An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions

A review of discrete-time optimization models for tactical production planning

This is an Accepted Manuscript of an article published in International Journal of Production Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721[EN] This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively; (6) most works perform numerical experiments with random created instances, while a small number of works were validated by real-world data from industrial firms, of which the most popular are sawmills, wood and furniture, automobile and semiconductors and electronic devices.This study has been funded by the Universitat Politècnica de València projects: ‘Material Requirement Planning Fourth Generation (MRPIV)’ (Ref. PAID-05-12) and ‘Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics’ (PAID-06-12).Díaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time optimization models for tactical production planning. International Journal of Production Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721S51715205521

Improved formulations, heuristics and metaheuristics for the dynamic demand coordinated lot-sizing problem

Coordinated lot sizing problems, which assume a joint setup is shared by a product family, are commonly encountered in supply chain contexts. Total system costs include a joint set-up charge each time period any item in the product family is replenished, an item set-up cost for each item replenished in each time period, and inventory holding costs. Silver (1979) and subsequent researchers note the occurrence of coordinated replenishment problems within manufacturing, procurement, and transportation contexts. Due to their mathematical complexity and importance in industry, coordinated lot-size problems are frequently studied in the operations management literature. In this research, we address both uncapacitated and capacitated variants of the problem. For each variant we propose new problem formulations, one or more construction heuristics, and a simulated annealing metaheuristic (SAM). We first propose new tight mathematical formulations for the uncapacitated problem and document their improved computational efficiency over earlier models. We then develop two forward-pass heuristics, a two-phase heuristic, and SAM to solve the uncapacitated version of the problem. The two-phase and SAM find solutions with an average optimality gap of 0.56% and 0.2% respectively. The corresponding average computational requirements are less than 0.05 and 0.18 CPU seconds. Next, we propose tight mathematical formulations for the capacitated problem and evaluate their performance against existing approaches. We then extend the two-phase heuristic to solve this more general capacitated version. We further embed the six-phase heuristic in a SAM framework, which improves heuristic performance at minimal additional computational expense. The metaheuristic finds solutions with an average optimality gap of 0.43% and within an average time of 0.25 CPU seconds. This represents an improvement over those reported in the literature. Overall the heuristics provide a general approach to the dynamic demand lot-size problem that is capable of being applied as a stand-alone solver, an algorithm embedded with supply chain planning software, or as an upper-bounding procedure within an optimization based algorithm. Finally, this research investigates the performance of alternative coordinated lotsizing procedures when implemented in a rolling schedule environment. We find the perturbation metaheuristic to be the most suitable heuristic for implementation in rolling schedules

Lot-Sizing of Several Multi-Product Families

Production planning problems and its variants are widely studied in operations management and optimization literature. One variation that has not garnered much attention is the presence of multiple production families in a coordinated and capacitated lot-sizing setting. While its single-family counterpart has been the subject of many advances in formulations and solution techniques, the latest published research on multiple family problems was over 25 years ago (Erenguc and Mercan, 1990; Mercan and Erenguc, 1993). Chapter 2 begins with a new formulation for this coordinated capacitated lot-sizing problem for multiple product families where demand is deterministic and time-varying. The problem considers setup and holding costs, where capacity constraints limit the number of individual item and family setup times and the amount of production in each period. We use a facility location reformulation to strengthen the lower bound of our demand-relaxed model. In addition, we combine Benders decomposition with an evolutionary algorithm to improve upper bounds on optimal solutions. To assess the performance of our approach, single-family problems are solved and results are compared to those produced by state-of-the-art heuristics by de Araujo et al. (2015) and Süral et al. (2009). For the multi-family setting, we first create a standard test bed of problems, then measure the performance of our heuristic against the SDW heuristic of Süral et al. (2009), as well as a Lagrangian approach. We show that our Benders approach combined with an evolutionary algorithm consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature. Lot-sizing problems also exist within a vendor-managed-inventory setting, with production-planning, distribution and vehicle routing problems all solved simultaneously. By considering these decisions together, companies achieve reduced inventory and transportation costs compared to when these decisions are made sequentially. We present in Chapter 3 a branch-and-cut algorithm to tackle a production-routing problem (PRP) consisting of multiple products and customers served by a heterogeneous fleet of vehicles. To accelerate the performance of this algorithm, we also construct an upper bounding heuristic that quickly solves production-distribution and routing subproblems, providing a warm-start for the branch-and-cut procedure. In four scenarios, we vary the degree of flexibility in demand and transportation by considering split deliveries and backorders, two settings that are not commonly studied in the literature. We confirm that our upper bounding procedure generates high quality solutions at the root node for reasonably-sized problem instances; as time horizons grow longer, solution quality degrades slightly. Overall costs are roughly the same in these scenarios, though cost proportions vary. When backorders are not allowed (Scenarios 1 and 3), inventory holding costs account for over 90% of total costs and transportation costs contribute less than 0.01%. When backorders are allowed (Scenarios 2 and 4), most of the cost burden is shouldered by production, with transportation inching closer to 0.1% of total costs. In our fifth scenario for the PRP with multiple product families, we employ a decomposition heuristic for determining dedicated routes for distribution. Customers are clustered through k-means++ and a location-alloction subproblem based on their contribution to overall demand, and these clusters remain fixed over the entire planning horizon. A routing subproblem dictates the order in which to visit customers in each period, and we allow backorders in the production-distribution routine. While the branch-and-cut algorithm for Scenarios 1 through 4 quickly finds high quality solutions at the root node, Scenario 5's dedicated routes heuristic boasts high vehicle utilization and comparable overall costs with minimal computational effort

