Robust optimization for a maritime inventory routing problem

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.publishe

Comparing techniques for modelling uncertainty in a maritime inventory routing problem

Uncertainty is inherent in many planning situations. One example is in maritime transportation, where weather conditions and port occupancy are typically characterized by high levels of uncertainty. This paper considers a maritime inventory routing problem where travel times are uncertain. Taking into account possible delays in the travel times is of main importance to avoid inventory surplus or shortages at the storages located at ports. Several techniques to deal with uncertainty, namely deterministic models with inventory buffers; robust optimization; stochastic programming and models incorporating conditional value-at-risk measures, are considered. The different techniques are tested for their ability to deal with uncertain travel times for a single product maritime inventory routing problem with constant production and consumption rates, a fleet of heterogeneous vessels and multiple ports. At the ports, the product is either produced or consumed and stored in storages with limited capacity. We assume two-stages of decisions, where the routing, the visit order of the ports and the quantities to load/unload are first-stage decisions (fixed before the uncertainty is revealed), while the visit time and the inventory levels at ports are second-stage decisions (adjusted to the observed travel times). Several solution approaches resulting from the proposed techniques are considered. A computational comparison of the resulting solution approaches is performed to compare the routing costs, the amount of inventory bounds deviation, the total quantities loaded and unloaded, and the running times. This computational experiment is reported for a set of maritime instances having up to six ports and five ships.publishe

An integrated shipment planning and storage capacity decision under uncertainty: a simulation study

Purpose – In transportation and distribution systems, the shipment decisions, fleet capacity, and storage capacity are interrelated in a complex way, especially when the authors take into account uncertainty of the demand rate and shipment lead time. While shipment planning is tactical or operational in nature, increasing storage capacity often requires top management’s authority. The purpose of this paper is to present a new method to integrate both operational and strategic decision parameters, namely shipment planning and storage capacity decision under uncertainty. The ultimate goal is to provide a near optimal solution that leads to a striking balance between the total logistics costs and product availability, critical in maritime logistics of bulk shipment of commodity items. Design/methodology/approach – The authors use simulation as research method. The authors develop a simulation model to investigate the effects of various factors on costs and service levels of a distribution system. The model mimics the transportation and distribution problems of bulk cement in a major cement company in Indonesia consisting of a silo at the port of origin, two silos at two ports of destination, and a number of ships that transport the bulk cement. The authors develop a number of “what-if” scenarios by varying the storage capacity at the port of origin as well as at the ports of destinations, number of ships operated, operating hours of ports, and dispatching rules for the ships. Each scenario is evaluated in terms of costs and service level. A full factorial experiment has been conducted and analysis of variance has been used to analyze the results. Findings – The results suggest that the number of ships deployed, silo capacity, working hours of ports, and the dispatching rules of ships significantly affect both total costs and service level. Interestingly, operating fewer ships enables the company to achieve almost the same service level and gaining substantial cost savings if constraints in other part of the system are alleviated, i.e., storage capacities and working hours of ports are extended. Practical implications – Cost is a competitive factor for bulk items like cement, and thus the proposed scenarios could be implemented by the company to substantially reduce the transportation and distribution costs. Alleviating storage capacity constraint is obviously an idea that needs to be considered when optimizing shipment planning alone could not give significant improvements. Originality/value – Existing research has so far focussed on the optimization of shipment planning/scheduling, and considers shipment planning/scheduling as the objective function while treating the storage capacity as constraints. The simulation model enables “what-if” analyses to be performed and has overcome the difficulties and impracticalities of analytical methods especially when the system incorporates stochastic variables exhibited in the case example. The use of efficient frontier analysis for analyzing the simulation results is a novel idea which has been proven to be effective in screening non-dominated solutions. This has provided the authors with near optimal solutions to trade-off logistics costs and service levels (availability), with minimal experimentation times

A maritime inventory routing problem with stochastic sailing and port times

This paper describes a stochastic short sea shipping problem where a company is responsible for both the distribution of oil products between islands and the inventory management of those products at consumption storage tanks located at ports. In general, ship routing and scheduling is associated with uncertainty in weather conditions and unpredictable waiting times at ports. In this work, both sailing times and port times are considered to be stochastic parameters. A two-stage stochastic programming model with recourse is presented where the first stage consists of routing, loading and unloading decisions, and the second stage consists of scheduling and inventory decisions. The model is solved using a decomposition approach similar to an L-shaped algorithm where optimality cuts are added dynamically, and this solution process is embedded within the sample average approximation method. A computational study based on real-world instances is presented

Modelos de otimização para a distribuição de combustíveis em curta distância marítima

