Logic-based Benders decomposition (LBBD) is a strategy for solving discrete optimisation problems. In LBBD, the optimisation problem is divided into a master problem and a subproblem and each part is solved separately. LBBD methods that combine mixed-integer programming and constraint programming have been successfully applied to solve large-scale scheduling and resource allocation problems. Such combinations typically solve an assignment-type master problem and a scheduling-type subproblem. However, a challenge with LBBD methods that have feasibility subproblems are that they do not provide a feasible solution until an optimal solution is found.  In this thesis, we show that feasible solutions can be obtained by finding and combining feasible parts of an infeasible master problem assignment. We use these insights to develop an acceleration technique for LBBD that solves a series of subproblems, according to algorithms for constructing a maximal feasible subset of constraints (MaFS). Using a multiprocessor scheduling problem as a benchmark, we study the computational impact from using this technique. We evaluate three variants of LBBD schemes. The first uses MaFS, the second uses irreducible subset of constraints (IIS) and the third combines MaFS with IIS. Computational tests were performed on an instance set of multiprocessor scheduling problems. In total, 83 instances were tested, and their number of tasks varied between 2794 and 10,661. The results showed that when applying our acceleration technique in the decomposition scheme, the pessimistic bounds were strong, but the convergence was slow. The decomposition scheme combining our acceleration technique with the acceleration technique using IIS showed potential to accelerate the method.

With the rise of online retailer giants like Amazon, and enhancements in internet and mobile technologies, online shopping is becoming increasingly popular. This has lead to new opportunities in online price optimization. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions. In Chapter 2 a multi-period revenue maximization and pricing optimization problem in the presence of reference prices is formulated as a mixed integer nonlinear program. Two algorithms are developed to solve the optimization problem: a generalized Benders' decomposition algorithm and a myopic heuristic. This is followed by numerical computations to illustrate the effciency of the solution approaches as well as some managerial pricing insights. In Chapter 3 a data-driven quadratic programming optimization model for online pricing in the presence of customer ratings is proposed. A new demand function is developed for a multi-product, nite horizon, online retail environment. To solve the optimization problem, a myopic pricing heuristic as well as exact solution approaches are introduced. Using customer reviews ratings data from Amazon.com, a new customer rating forecasting model is validated. This is followed by several analytical and numerical insights. In Chapter 4 a multinomial choice model is used for customer purchase decision to find optimal personalized price discounts for an online retailer that incorporates customer locations and feedback from their reviews. Closed form solutions are derived for two special cases of this problem. To gain some analytical insights extensive numerical experiments are carried followed by several analytical and numerical insights. / Thesis / Doctor of Philosophy (PhD) / The increase in online retail and the improvements in mobile technologies has lead to advantages and opportunities for both customers and retailers. One of these advantages is the ability to keep and efficiently access records of historical orders for both customers and retailers. In addition, online retailing has dramatically decreased the cost of price adjustments and discounts compared to the brick and mortar environment. At the same time, with the increase in online retailing we are witnessing proliferations of online reviews in e-commerce platforms. Given this availability of data and the new capabilities in an online retail environment, there is a need to develop pricing optimization models that integrate all these new features. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions.