Fuzzy Mathematical Model For A Lot-Sizing Problem In Closed-Loop Supply Chain

The aim of lot sizing problems is to determine the periods where production takes place and the quantities to be produced in order to satisfy the customer demand while minimizing the total cost. Due to its importance on the efficiency of the production and inventory systems, Lot sizing problems are one of the most challenging production planning problems and have been studied for many years with different modeling features. In this paper, we propose a fuzzy mathematical model for the single-item capacitated lot-sizing problem in closed-loop supply chain. The possibility approach is chosen to convert the fuzzy mathematical model to crisp mathematical model. The obtained crisp model is in the form of mixed integer linear programming (MILP), which can be solved by existing solver in crisp environment to find optimal solution. Due to the complexity of the problems harmony search (HS) algorithm and genetic algorithm (GA) have been used to solve the model for fifteen problem. To verify the performance of the algorithm, we computationally compared the results obtained by the algorithms with the results of the branch-and-bound method. Additionally, Taguchi method was used to calibrate the parameters of the meta-heuristic algorithms. The computational results show that, the objective values obtained by HS are better from GA results for large dimensions test problems, also CPU time obtained by HS are better than GA for Large dimensions

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

Variable neighborhood search for the multi-level capacitated lotsizing problem

Das dynamische mehrstufige kapazitierte Losgrößenproblem (MLCLSP) behandelt im Rahmen der Produktionsplanung die wichtige Entscheidung über die optimalen Losgrößen, angefangen bei Endprodukten über Komponenten bis hin zu Rohstoffen, bei gleichzeitiger Berücksichtigung beschränkter Kapazitäten der zur Produktion benötigten Ressourcen. Da es sich um ein NP-schweres Problem handelt, stoßen exakte Lösungsverfahren an ihre Grenzen, sobald die Problemdimensionen ein größeres – man könnte durchaus sagen realistisches – Ausmaß erreichen. In der Praxis dominieren deshalb Methoden, die die Losgrößen der einzelnen Produkte sequenziell festlegen und überdies etwaige Kapazitätsbeschränkungen im Nachhinein, falls überhaupt, berücksichtigen. In der Literatur finden sich zahlreiche approximative Ansätze zur Lösung dieses komplexen betriebswirtschaftlichen Problems. Lokale Suche und auf ihr basierende Metaheuristiken stellen vielversprechende Werkzeuge dar, um die Defizite der aktuell eingesetzten Trial-and-Error Ansätze zu beheben und letzten Endes zulässige sowie kostenoptimale Produktionspläne zu erstellen. Die in dieser Diplomarbeit vorgestellte Studie beschäftigt sich mit lokalen Suchverfahren für das MLCLSP. Acht Nachbarschaftsstrukturen, die sich aus einer Veränderung der Rüstvariablen ergeben, werden präsentiert und evaluiert. Grundlegende Optionen bei der Gestaltung eines iterativen Verbesserungsverfahrens, wie beispielsweise unterschiedliche Schrittfunktionen oder die temporäre Berücksichtigung unzulässiger Lösungen, werden getestet und verglichen. Obwohl nur die Switch Nachbarschaft, die durch das Ändern einer einzigen Rüstvariable definiert wird, wirklich überzeugende Resultate liefert, können die übrigen Nachbarschaftsstrukturen durchaus als Perturbationsmechanismen im Rahmen einer Variablen Nachbarschaftssuche (VNS) zum Einsatz kommen. Die Implementierung dieser Metaheuristik, geprägt von den Ergebnissen der einfachen lokalen Suchverfahren, kann allerdings nicht vollkommen überzeugen. Die entwickelte VNS Variante kann die Lösungsgüte anderer zum Vergleich herangezogener Lösungsverfahren nicht erreichen und benötigt relativ lange Laufzeiten. Andererseits sind die Ergebnisse mit einer durchschnittlichen Abweichung zur besten bekannten Lösung von etwa vier Prozent über sämtliche untersuchte Problemklassen weit entfernt von einem Totalversagen. Es überwiegt der Eindruck, dass es sich um eine robuste Methode handelt, die in der Lage ist, Lösungen von hoher, teils sehr hoher Qualität nicht nur in Ausnahmefällen zu liefern. Etwaige Nachjustierungen könnten das Verfahren durchaus zu einem ernstzunehmenden Konkurrenten für bereits existierende Lösungsmethoden für das MLCLSP machen.The Multi-Level Capacitated Lotsizing Problem (MLCLSP) depicts the important decision in production planning of determining adequate lot sizes from final products onward, to subassemblies, parts and raw materials, all the while assuming limited capacities of the resources employed for manufacture. It is an NP-hard problem where exact methods fail in solving larger – one could say realistic – problem instances. Sequential approaches that tackle the problem item by item and postpone capacity considerations dominate current practice; approximate solution methods abound throughout the literature. Local search and metaheuristics based on it constitute a class of approximate methods well-equipped to take on the challenge of eventually replacing the trial-and-error process that impedes manufacturing companies in establishing feasible and cost-minimal production plans. This thesis presents a study of local search based procedures for solving the MLCLSP. Eight different neighborhood structures, resulting from manipulations of the setup variables, are devised and evaluated. Fundamental options when designing an iterative improvement algorithm, such as best-improvement versus first-improvement step functions or the inclusion of infeasible solutions during the search are explored and compared. Although only the Switch move, which alters the value of a single setup value, is convincing as a stand-alone neighborhood structure, the other neighborhoods can in any case be employed for the perturbation of solutions during the shaking step of a Variable Neighborhood Search (VNS). The implementation of this metaheuristic, shaped by the findings from testing the basic local search variants, led to mixed results. The procedure designed to tackle the MLCLSP cannot outperform the compared heuristics. Neither does it produce results that are terribly off – the average gap to the best known solutions settles around four percent over all problem classes tested. Nonetheless, the impression is supported that the VNS procedure is a robust method leading to good, sometimes even very good solutions at a regular basis that is amenable to further adjustments and thus eventually becoming a serious competitor for existing methods dealing with multi-level capacitated lotsizing decisions

