[pt] O problema de roteamento de navios com gestão de estoques (conhecido pelo termo em inglês Maritime inventory routing ou MIR) representa um problema prático de logística onde o transportador da carga também é responsável pela manutenção dos estoques do produto transportado nos portos de carga e descarga. Esta tese estuda um caso real do problema MIR. Um conjunto de testes é apresentado de modo a comparar diferentes formulações matemáticas da literatura, a fim de encontrar aquela mais aderente ao problema real. Em função da complexidade computacional do problema, é apresentada uma abordagem heurística que consegue encontrar soluções similares e reduz consideravelmente o tempo computacional quando comparadas com as formulações baseadas em PLIM. No entanto, problemas reais são muito influenciados por aspectos incertos. Sendo assim, é apresentada uma abordagem robusta para a otimização do problema MIR, que considera incerteza no tempo de estadia do navio nos portos. A abordagem apresentada produz soluções para diferentes níveis de robustez. Em outras palavras, considera o risco de variação no tempo de estadia do navio em um porto durante uma operação de carga ou descarga. Assim, é capaz de determinar a probabilidade de inviabilidade da solução encontrada para cada nível de robustez oferecido, além do impacto no custo de transporte à medida que soluções mais robustas são apresentadas. Esta abordagem oferece ao tomador de decisão a medida do trade-off entre robustez e custo de transporte. Desta forma, o mesmo pode determinar qual o nível de conservadorismo irá adotar em sua programação de navios e quanto isto irá impactar o custo de transporte. Os experimentos apresentados identificaram que, aumentos sutís no nível de robustez (com pequeno impacto no custo de transporte) podem reduzir consideravelmente a probabilidade de inviabilidade de uma solução. / [en] Maritime inventory routing (MIR) problem is an academic name for a practical logistic problem that represents the routing or scheduling of vessels to carry product(s) between ports. Meanwhile, the product(s) inventory levels in these ports must remain between operational bounds during the entire planning horizon. This thesis focus on how to support decision on a real-life MIR problem faced by a Brazilian petroleum company. To do so, we structure a set of tests to compare different formulation from literature and identify which is more adherent to real problem. Due to computational complexity of the problem, we present an heuristic approach that provides reasonably good solutions when compared to deterministic mixed integer linear programming (MILP) formulations and reduces considerably the computational time of solving real-life instances. However, uncertainty events have great impact in the ship scheduling planning. Therefore, we propose a robust optimization approach that considers uncertainty in the time spent at ports in each ship visit. Our approach is able to determine the probability of infeasibility and the impact in the objective function for each level of robustness, helping to measure the uncertain aversion of the decision maker. Our experiments identified that, for a certain instance, varying the level of robustness one may reduce the probability of infeasibility from 87 per cent (of deterministic solution) to 2 per cent and it represents an increase in the transportation costs of about 13 per cent.

The primary aim of this thesis is to develop effective solution techniques for large-scale maritime inventory routing problems that possess a core substructure common in many real-world applications. We use the term “large-scale” to refer to problems whose standard mixed-integer linear programming (MIP) formulations involve tens of thousands of binary decision variables and tens of thousands of constraints and require days to solve on a personal computer. Although a large body of literature already exists for problems combining vehicle routing and inventory control for road-based applications, relatively little work has been published in the realm of maritime logistics. A major contribution of this research is in the advancement of novel methods for tackling problems orders of magnitude larger than most of those considered in the literature. Coordinating the movement of massive vessels all around the globe to deliver large quantities of high value products is a challenging and important problem within the maritime transportation industry. After introducing a core maritime inventory routing model to aid decision-makers with their coordination efforts, we make three main contributions. First, we present a two-stage algorithm that exploits aggregation and decomposition to produce provably good solutions to complex instances with a 60-period (two-month) planning horizon. Not only is our solution approach different from previous methods discussed in the maritime transportation literature, but computational experience shows that our approach is promising. Second, building on the recent successes of approximate dynamic programming (ADP) for road-based applications, we present an ADP procedure to quickly generate good solutions to maritime inventory routing problems with a long planning horizon of up to 365 periods. For instances with many ports (customers) and many vessels, leading MIP solvers often require hours to produce good solutions even when the planning horizon is limited to 90 periods. Our approach requires minutes. Our algorithm operates by solving many small subproblems and, in so doing, collecting and learning information about how to produce better solutions. Our final research contribution is a polyhedral study of an optimization problem that was motivated by maritime inventory routing, but is applicable to a more general class of problems. Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) that we study captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program and derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Finally, a computational study demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB.