Doutoramento em Matemática e AplicaçõesO transporte marítimo e o principal meio de transporte de mercadorias em todo o mundo. Combustíveis e produtos petrolíferos representam grande parte das mercadorias transportadas por via marítima. Sendo Cabo Verde um arquipelago o transporte por mar desempenha um papel de grande relevância na economia do país. Consideramos o problema da distribuicao de combustíveis em Cabo Verde, onde uma companhia e responsavel por coordenar a distribuicao de produtos petrolíferos com a gestão dos respetivos níveis armazenados em cada porto, de modo a satisfazer a procura dos varios produtos. O objetivo consiste em determinar políticas de distribuicão de combustíveis que minimizam o custo total de distribuiçao (transporte e operacões) enquanto os n íveis de armazenamento sao mantidos nos n íveis desejados. Por conveniencia, de acordo com o planeamento temporal, o prob¬lema e divido em dois sub-problemas interligados. Um de curto prazo e outro de medio prazo. Para o problema de curto prazo sao discutidos modelos matemáticos de programacao inteira mista, que consideram simultaneamente uma medicao temporal cont ínua e uma discreta de modo a modelar multiplas janelas temporais e taxas de consumo que variam diariamente. Os modelos sao fortalecidos com a inclusão de desigualdades validas. O problema e então resolvido usando um "software" comercial. Para o problema de medio prazo sao inicialmente discutidos e comparados varios modelos de programacao inteira mista para um horizonte temporal curto assumindo agora uma taxa de consumo constante, e sao introduzidas novas desigualdades validas. Com base no modelo escolhido sao compara¬das estrategias heurísticas que combinam três heur ísticas bem conhecidas: "Rolling Horizon", "Feasibility Pump" e "Local Branching", de modo a gerar boas soluçoes admissíveis para planeamentos com horizontes temporais de varios meses. Finalmente, de modo a lidar com situaçoes imprevistas, mas impor¬tantes no transporte marítimo, como as mas condicões meteorológicas e congestionamento dos portos, apresentamos um modelo estocastico para um problema de curto prazo, onde os tempos de viagens e os tempos de espera nos portos sao aleatórios. O problema e formulado como um modelo em duas etapas, onde na primeira etapa sao tomadas as decisões relativas as rotas do navio e quantidades a carregar e descarregar e na segunda etapa (designada por sub-problema) sao consideradas as decisoes (com recurso) relativas ao escalonamento das operacões. O problema e resolvido por um metodo de decomposto que usa um algoritmo eficiente para separar as desigualdades violadas no sub-problema.Maritime transportation is a major mode of transportation of goods worldwide. Most of cargo of the maritime transport accounted for liquid cargo oil and petroleum products. As Cape Verde is an archipelago, maritime transportation is of great importance for the local economic activity. We consider a fuel oil distribution problem where an oil company is responsible for the coordination of the distribution of oil products with the inventory management of those products at ports in order to satisfy the demands for the several oil products. The objective is to determine distribution policies that minimize the routing and operating costs, while inventory levels are maintained within given limits. For convenience, the planning problem is divided into two related subproblems accordingly to the length of the planning horizon: A short- term and medium-term planning. For the short-term planning problem we discuss mathematical mixed integer programming models that combine continuous and discrete time measures in order to handle with multiple time windows and a daily varying consumption rate of the various oil products. These models are strengthened with valid inequalities. Then the problem is solved using a commercial software. For the second subproblem several mixed integer formulations are discussed and compared for a short time horizon, and assuming constant consumption rates and new valid inequalities are introduced. Then, based on the chosen model, we compare several heuristic strategies that combine the well-known Rolling Horizon, Feasibility Pump and Local Branching heuristics, in or¬der to derive good feasible solutions for planning horizons of several months. Finally, as weather conditions and ports congestion are very impor¬tant in maritime transportation, we present a stochastic model for a short sea shipping problem, where traveling and waiting time are random. The problem is formulated as a two stage recourse problem, where in the first stage the routing and the load/unload quantities are defined, and in the second stage (subproblem) the scheduling of operations is determined. The problem is solved by a decomposition method that uses an efficient separation algorithm to include inequalities from the subproblem

A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges

Load-dependent speed optimization in maritime inventory routing

Maritime inventory routing problems involve determining optimal routes for seagoing vessels between ports while managing the inventory of each port. Normally, such problems are considered with the vessels operating at fixed sailing speeds. However, the speed of vessels can typically be adjusted within an interval, and the actual fuel consumption depends on both the load and the speed of the vessel. The fuel consumption function combines speed and load in a non-linear manner, but can be approximated through linearization. In this work, to evaluate the importance of taking into account that both speeds and load levels influence the fuel costs, the resulting solutions are contrasted with solutions from the case where speeds and travel costs are taken as constants, as well as the case where speed is a decision, but the cost considered to be independent of the load. For either of these cases, load-dependent speed optimization can be added as a post-processing step. Computational experiments show that combining speed and load do have an impact on the selection of routes in maritime inventory routing problems, and that proper modelling of the fuel consumption can reduce sailing costs significantly. On the test instances considered, taking into account speed while ignoring the load leads to cost savings of around 38%. Considering the fuel consumption as a function of speed and load when planning leads to additional cost savings of 28%. Keywords: mixed integer programming, non-linear, fuel consumption, transportpublishedVersio

Hierarchical clique analysis in social networks due to common knowledge of proverbs.

24th European Conference on Operational Research (EURO XXIV). Lisboa, 11 a 14 de Julho de 2010 (Comunicação).We present the Hierarchical Clique Analysis, a new algorithm for social networks analysis. The algorithm is exemplified with data about the recognition of proverbs collected in interviews in all Azorean islands and also in three Azorean emigration locations in the USA. Interpreting the set of this data as an incidence matrix of a graph, we obtain 8 oriented and isolated sub-graphs which distinguish the society in a kind of different families of proverbial users. The Hierarchical Clique Analysis finds distinct clusters with a high inner homogeneity