In this work, we address a variety of problems with applications to `ethanol production from biomass', `agile manufacturing' and `mass customization' domains. Our motivation stems from the potential use of biomass as an alternative to non-renewable fuels, the prevalence of `flexible manufacturing systems', and the popularity of `mass customization' in today's highly competitive markets. Production scheduling and design and optimization of logistics network mark the underlying topics of our work. In particular, we address three problems, Biomass Logistics Problem, Hybrid Flow Shop Scheduling Problem, and Stochastic Demand Assembly Job Scheduling Problem. The Biomass Logistics Problem is a strategic cost analysis for setup and operation of a biomass supply chain network that is aimed at the production of ethanol from switchgrass. We discuss the structural components and operations for such a network. We incorporate real-life GIS data of a geographical region in a model that captures this problem. Consequently, we develop and demonstrate the effectiveness of a `Nested Benders' based algorithm for an efficient solution to this problem. The Hybrid Flow Shop Scheduling Problem concerns with production scheduling of a lot over a two-stage hybrid flow shop configuration of machines, and is often encountered in `flexible manufacturing systems'. We incorporate the use of `lot-streaming' in order to minimize the makespan value. Although a general case of this problem is NP-hard, we develop a pseudo-polynomial time algorithm for a special case of this problem when the sublot sizes are treated to be continuous. The case of discrete sublot sizes is also discussed for which we develop a branch-and-bound-based method and experimentally demonstrate its effectiveness in obtaining a near-optimal solution. The Stochastic Demand Assembly Job Scheduling Problem deals with the scheduling of a set of products in a production setting where manufacturers seek to fulfill multiple objectives such as `economy of scale' together with achieving the flexibility to produce a variety of products for their customers while minimizing delivery lead times. We design a novel methodology that is geared towards these objectives and propose a Lagrangian relaxation-based algorithm for efficient computation. / Doctor of Philosophy / In this work, we organize our research efforts in three broad areas - Biomass Supply Chain, Hybrid Flow Shop, and Assembly Job Shop, which are separate in terms of their application but connected by scheduling and logistics as the underlying functions. For each of them, we formulate the problem statement and identify the challenges and opportunities from the viewpoint of mathematical decision making. We use some of the well known results from the theory of optimization and linear algebra to design effective algorithms in solving these specific problems within a reasonable time limit. Even though the emphasis is on conducting an algorithmic analysis of the proposed solution methods and in solving the problems analytically, we strive to capture all the relevant and practical features of the problems during formulation of each of the problem statement, thereby maintaining their applicability. The Biomass Supply Chain pertains to the production of fuel grade ethanol from naturally occurring biomass in the form of switchgrass. Such a system requires establishment of a supply chain and logistics network that connects the production fields at its source, the intermediate points for temporary storage of the biomass, and bio-energy plant and refinery at its end for conversion of the cellulosic content in the biomass to crude oil and ethanol, respectively. We define the components and operations necessary for functioning of such a supply chain. The Biomass Logistics Problem that we address is a strategic cost analysis for setup and operation of such a biomass supply chain network. We focus our attention to a region in South Central Virginia and use the detailed geographic map data to obtain land use pattern in the region. We conduct survey of existing literature to obtain various transportation related cost factors and costs associated with the use of equipment. Our ultimate aim here is to understand the feasibility of running a biomass supply chain in the region of interest from an economic standpoint. As such, we represent the Biomass Logistics Problem with a cost-based optimization model and solve it in a series of smaller problems. A Hybrid Flow Shop (HFS) is a configuration of machines that is often encountered in the flexible manufacturing systems, wherein a particular station of machines can execute processing of jobs/tasks simultaneously. In our work, we approach a specific type of HFS, with a single machine at the first stage and multiple identical machines at the second stage. A batch or lot of jobs/items is considered for scheduling over such an HFS. Depending upon the area of application, such a batch is either allowed to be split into continuous sections or restricted to be split in discrete sizes only. The objective is to minimize the completion time of the last job on its assigned machine at the second stage. We call this problem, Hybrid Flow Shop Scheduling Problem, which is known to be a hard problem in literature. We aim to derive the results which will reduce the complexity of this problem, and develop both exact as well as heuristic methods in order to obtain near-optimal solution to this problem. An Assembly Job Shop is a variant of the classical Job Shop which considers scheduling a set of assembly operations over a set of assembly machines. Each operation can only be started once all the other operations in its precedence relationship are completed. Assembly Job Shop are at the core of some of the highly competitive manufacturing facilities that are principled on the philosophy of Mass Customization. Assuming an inherent nature of demand uncertainty, this philosophy aims to achieve ‘economy of scale’ together with flexibility to produce a variety of products for the customers while minimizing the delivery lead times simultaneously. We incorporate some of these challenges in a concise framework of production scheduling and call this problem as Stochastic Demand Assembly Job Scheduling Problem. We design a novel methodology that is geared towards achieving the set objectives and propose an effective algorithm for efficient computation.