La gestion des stocks et la maîtrise de la distribution sont les deux activités importantes dans le management de la chaîne logistique. L’optimisation simultanée de ces deux activités est connue sous l’intitulé du problème de gestion de stock et de tournée de livraison (Inventory Routing Problem, IRP). L’IRP traditionnelle est confronté aux différents problèmes, causé principalement par le manque d'informations complètes et/ou temps réel, tels que les changements de la demande, l’embouteillage soudain causé par un accident, etc. Le partage et la mise à jour d'information logistique peut améliorer l'efficacité d’IRP. De plus, en raison de la spécificité de l'IRP dans la logistique urbaine, il est important de considérer d'autres critères comme les critères sociaux, environnementaux et le niveau de service qui pourraient être en conflictuel. L’objectif principal de cette thèse est de développer des modèles et des méthodes des IRP avec la prise en compte des incertitudes, du niveau de service et de l’impact environnemental, social en finalement les informations du temps réel (IRP dynamique). Dans cette thèse, trois modèles mathématiques sont proposés. Le premier modèle multi-objectif est pour identifier un compromis entre le niveau de service, les critères environnementaux et économiques. Pour gérer des paramètres incertains, on applique une approche floue. Dans le deuxième modèle, nous avons étudié l'impact des critères sociaux sur les IRPs en proposant un modèle mathématique bi-objectif. Une approche stochastique basée sur des scénarios est développée pour faire face à l'incertitude dans le modèle. Enfin, le troisième model concerne l'impact de l'utilisation d'informations du temps réel dans les IRP. Il est à noter que, selon la durée de vie du produit tant sur le plan financier que sur le plan écologique, les produits périssables sont considérés dans les trois modèles proposés. Les résultats montrent une gestion dynamique est beaucoup plus efficace que la statique. / The inventory management and transportation are two main activities of supply chain management. The joint optimization of these two activities is known as Inventory Routing Problem (IRP). The main objective of IRP is to determine the set of retailers to be delivered to in each period, the delivery sequence for each vehicle, and the quantities of goods delivered to each retailer for each period of a planning horizon. The traditional IRPs are faced different problems, caused mainly by lack of complete and/or timely information such as shifts in demand, traffic caused by a sudden vehicles accident, etc. sharing of updated and reliable logistics information can meaningful improve the efficiency of IRP. Moreover, because of the specificity of IRP in urban logistic, it is important to tack into account other criteria as social, environmental criteria and service level that could be in conflict. The main objective of this thesis is to (i) choose appropriate social, environmental and service level criteria, (ii) integrate them in mathematical models, and (iii) study the impact of these criteria on dynamic optimization of IRPs for perishable products under uncertain parameters. For this purpose, three mathematical models are proposed. The first model is multi-objective mathematical model in order to make a trade-off between service level, environmental criteria and economic. To decrease quantity of expired products, a nonlinear step function as holding cost function is integrated in the model. Moreover, to solve the problem a fuzzy possibilistic approach is applied to handle uncertain parameters. In the second model, a bi-objective mathematical model is proposed to study impact of social issues on the IRPs. In the proposed model, first objective function concerns economic criteria while the second one social issues. A scenario-based stochastic approach is developed to cope with uncertainty in the model. Finally, the third model concerns impact of using real-time information in efficiency of IRPs. It is noteworthy that, according significant role of perishable products in the both financially and ecology sides of IRPs, perishable products are considered in all three proposed model while even proposed models are appropriate to nonperishable ones as well. The results show that a dynamic management is more efficient than the static one.

