutions are obtained. Yet, the exclusion of real-world restrictions harms the applicability of those methods. What the industry needs are systems for optimised production scheduling that adjust exactly to the conditions in the production plant and that generates good solutions in very little time. This is exactly the objective in this thesis, that is, to treat more realistic scheduling problems and to help closing the gap between the literature and practice. The considered scheduling problem is called the hybrid flowshop problem, which consists in a set of jobs that flow through a number of production stages. At each of the stages, one of the machines that belong to the stage is visited. A series of restriction is considered that include the possibility to skip stages, non-eligible machines, precedence constraints, positive and negative time lags and sequence dependent setup times. In the literature, such a large number of restrictions has not been considered simultaneously before. Briefly, in this thesis a very realistic production scheduling problem is studied. Various optimisation methods are presented for the described scheduling problem. A mixed integer programming model is proposed, in order to obtaiUrlings ., T. (2010). Heuristics and metaheuristics for heavily constrained hybrid flowshop problems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8439Palanci