[pt] No Brasil, as três principais fontes renováveis de energia elétrica são eólica, pequenas centrais hidrelétricas (PCHs) e biomassa. A comercialização da energia proveniente dessas fontes ocorre majoritariamente no ambiente de contratação regulada (ACR), através de leilões, em detrimento do ambiente de contratação livre (ACL). Isso devido ao fato de seus recursos naturais serem sazonais, estabelecendo o risco de preço-quantidade no ACL, em que o excesso ou déficit de energia gerada em relação à quantidade contratada é liquidado ao preço de liquidação de diferenças (PLD), uma variável sistêmica e altamente volátil. Contudo, a complementaridade dessas fontes permite reduzir esses riscos quando a energia é comercializada de forma conjunta, através de um fundo de energia que gera aumento do valor do portfólio com relação à comercialização individual. Esta dissertação utiliza a teoria de jogos cooperativos para analisar formas de repartir o benefício gerado, através da alocação de quotas financeiras. O conjunto de soluções onde o resultado individual das fontes no fundo é maior do que o resultado individual em qualquer subcoalisão define o núcleo do jogo. Assim, a complexidade de encontrar uma solução dentro do núcleo depende do número de subcoalizões, que cresce exponencialmente com o número de jogadores. Nesse contexto, este trabalho se propôs a apresentar: (i) um modelo de portfólio que incentiva a participação de fontes renováveis no ACL; (ii) um modelo de programação linear que busca o núcleo do jogo; (iii) uma metodologia eficiente baseada em decomposição de Benders, capaz de suprimir a questão da explosão combinatória do problema. / [en] In Brazil, the three main sources of renewable energy are wind, small run-of-river hidros (SH) and biomass. The energy sale of such sources occurs mainly in the Regulated Trading Environment (RTE), through auctions, with shy occurrences in the Free Trading Environment (FTE). This is due to the fact that their natural resources are seasonal, establishing the so-called price-quantity risk in the FTE, as the surplus or deficit of energy generated relative to the contracted amount is settled at the market’s spot price, a systemic and highly volatile variable. However, the complementary nature of these sources allows risk reduction if their energy are trade jointly, through an energy hedge pool that increases the value of the portfolio in comparison to individual strategies. This work makes use of cooperative games theory to analyze ways of sharing the generated benefit, through financial quotas allocation. The set of solutions where the individual sources results in the pool are greater than its results at any possible subcoalition defines the core of the game. Thus, the challenge of finding a solution inside the core depends on the number of subcoalitions, which grows exponentially with the number of players. In this context, this work proposes to present: (i) a model of portfolio that encourages the penetration of renewable sources in the FTE; (ii) a linear programming model that pursuits the game’s core; (iii) an efficient methodology based on Benders decomposition that is capable of suppress the problem of combinatorial explosion, typical of cooperative games with many players.

This thesis study focuses on transmission expansion planning (TEP) problem for restructured power systems and addresses challenges specifically in countries where electricity market is in developing phase after liberalization of power industry for establishing a competitive market, like Turkey. A novel multi-year TEP approach is developed which considers generation investment cost and transmission congestion level in the planning horizon. The model assesses the impact of generation investments on TEP problem. Benders decomposition methodology is utilized successfully to decompose the complex mixed-integer programming TEP problem into a master problem and two subproblems. Security subproblem assesses single-contingency criteria. Transmission congestion cost is considered within operational subproblem given that congestion level is a proper criterion for measuring competitiveness level of an electricity market. The proposed approach is applied to the Turkish power system. The proposed approach could be utilized to provide indicative plans, which might be quite necessary particularly during development of a competitive market. However, there is no guarantee that independent power producers (IPPs) will follow those plans which concern the maximization of social-welfare. Given the necessity of coordinating monopoly transmission and decentralized generator investment decisions, the proposed approach is improved further to include promoting decentralized generator investments through incentive payments. Such incentives might be necessary to trigger IPPs earlier than their projections, as illustrated by numerical examples including IEEE 30-bus system.