Fornecedores necessitam atender a demanda de seus clientes da forma mais adequada possível e mantendo a qualidade de seu serviço, porém em muitos casos essa demanda é desconhecida. Esse problema pode ser modelado como um problema de roteirização e estoque com demanda estocástica o qual inclui o controle de estoque, transporte do produto e decisões de agendamento da entrega. Existem vários trabalhos na literatura para resolver esse problema, porém nenhum deles lida com janela de tempo de atendimento, capacidade máxima de estoque tanto no cliente quanto no depósito e o nível de confiança de atendimento individualizado para cada cliente. O objetivo principal deste trabalho é propor um novo algoritmo baseado em otimização matemática para lidar com esse problema mais realista. Além disso, este trabalho tem como objetivo secundário melhorar o algoritmo de estado da arte baseado em otimização matemática, visando encontrar soluções com um menor tempo computacional e custo. Foram realizados experimentos com instâncias sintéticas com 15 até 50 clientes, as quais são geradas aleatoriamente, e com uma instância real, baseada na experiência profissional no mercado empresarial e em cenários reais de distribuição na cidade de São Paulo / Providers need to supply the demand of their clients as optimally as possible and maintaining the quality of their service, however in many cases this demand is unknown. This problem can be modeled as a inventory routing problem with stochastic demand, which includes inventory control, product transportation and delivery scheduling decisions. There are several papers in the literature to solve this problem, but none of them deals with service time window, maximum stock capacity for both the customer and the depot and individualized confidence level for each costumer. The main objective of this work is to propose a new algorithm based on mathematical optimization to deal with this more realistic problem. In addition, this work has as secondary objective to improve the state of the art algorithm based on mathematical optimization, aiming to find solutions with a lower computational time and cost. Experiments were performed with synthetic instances with 15 to 50 clients, which are randomly generated, and with a real instance, based on professional experience in the business market and in real distribution scenarios in the city of São Paulo

Fornecedores necessitam atender a demanda de seus clientes da forma mais adequada possível e mantendo a qualidade de seu serviço, porém em muitos casos essa demanda é desconhecida. Esse problema pode ser modelado como um problema de roteirização e estoque com demanda estocástica o qual inclui o controle de estoque, transporte do produto e decisões de agendamento da entrega. Existem vários trabalhos na literatura para resolver esse problema, porém nenhum deles lida com janela de tempo de atendimento, capacidade máxima de estoque tanto no cliente quanto no depósito e o nível de confiança de atendimento individualizado para cada cliente. O objetivo principal deste trabalho é propor um novo algoritmo baseado em otimização matemática para lidar com esse problema mais realista. Além disso, este trabalho tem como objetivo secundário melhorar o algoritmo de estado da arte baseado em otimização matemática, visando encontrar soluções com um menor tempo computacional e custo. Foram realizados experimentos com instâncias sintéticas com 15 até 50 clientes, as quais são geradas aleatoriamente, e com uma instância real, baseada na experiência profissional no mercado empresarial e em cenários reais de distribuição na cidade de São Paulo / Providers need to supply the demand of their clients as optimally as possible and maintaining the quality of their service, however in many cases this demand is unknown. This problem can be modeled as a inventory routing problem with stochastic demand, which includes inventory control, product transportation and delivery scheduling decisions. There are several papers in the literature to solve this problem, but none of them deals with service time window, maximum stock capacity for both the customer and the depot and individualized confidence level for each costumer. The main objective of this work is to propose a new algorithm based on mathematical optimization to deal with this more realistic problem. In addition, this work has as secondary objective to improve the state of the art algorithm based on mathematical optimization, aiming to find solutions with a lower computational time and cost. Experiments were performed with synthetic instances with 15 to 50 clients, which are randomly generated, and with a real instance, based on professional experience in the business market and in real distribution scenarios in the city of São Paulo

