Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Models and Algorithms for the Optimisation of Replenishment, Production and Distribution Plans in Industrial Enterprises

Tesis por compendio[ES] La optimización en las empresas manufactureras es especialmente importante, debido a las grandes inversiones que realizan, ya que a veces estas inversiones no obtienen el rendimiento esperado porque los márgenes de beneficio de los productos son muy ajustados. Por ello, las empresas tratan de maximizar el uso de los recursos productivos y financieros minimizando el tiempo perdido y, al mismo tiempo, mejorando los flujos de los procesos y satisfaciendo las necesidades del mercado. El proceso de planificación es una actividad crítica para las empresas. Esta tarea implica grandes retos debido a los cambios del mercado, las alteraciones en los procesos de producción dentro de la empresa y en la cadena de suministro, y los cambios en la legislación, entre otros. La planificación del aprovisionamiento, la producción y la distribución desempeña un papel fundamental en el rendimiento de las empresas manufactureras, ya que una planificación ineficaz de los proveedores, los procesos de producción y los sistemas de distribución contribuye a aumentar los costes de los productos, a alargar los plazos de entrega y a reducir los beneficios. La planificación eficaz es un proceso complejo que abarca una amplia gama de actividades para garantizar que los equipos, los materiales y los recursos humanos estén disponibles en el momento y el lugar adecuados. Motivados por la complejidad de la planificación en las empresas manufactureras, esta tesis estudia y desarrolla herramientas cuantitativas para ayudar a los planificadores en los procesos de la planificación del aprovisionamiento, producción y distribución. Desde esta perspectiva, se proponen modelos realistas y métodos eficientes para apoyar la toma de decisiones en las empresas industriales, principalmente en las pequeñas y medianas empresas (PYMES). Las aportaciones de esta tesis suponen un avance científico basado en una exhaustiva revisión bibliográfica sobre la planificación del aprovisionamiento, la producción y la distribución que ayuda a comprender los principales modelos y algoritmos utilizados para resolver estos planes, y pone en relieve las tendencias y las futuras direcciones de investigación. También proporciona un marco holístico para caracterizar los modelos y algoritmos centrándose en la planificación de la producción, la programación y la secuenciación. Esta tesis también propone una herramienta de apoyo a la decisión para seleccionar un algoritmo o método de solución para resolver problemas concretos de la planificación del aprovisionamiento, producción y distribución en función de su complejidad, lo que permite a los planificadores no duplicar esfuerzos de modelización o programación de técnicas de solución. Por último, se desarrollan nuevos modelos matemáticos y enfoques de solución de última generación, como los algoritmos matheurísticos, que combinan la programación matemática y las técnicas metaheurísticas. Los nuevos modelos y algoritmos comprenden mejoras en términos de rendimiento computacional, e incluyen características realistas de los problemas del mundo real a los que se enfrentan las empresas de fabricación. Los modelos matemáticos han sido validados con un caso de una importante empresa del sector de la automoción en España, lo que ha permitido evaluar la relevancia práctica de estos novedosos modelos utilizando instancias de gran tamaño, similares a las existentes en la empresa objeto de estudio. Además, los algoritmos matheurísticos han sido probados utilizando herramientas libres y de código abierto. Esto también contribuye a la práctica de la investigación operativa, y proporciona una visión de cómo desplegar estos métodos de solución y el tiempo de cálculo y rendimiento de la brecha que se puede obtener mediante el uso de software libre o de código abierto.[CA] L'optimització a les empreses manufactureres és especialment important, a causa de les grans inversions que realitzen, ja que de vegades aquestes inversions no obtenen el rendiment esperat perquè els marges de benefici dels productes són molt ajustats. Per això, les empreses intenten maximitzar l'ús dels recursos productius i financers minimitzant el temps perdut i, alhora, millorant els fluxos dels processos i satisfent les necessitats del mercat. El procés de planificació és una activitat crítica per a les empreses. Aquesta tasca implica grans reptes a causa dels canvis del mercat, les alteracions en els processos de producció dins de l'empresa i la cadena de subministrament, i els canvis en la legislació, entre altres. La planificació de l'aprovisionament, la producció i la distribució té un paper fonamental en el rendiment de les empreses manufactureres, ja que una planificació ineficaç dels proveïdors, els processos de producció i els sistemes de distribució contribueix a augmentar els costos dels productes, allargar els terminis de lliurament i reduir els beneficis. La planificació eficaç és un procés complex que abasta una àmplia gamma d'activitats per garantir que els equips, els materials i els recursos humans estiguen disponibles al moment i al lloc adequats. Motivats per la complexitat de la planificació a les empreses manufactureres, aquesta tesi estudia i desenvolupa eines quantitatives per ajudar als planificadors en els processos de la planificació de l'aprovisionament, producció i distribució. Des d'aquesta perspectiva, es proposen models realistes i mètodes eficients per donar suport a la presa de decisions a les empreses industrials, principalment a les petites i mitjanes empreses (PIMES). Les aportacions d'aquesta tesi suposen un avenç científic basat en una