Made available in DSpace on 2016-06-02T19:51:37Z (GMT). No. of bitstreams: 1 2228.pdf: 979050 bytes, checksum: ffa6f96c8eada124b6f1e6ba3ebe02da (MD5) Previous issue date: 2008-12-11 / Financiadora de Estudos e Projetos / Cutting and packing problems are important in the production planning of various industrial segments involving goals such as minimizing the negative efects generated by waste of materials or idle spaces. The loss of material due to an inadequate programming of the cutting or packing patterns, can be substantial, and, in general, parts of these losses can be avoided only with a more eficient production planning, not resulting in additional investments in production processes. This study aimed at evaluating the performance of the Benders decomposition method, applied to the manufacturer and distributor pallet loading models. The manufacturer pallet loading model involves packing equal boxes on a pallet, so as to optimize its use. The distributor pallet loading model involves packing boxes of diferent sizes on a pallet, also a way to optimize its use. The approach based on Benders decomposition, defines a relaxation algorithm that partitions the original problem in two other problems easier to be solved. To check the effectiveness of the approach, computational tests were carried out by comparing the results with those obtained by a computational package composed of a modeling language (GAMS) and a last generation optimization solver (CPLEX ). / Os problemas de corte e empacotamento são importantes no planejamento da produção de vários segmentos industriais envolvendo objetivos como, por exemplo, minimizar os efeitos negativos gerados por desperdício de materiais ou espaços ociosos. As perdas de material, devido a uma programação pouco adequada dos padrões de corte ou empacotamento, podem ser substanciais, sendo que, em geral, parte destas perdas pode ser evitada apenas com uma programação da produção mais eficiente, não implicando em investimentos adicionais nos processos de produção. O objetivo deste estudo é verificar o desempenho do método de decomposição de Benders aplicado a modelos de carregamento de paletes do produtor e do distribuidor. O problema de carregamento de paletes do produtor envolve empacotar caixas iguais sobre um palete, de maneira a otimizar o aproveitamento deste. O problema de carregamento de paletes do distribuidor envolve empacotar caixas de tamanhos diferentes sobre um palete, também de maneira a otimizar o aproveitamento deste. A abordagem baseada na reformulação de Benders define um algoritmo de relaxação que particiona o problema original em dois outros problemas mais simples de serem resolvidos. Para verificar a eficiência da abordagem, realizaram-se testes computacionais, comparando os resultados obtidos com os obtidos pelo pacote computacional composto de uma linguagem de modelagem (GAMS) e um software de otimização de última geração (CPLEX).

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-04-11T14:02:57Z No. of bitstreams: 1 joseantoniochiabaibento.pdf: 931983 bytes, checksum: e18793314d0e558922ed90cb19474dbb (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T03:37:26Z (GMT) No. of bitstreams: 1 joseantoniochiabaibento.pdf: 931983 bytes, checksum: e18793314d0e558922ed90cb19474dbb (MD5) / Made available in DSpace on 2016-04-24T03:37:26Z (GMT). No. of bitstreams: 1 joseantoniochiabaibento.pdf: 931983 bytes, checksum: e18793314d0e558922ed90cb19474dbb (MD5) Previous issue date: 2013-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A penetração de parques eólicos nos sistemas elétricos de potência tem apresentado um grande crescimento no Brasil e no mundo devido à disponibilidade da matéria prima, os ventos, e à necessidade de reformulação das matrizes energéticas a fim de reduzir os impactos ambientais decorrentes da geração de energia elétrica. Porém, as usinas eólicas apresentam variações nos despachos de potência devido à variabilidade de velocidade dos ventos. Estas variações causam impactos no sistema, podendo afetar a confiabilidade e a estabilidade de tensão. Além disto, a operação de determinados tipos de aerogeradores requer suporte adicional de potência reativa. Uma opção para aumentar as margens operativas e acomodar as intermitências de regime dos ventos em sistemas elétricos de potência consiste na utilização de compensadores estáticos de reativos (CER) junto às usinas eólicas. Estes equipamentos FACTS (Flexible AC Transmission Systems) provêm suporte de potência reativa variável e de rápido controle, de acordo com os requisitos operacionais dos aerogeradores. Neste sentido, o presente trabalho apresenta uma metodologia para ajuste ótimo dos parâmetros do CER visando dar suporte de potência reativa para a operação de usinas eólicas em sistemas elétricos de potência. Para representar as intermitências no despacho de potência dos aerogeradores, a metodologia proposta considera diferentes cenários de vento. O problema é modelado através de fluxo de potência ótimo (FPO), associado à técnica de decomposição matemática de Benders. Os parâmetros de ajuste do CER são a tensão de referência e o coeficiente de inclinação da curva característica deste equipamento em regime permanente. Destaca-se que o ajuste ótimo deste coeficiente é inédito na literatura especializada. Testes com sistemas do IEEE são realizados para validar a metodologia proposta. / The penetration of wind farms in power systems has shown tremendous growth in Brazil and in the world due to the availability of the raw material, the wind, and the need to redefine the energy mix to reduce the environmental impacts from the electrical energy generation. However, the wind farms have variable outputs due to the variation of wind speeds. These outputs impact the power system and can affect the reliability and the voltage stability. Besides, the operation of some aerogenerators requires additional support of reactive power. An option for handling this feature and increasing the operative margins of power systems is the use of static VAr compensators (SVC) together with the wind farms. These FACTS devices (Flexible AC Transmission Systems) provide a variable reactive power support, with a fast control according to the operational requirements of the aerogenerators. In this sense, this work presents a methodology for the optimal adjustment of the SVC parameters to give reactive power support for wind farms operating in power systems. The proposed methodology considers different wind scenarios to represent the variations of the wind farms outputs. The problem is modeled through an optimal power flow (OPF) and the Benders decomposition technique. The SVC parameters for adjustment are its reference voltage and the coefficient of its characteristic curve in stable state. It can be highlighted that the adjustment of this coefficient is innovative for the literature. Tests with systems of the IEEE are performed to validate the proposed methodology.