Almost everywhere, routing plays an important role in everyday life. This thesis consists of three parts, each studying different applications where routing decisions are coordinated with other decisions. A common denominator in all applications is that an intelligent utilization of a fleet of vehicles is crucial for the performance of the system. In the first part, routing and inventorymanagement decisions are coordinated, in the second part, routing decisions concerning different modes of transportation are coordinated with inventory management, and in the third part, location decision and routing are coordinated. In the first part, an application concerning waste management is presented. Many industries generate garbage, and instead of handling the waste disposal themselves, other companies, specialized in garbage collection, handle the disposal. Each industry rents containers from a company to be used for waste, and the garbage collection companies handle the collection. The industries buy a service including one or more containers at the industry and the garbage collection companies are obliged to make sure that the containers never become overfull. The idea is that the industries buy this service and in return, the garbage collection company can plan the collection so that the overall cost and the number of overfull containers is minimized. Two models for the problem facing the garbage collection company are proposed. The first is solved using a Lagrangean relaxation approach on a flow based model, and the second is solved using Benders decomposition on a column based model. The second part investigates a distribution chain management problem taken from the Swedish pulp industry. Given fixed production plans at the mills, and fixed customer demands, the problem is to minimize the distribution cost. Unlike many other models for marine distribution chains, the customers are not located at the harbors. This means that the model proposed also incorporates the distribution planning from the harbors to the customers. All customers are not served from the harbors; some are served directly from the mills using trucks and trains to distribute the pulp, and these decisions are also included. The problem is modeled as a mixed integer linear program and solved using a branch and price scheme. Due to the complexity of the problem, the solution strategy is divided into two phases, where the first emphasizes the generation of schedules for the vessels operated by the company, while the second deals with the chartering of vessels on the spot market. In the third part, routing is combined with location decisions in the location-routing problem. Special emphasis is given to strategic management where decision makers must make location, capacity and routing decisions over a long planning period. The studied application comes fromstrategic schoolmanagement, where the location and capacity of the schools as well as their catchment areas are under consideration. The problem is modeled as a mixed integer linear program. The computational study shows the importance of incorporating a routing component allowing multiple visits, as well as the danger of having a too short planning period.

We consider a one-warehouse multi-retailer system where the warehouse orders or receives from its supplier and replenishes multiple retailers with direct shipping or multi-stop routing over a finite time horizon. The warehouse has the knowledge of external (deterministic) demands at the retailers and manages their inventories while ensuring no stock-out. We consider two problems with direct shipping policy and two problems with routing policy. For the direct shipping policy, the problem is to determine the optimal replenishments for the warehouse and retailers such that the system-wide costs are minimized. In one problem, the warehouse decides about how much and when to ship to the retailers while in the other problem, inventory level of the retailer has to be raised up to a predetermined level whenever replenished. We propose strong mixed integer programming formulations for these problems. Computational experiments show that our formulations are better than their competitors and are very successful in solving the problems to optimality. For the routing policy, the problem is to decide on when and in what sequence to visit the retailers and how much to ship to a retailer so as to minimize system-wide costs. In one problem, the warehouse receives given amounts from its supplier while in the other the warehouse decides on its own replenishments. We propose branch-and-cut algorithms and heuristics based on strong formulations for both problems. Computational results reveal that our procedures perform better than their competitors in the literature for both problems.

This study is concerned with the inventory routing problem with deterministic, dynamic demand and order-up-to level inventory policy. The problem mainly arises in the supply chain management context. It incorporates simultaneous decision making on inventory management and vehicle routing with the purpose of gaining advantage from coordinated decisions. An integrated mathematical model that represents the features of the problem is presented. Due to the magnitude of the model, lagrangean relaxation solution procedures that identify upper bounds and lower bounds for the problem are developed. Satisfactory computational results are obtained with the solution procedures suggested on the test instances taken from the literature.