exhaustiva revisió bibliogràfica sobre la planificació de l'aprovisionament, la producció i la distribució que ajuda a comprendre els principals models i algorismes utilitzats per resoldre aquests plans, i posa de relleu les tendències i les futures direccions de recerca. També proporciona un marc holístic per caracteritzar els models i algorismes centrant-se en la planificació de la producció, la programació i la seqüenciació. Aquesta tesi també proposa una eina de suport a la decisió per seleccionar un algorisme o mètode de solució per resoldre problemes concrets de la planificació de l'aprovisionament, producció i distribució en funció de la seua complexitat, cosa que permet als planificadors no duplicar esforços de modelització o programació de tècniques de solució. Finalment, es desenvolupen nous models matemàtics i enfocaments de solució d'última generació, com ara els algoritmes matheurístics, que combinen la programació matemàtica i les tècniques metaheurístiques. Els nous models i algoritmes comprenen millores en termes de rendiment computacional, i inclouen característiques realistes dels problemes del món real a què s'enfronten les empreses de fabricació. Els models matemàtics han estat validats amb un cas d'una important empresa del sector de l'automoció a Espanya, cosa que ha permés avaluar la rellevància pràctica d'aquests nous models utilitzant instàncies grans, similars a les existents a l'empresa objecte d'estudi. A més, els algorismes matheurístics han estat provats utilitzant eines lliures i de codi obert. Això també contribueix a la pràctica de la investigació operativa, i proporciona una visió de com desplegar aquests mètodes de solució i el temps de càlcul i rendiment de la bretxa que es pot obtindre mitjançant l'ús de programari lliure o de codi obert.[EN] Optimisation in manufacturing companies is especially important, due to the large investments they make, as sometimes these investments do not obtain the expected return because the profit margins of products are very tight. Therefore, companies seek to maximise the use of productive and financial resources by minimising lost time and, at the same time, improving process flows while meeting market needs. The planning process is a critical activity for companies. This task involves great challenges due to market changes, alterations in production processes within the company and in the supply chain, and changes in legislation, among others. Planning of replenishment, production and distribution plays a critical role in the performance of manufacturing companies because ineffective planning of suppliers, production processes and distribution systems contributes to higher product costs, longer lead times and less profits. Effective planning is a complex process that encompasses a wide range of activities to ensure that equipment, materials and human resources are available in the right time and the right place. Motivated by the complexity of planning in manufacturing companies, this thesis studies and develops quantitative tools to help planners in the replenishment, production and delivery planning processes. From this perspective, realistic models and efficient methods are proposed to support decision making in industrial companies, mainly in small- and medium-sized enterprises (SMEs). The contributions of this thesis represent a scientific breakthrough based on a comprehensive literature review about replenishment, production and distribution planning that helps to understand the main models and algorithms used to solve these plans, and highlights trends and future research directions. It also provides a holistic framework to characterise models and algorithms by focusing on production planning, scheduling and sequencing. This thesis also proposes a decision support tool for selecting an algorithm or solution method to solve concrete replenishment, production and distribution planning problems according to their complexity, which allows planners to not duplicate efforts modelling or programming solution techniques. Finally, new state-of-the-art mathematical models and solution approaches are developed, such as matheuristic algorithms, which combine mathematical programming and metaheuristic techniques. The new models and algorithms comprise improvements in computational performance terms, and include realistic features of real-world problems faced by manufacturing companies. The mathematical models have been validated with a case of an important company in the automotive sector in Spain, which allowed to evaluate the practical relevance of these novel models using large instances, similarly to those existing in the company under study. In addition, the matheuristic algorithms have been tested using free and open-source tools. This also helps to contribute to the practice of operations research, and provides insight into how to deploy these solution methods and the computational time and gap performance that can be obtained by using free or open-source software.This work would not have been possible without the following funding sources: Conselleria de Educación, Investigación, Cultura y Deporte, Generalitat Valenciana for hiring predoctoral research staff with Grant (ACIF/2018/170) and the European Social Fund with the Grant Operational Programme of FSE 2014-2020. Conselleria de Educación, Investigación, Cultura y Deporte, Generalitat Valenciana for predoctoral contract students to stay in research centers outside the research centers outside the Valencian Community (BEFPI/2021/040) and the European Social Fund.Guzmán Ortiz, BE. (2022). Models and Algorithms for the Optimisation of Replenishment, Production and Distribution Plans in Industrial Enterprises [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/187461Compendi