Dans plusieurs pays européens, la capacité de l’infrastructure est complètement exploitée aux heures de pointe et aux points critiques : une grande quantité de trains traversent ces points critiques dans un laps de temps très réduit. Dans cette situation le retard d’un train provoqué par un conflit de circulation peut se propager dans tout le réseau. Le problème de la gestion opérationnelle du trafic ferroviaire consiste à trouver les modifications des itinéraires et des ordonnancements des trains qui minimisent la propagation des retards. Dans cette thèse, nous proposons une approche de décomposition de Benders pour la formulation linéaire en nombres entiers à variables mixtes utilisée dans l’algorithme RECIFE-MILP. Après avoir constaté que l’approche de décomposition standard de Benders ne permet pas de trouver rapidement une solution de bonne qualité pour certaines instances du problème, nous étudions trois approches alternatives afin d’améliorer la performance de notre algorithme. Nous proposons d’abord une approche que nous appelons la reformulation réduite de Benders. Ensuite, nous introduisons des inégalités dans la formulation du problème maître de Benders. Finalement, nous scindons le processus de résolution en trois étapes au lieu de deux comme dans la décomposition standard de Benders. L'analyse expérimentale montre que la combinaison de la première et dernière approche surpasse l’algorithme original RECIFE-MILP dans la résolution de grandes instances sous certaines conditions. / In railway systems, during congested traffic situations, the infrastructure capacity is completely exploited for trains circulation. In these situations, when traffic is perturbed some trains must be stopped or slowed down for ensuring safety, and delays occur. The real-time Railway Traffic Management Problem (rtRTMP) is the problem of modifying trains route and schedule to limit delay propagation. In this thesis, we propose a Benders decomposition of a MILP-based algorithm for this problem, named RECIFE-MILP. After observing that the standard Benders decomposition (BD) does not allow the effective solution of rtRTMP instances, we study three possible approaches to improve the performance. Specifically, we first propose a modification of the problem reformulation which is typical of BD, obtaining what we call reduced BD. Then, we introduce some inequalities to the Benders master problem. Finally, we split the solution process in three steps rather than two as in the standard BD. As we show in a thorough experimental analysis, the combination of the first and last approaches outperforms the original RECIFE-MILP algorithm when tackling large instances with some specific features.

Dans cette thèse, nous étudions différents modèles, déterministes et stochastiques, pour les problèmes de dimensionnement de réseaux. Nous examinons également le problème du sac-à-dos stochastique ainsi que, plus généralement, les contraintes de capacité en probabilité.<p>\ / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Le placement de production (UC pour unit commitment) est une famille de problèmes d'optimisation qui déterminent l’état et la puissance de consigne des groupes de production pour satisfaire la demande électrique à moindre coût. Traditionnellement, une contrainte de sûreté détermine un certain volume de capacité raccordée disponible, appelé la réserve, destinée à gérer l'incertitude. Néanmoins, dans les petits systèmes la contrainte de réserve fixe peut entraîner dans certains cas une violation du critère N-1 bien que le volume de réserve minimale soit respecté. Plus récemment, la part croissante de production variable à partir de sources renouvelables (ENR) peut conduire à des programmes d’appel qui ne garantissent plus la sûreté même dans les grands systèmes.Pour y faire face, différentes techniques d'atténuation des impacts ont été proposées telle que la révision des modèles de placement de la production pour inclure une meilleure représentation de la dynamique du système. Cette sous-famille des problèmes UC est formellement définie dans ces travaux comme le problème FCUC (frequency constrained unit commitment). Elle vise à maintenir la fréquence au-dessus d'un certain seuil, et éviter ainsi le délestage par sous-fréquence (DSF).La première partie de ces travaux identifie les défis dans la formulation du problème FCUC. D’une part, la contrainte de fréquence est fortement non-linéaire par rapport aux variables de décision du problème UC. D’autre part, elle est difficile à approcher par des fonctions analytiques. La simulation séquentielle d'un modèle UC classique et d’un modèle de réponse primaire de la fréquence est alors proposée. L’intérêt d’une formulation plus fidèle de la contrainte de sûreté est donc révélé. La deuxième partie de ces travaux étudie l'impact des ENR sur la réponse primaire de la fréquence. Le besoin de formuler des modèles de FCUC plus précis est mis en avant.La troisième partie des travaux examine le coût, les bénéfices et les limitations des modèles FCUC, basés sur des contraintes indirectes sur certains paramètres dynamiques des unités de