Spare parts planning and control for maintenance operations

This paper presents a framework for planning and control of the spare parts supply chain inorganizations that use and maintain high-value capital assets. Decisions in the framework aredecomposed hierarchically and interfaces are described. We provide relevant literature to aiddecision making and identify open research topics. The framework can be used to increasethe e¿ciency, consistency and sustainability of decisions on how to plan and control a spareparts supply chain. This point is illustrated by applying it in a case-study. Applicability of theframework in di¿erent environments is also investigated

A collaborative framework in outbound logistics for the us automakers

The competitive landscape of the U.S. automotive market has transformed from the traditional Big Three players to too many viable players. In 2008-2009, the harsh market conditions, excess production capacity, capital asset redundancies, and many inefficient strategies submerged as the roadblocks for the US automakers to stay competitive and profitable in the North American market. In this new competitive era, cross-company collaboration in product development, standardizing and communizing supply base, sharing flexible manufacturing platforms, using common inbound and out bound logistics service providers and warehousing etc. can play vital roles for the US automakers to reduce overall cost and return to profitability. Through the horizontal collaboration in the outbound logistics operations, these companies can create close-knit business partnership and act faster than the foreign rivals in delivering finished vehicles at the optimum cost. The optimization of outbound logistics operations through consolidation and collaboration among OEMs has tremendous potential to contribute to the profitability by lowering the cost of transportation, in-house inventory, transportation time, and facility costs. The collaboration in the intra- and inter-OEM outbound logistics operations is a critical area that the US automakers need to pay attention and prioritize in their cost reduction initiatives. This research presents an integrated collaboration framework for the outbound logistics operations of the US automakers. In our framework, we propose three potential levels for the US automakers to form outbound logistics collaboration: operational, tactical, and strategic. Our research proposition is to improve the performance of outbound logistics systems of automotive OEMs by means of horizontal collaboration between plants and competing OEMs. The proposed research thus relates to the literature on logistics system design and management and horizontal collaboration in supply chain management. The collaboration framework is demonstrated through a real world case study in US automotive industry. The contribution of this research is the introduction of a framework for intra- and inter-OEM collaboration and the development of novel logistics network design and flow models integrated with inventory models, lost sales, and expedited shipment. Besides the contribution to the academic literature, the proposed collaborative distribution system is a new concept in the automotive industry. Hence, this novel research work will also benefit to the practitioners. Keywords: Operational Collaboration, Tactical Collaboration, Strategic Collaboration, Frequency based Inventory, Customer Patience and Lost Sales, Expedited Shipments