Risk-Based Optimal Scheduling for the Predictive Maintenance of Railway Infrastructure

In this thesis a risk-based decision support system to schedule the predictive maintenance activities, is proposed. The model deals with the maintenance planning of a railway infrastructure in which the due-dates are defined via failure risk analysis.The novelty of the approach consists of the risk concept introduction in railway maintenance scheduling, according to ISO 55000 guidelines, thus implying that the maintenance priorities are based on asset criticality, determined taking into account the relevant failure probability, related to asset degradation conditions, and the consequent damages

Model-Based Heuristics for Combinatorial Optimization

Many problems arising in several and different areas of human knowledge share the characteristic of being intractable in real cases. The relevance of the solution of these problems, linked to their domain of action, has given birth to many frameworks of algorithms for solving them. Traditional solution paradigms are represented by exact and heuristic algorithms. In order to overcome limitations of both approaches and obtain better performances, tailored combinations of exact and heuristic methods have been studied, giving birth to a new paradigm for solving hard combinatorial optimization problems, constituted by model-based metaheuristics. In the present thesis, we deepen the issue of model-based metaheuristics, and present some methods, belonging to this class, applied to the solution of combinatorial optimization problems

Modeling and Solution Methodologies for Mixed-Model Sequencing in Automobile Industry

The global competitive environment leads companies to consider how to produce high-quality products at a lower cost. Mixed-model assembly lines are often designed such that average station work satisfies the time allocated to each station, but some models with work-intensive options require more than the allocated time. Sequencing varying models in a mixed-model assembly line, mixed-model sequencing (MMS), is a short-term decision problem that has the objective of preventing line stoppage resulting from a station work overload. Accordingly, a good allocation of models is necessary to avoid work overload. The car sequencing problem (CSP) is a specific version of the MMS that minimizes work overload by controlling the sequence of models. In order to do that, CSP restricts the number of work-intensive options by applying capacity rules. Consequently, the objective is to find the sequence with the minimum number of capacity rule violations. In this dissertation, we provide exact and heuristic solution approaches to solve different variants of MMS and CSP. First, we provide five improved lower bounds for benchmark CSP instances by solving problems optimally with a subset of options. We present four local search metaheuristics adapting efficient transformation operators to solve CSP. The computational experiments show that the Adaptive Local Search provides a significant advantage by not requiring tuning on the operator weights due to its adaptive control mechanism. Additionally, we propose a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provide improvements to the second-stage problem. To tackle the exponential number of scenarios, we employ the sample average approximation approach and two solution methodologies. On one hand, we develop an L-shaped decomposition-based algorithm, where the computational experiments show its superiority over solving the deterministic equivalent formulation with an off-the-shelf solver. We also provide a tabu search algorithm in addition to a greedy heuristic to tackle case study instances inspired by our car manufacturer partner. Numerical experiments show that the proposed solution methodologies generate high-quality solutions by utilizing a sample of scenarios. Particularly, a robust sequence that is generated by considering car failures can decrease the expected work overload by more than 20\% for both small- and large-sized instances. To the best of our knowledge, this is the first study that considers stochastic failures of products in MMS. Moreover, we propose a two-stage stochastic program and formulation improvements for a mixed-model sequencing problem with stochastic product failures and integrated reinsertion process. We present a bi-objective evolutionary optimization algorithm, a two-stage bi-objective local search algorithm, and a hybrid local search integrated evolutionary optimization algorithm to tackle the proposed problem. Numerical experiments over a case study show that while the hybrid algorithm provides a better exploration of the Pareto front representation and more reliable solutions in terms of waiting time of failed vehicles, the local search algorithm provides more reliable solutions in terms of work overload objective. Finally, dynamic reinsertion simulations are executed over industry-inspired instances to assess the quality of the solutions. The results show that integrating the reinsertion process in addition to considering vehicle failures can keep reducing the work overload by around 20\% while significantly decreasing the waiting time of the failed vehicles