In this study, we consider a logistics system, in which a single supplier delivers a product to multiple retailers over a finite time horizon. Supplier decides on the amount to order in each period and services retailers facing deterministic dynamic demand via a fleet of vehicles having limited capacity. Each retailer has specific minimum and maximum levels of inventory in an order-up-to level inventory policy setting. The problem is to simultaneously determine the quantity of product to order to the supplier, retailers to be visited, the quantity of product to be delivered to retailers and routes of vehicles in each period so as to minimize system-wide costs. We present a mathematical formulation for the problem, for which we develop several Lagrangian relaxation based solution procedures providing both upper and lower bounds to the problem. We implement these solution procedures on test instances and present the results. Computational study shows that our solution procedures generate good feasible solutions in reasonable time.

[pt] Tema: Este estudo investiga o Problema de Roteamento de Inventário (IRP) no contexto do Gerenciamento de Inventário pelo Fornecedor (VMI), uma prática comum na cadeia de suprimentos onde os fornecedores assumem a responsabilidade pela reposição. O IRP, um problema combinatório estudado amplamente há quase 40 anos, engloba três subproblemas distintos: programação de entregas, gerenciamento de estoque e roteamento de veículos. Problema: Apesar de sua idade, o IRP continua a atrair a atenção da indústria e da academia. O recente décimo segundo Desafio de Implementação DIMACS dedicou uma categoria ao IRP, e entre os benchmarks comumente utilizados, 401 instâncias ainda não possuem soluções ótimas, especialmente no desafiador subconjunto de instâncias grandes. Hipótese e Justificativa: O framework HGS proposto por Vidal et al. (2012) surgiu como uma ferramenta proeminente utilizada por várias equipes de forma satisfatória na competição. No entanto, até onde sabemos, o framework HGS não foi testada para o IRP. Este estudo propõe uma solução que combina o framework HGS com uma estratégia de busca local eficiente, o método NSIRP proposto por Diniz et al. (2020), para abordar o IRP. Metodologia: Implementamos a solução proposta e comparamos seu desempenho com 21 abordagens existentes, utilizando os benchmarks da literatura. Resumo dos Resultados: Nossa abordagem identificou 79 novas Melhores Soluções Conhecidas (BKS) dentre 1100 instâncias. Se aplicada sob as mesmas regras da competição DIMACS, nossa solução teria garantido o primeiro lugar. Contribuições e Impactos: Este trabalho contribui para o desenvolvimento contínuo de soluções para o IRP, oferecendo uma abordagem eficiente e competitiva que pode inspirar futuras pesquisas e aplicações práticas no campo do gerenciamento de estoque e roteamento de veículos. / [en] Theme: This study investigates the Inventory Routing Problem (IRP) within the context of Vendor-Managed Inventory (VMI), a prevalent supply chain practice where suppliers assume responsibility for replenishment. The IRP, a combinatorial problem that has been widely studied for almost 40 years, encompasses three distinct subproblems: delivery scheduling, inventory management, and vehicle routing. Problem: Despite its age, the IRP continues to attract industry and academia attention. The recent 12th DIMACS Implementation Challenge dedicated a track to the IRP, and among the commonly used benchmarks, 401 instances still lack optimal solutions, particularly in the challenging Large instance subset. Hypothesis and Justification: The HGS framework proposed by Vidal et al. (2012) emerged as a prominent tool used successfully by numerous teams in the competition. However, to the best of our knowledge, the HGS framework has not been tested for the IRP. This study proposes a method combining the HGS framework with an efficient local search strategy, namely NSIRP proposed by Diniz et al. (2020), to tackle the IRP. Methodology: We implemented the proposed method and compared its performance to 21 existing methods using the literature benchmarks. Summary of Results: Our approach identified 79 new Best Known Solutions (BKS) out of 1100 instances. If applied under the same rules as the DIMACS competition, our method would have secured the first place. Contributions and Impacts: This work contribute to the ongoing development of IRP methods, offering an efficient and competitive approach that may inspire further research and practical applications in the realm of inventory management and vehicle routing.