production. Il est montré que, bien que l'application de contraintes de sécurité indirectes assure la sûreté dans certains pas horaires, l'effet inverse peut apparaître à un autre instant. Ainsi, l’efficacité des leviers dépend fortement du point de fonctionnement du système. Il en est de même pour le coût de la solution. Cette étude met en évidence la nécessité de nouvelles méthodes pour traiter correctement la contrainte sur le creux de fréquence afin d'assurer l'optimalité et efficacité de la solution.Finalement, la quatrième partie des travaux offre une nouvelle formulation du problème FCUC suivant une approche de décomposition de Bender. La décomposition de Bender sépare un problème d'optimisation avec une certaine structure en deux parties : le problème maître et le problème esclave. Dans le cas du FCUC, le problème maître propose des plans de production candidats (états des groupes) et le problème esclave assure le respect des contraintes de fréquence par le biais d'un modèle de plans sécants. Les résultats de simulation montrent que la représentation plus précise du creux de fréquence au niveau du problème esclave réduit le risque de DSF et le coût de la sécurité par rapport à d'autres modèles de FCUC. / The Unit Commitment problem (UC) is a family of optimisation models for determining the optimal short-term generation schedule to supply electric power demand with a defined risk level. The UC objective function is given by the operational costs over the optimisation horizon. The constraints include, among others, technical, operational and security limits. Traditionally, the security constraints are given by the requirement of a certain volume of on-line spare capacity, which is called the reserve and is meant to handle uncertainty, while preventing the interruption of power supply. It is commonly specified following a static reliability criterion, such as the N-1 rule.Nevertheless, in small systems the fixed, and a priori defined, reserve constraint could entail a violation of the N-1 criterion, although the reserve constraint was met. More recently, the increasing share of variable generation from renewable sources (V-RES), such as wind and solar, may lead to UC solutions that no longer ensure system security. Therefore, different impact mitigation techniques have been proposed in literature, which include the revision of UC models to provide a better representation of the system dynamics. This subfamily of UC models is formally defined in this work as the frequency constrained UC problem (FCUC), and aims to keep the frequency above a certain threshold, following pre-defined contingencies, by adding enhanced security constraints. In this work this topic is addressed in four parts.The first part identifies the main challenge of formulating the FCUC problem. Indeed, the frequency minimum, also called the frequency nadir, constraint is strongly non-linear on the decision variables of the UC model. Moreover, the behaviour of the frequency nadir regarding the binary decision variables is hard to approximate by analytical functions. Thus, a sequential simulation approach is proposed, based on a classic UC model and a reduced order model of the primary frequency response. The potential benefits of a smarter allocation of the primary reserve is revealed.The second part of this work investigates the impact of V-RES sources on the primary frequency response. The underlying processes that lead to the increase of the Under-Frequency Load Shedding (UFLS) risk are thoroughly discussed. The need of formulating more accurate FCUC models is highlighted.The third part of this work examines the cost/benefit and limitation of FCUC models based on indirect constraints over certain dynamic parameters of the generating units. A methodology is proposed that assesses the effectiveness and optimality of some existing V-RES impact mitigation techniques, such as the increase of the primary reserve requirement, the prescription of an inertia requirement, the authorisation of V-RES dispatch-down or the consideration of fast non-synchronous providers of frequency regulation services. This study showed the need for new methods to properly handle the frequency nadir constraint in order to ensure optimality, without compromising the optimisation problem’s tractability.The fourth part of this work offers a new formulation of the FCUC problem following a Bender’s decomposition approach. This method is based on the decomposition of an optimisation problem into two stages: the master and the slave problems. Here, the master problem deals with the generating unit states and the slave problem handles the frequency nadir constraints through a cutting plane model. Simulation results showed that the more accurate representation of the frequency nadir in the slave problem reduces the risk of UFLS and the security cost, with respect to other FCUC models, such as those based on inertia constraints. In addition, the optimality of the global solution is guaranteed; although the convergence of the master problem is slow, due to the well-known tailing off effect of cutting plane methods.