Cost Factor Focused Scheduling and Sequencing: A Neoteric Literature Review

The hastily emergent concern from researchers in the application of scheduling and sequencing has urged the necessity for analysis of the latest research growth to construct a new outline. This paper focuses on the literature on cost minimization as a primary aim in scheduling problems represented with less significance as a whole in the past literature reviews. The purpose of this paper is to have an intensive study to clarify the development of cost-based scheduling and sequencing (CSS) by reviewing the work published over several parameters for improving the understanding in this field. Various parameters, such as scheduling models, algorithms, industries, journals, publishers, publication year, authors, countries, constraints, objectives, uncertainties, computational time, and programming languages and optimization software packages are considered. In this research, the literature review of CSS is done for thirteen years (2010-2022). Although CSS research originated in manufacturing, it has been observed that CSS research publications also addressed case studies based on health, transportation, railway, airport, steel, textile, education, ship, petrochemical, inspection, and construction projects. A detailed evaluation of the literature is followed by significant information found in the study, literature analysis, gaps identification, constraints of work done, and opportunities in future research for the researchers and experts from the industries in CSS

Models and algorithms for berth allocation problems in port terminals

Seaports play a key role in maritime commerce and the global market economy. Goods of different kinds are carried in specialized vessels whose handling requires ad hoc port facilities. Port terminals comprise the quays, infrastructures, and services dedicated to handling the inbound and outbound cargo carried on vessels. Increasing seaborne trade and ever-greater competition between port terminals to attract more traffic have prompted new studies aimed at improving their quality of service while reducing costs. Most terminals implement operational planning to achieve more efficient usage of resources, and this poses new combinatorial optimization problems which have attracted increasing attention from the Operations Research community. One of the most important problems confronted at the quayside is the efficient allocation of quay space to the vessels calling at the terminal over time, also known as the Berth Allocation Problem. A closely related problem arising in terminals that specialize in container handling concerns the efficient assignment of quay cranes to vessels, which, together with quay space planning, leads to the Berth Allocation and Quay Crane Assignment Problem. These problems are known to be especially hard to solve, and therefore require designing methods capable of attaining good solutions in reasonable computation times. This thesis studies different variants of these problems considering well-known and new real-world aspects, such as terminals with multiple quays or irregular layouts. Mathematical programming and metaheuristics techniques are extensively used to devise tailored solution methods. In particular, new integer linear models and heuristic algorithms are developed to deal with problem instances of a broad range of sizes representing real situations. These methods are evaluated and compared with other state-of-the-art proposals through various computational experiments on different benchmark sets of instances. The results obtained show that the integer models proposed lead to optimal solutions on small instances in short computation times, while the heuristic algorithms obtain good solutions to both small and large instances. Therefore, this study proves to be an effective contribution to the efforts aimed at improving port efficiency and provides useful insights to better tackle similar combinatorial optimization problems