Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

Robust optimisation of dry port network design in the container shipping industry under uncertainty

PhD ThesisThe concept of dry port has attracted the attention of many researchers in the field of containerised transport industry over the past few decades. Previous research on dry port container network design has dealt with decision-making at different levels in an isolated manner. The purpose of this research is to develop a decision-making tool based on mathematical programming models to integrate strategic level decisions with operational level decisions. In this context, the strategic level decision making comprises the number and location of dry ports, the allocation of customers demand, and the provision of arcs between dry ports and customers within the network. On the other hand, the operational level decision making consists of containers flow, the selection of transportation modes, empty container repositioning, and empty containers inventory control. The containers flow decision involves the forward and backward flow of both laden and empty containers. Several mathematical models are developed for the optimal design of dry port networks while integrating all these decisions. One of the key aspects that has been incorporated in this study is the inherent uncertainty of container demands from end customers. Besides, a dynamic setting has to be adopted to consider the inevitable periodic fluctuation of demands. In order to incorporate the abovementioned decision-making integration with uncertain demands, several models are developed based on twostage stochastic programming approach. In the developed models, the strategic decisions are made in the first stage while the second-stage deals with operational decisions. The models are then solved through a robust sample average approximation approach, which is improved with the Benders Decomposition method. Moreover, several acceleration algorithms including multi-cut framework, knapsack inequalities, and Pareto-optimal cut scheme are applied to enhance the solution computational time. The proposed models are applied to a hypothetical case of dry port container network design in North Carolina, USA. Extensive numerical experiments are conducted to validate the dry port network design models. A large number of problem instances are employed in the numerical experiments to certify the capability of models. The quality of generated solutions is examined via a statistical validation procedure. The results reveal that the proposed approach can produce a reliable dry port container network under uncertain environment. Moreover, the experimental results underline the sensitivity of the configuration of the network to the inventory holding costs iii and the value of coefficients relating to model robustness and solution robustness. In addition, a number of managerial insights are provided that may be widely used in container shipping industry: that the optimal number of dry ports is inversely proportional to the empty container holding costs; that multiple sourcing is preferable when there are high levels of uncertainty; that rail tends to be better for transporting laden containers directly from seaports to customers with road being used for empty container repositioning; service level and fill rate improve when the design targets more robust solutions; and inventory turnover increases with high levels of holding cost; and inventory turnover decreases with increasing robustness

Integrated Production-Inventory Models in Steel Mills Operating in a Fuzzy Environment

Despite the paramount importance of the steel rolling industry and its vital contributions to a nation’s economic growth and pace of development, production planning in this industry has not received as much attention as opposed to other industries. The work presented in this thesis tackles the master production scheduling (MPS) problem encountered frequently in steel rolling mills producing reinforced steel bars of different grades and dimensions. At first, the production planning problem is dealt with under static demand conditions and is formulated as a mixed integer bilinear program (MIBLP) where the objective of this deterministic model is to provide insights into the combined effect of several interrelated factors such as batch production, scrap rate, complex setup time structure, overtime, backlogging and product substitution, on the planning decisions. Typically, MIBLPs are not readily solvable using off-the-shelf optimization packages necessitating the development of specifically tailored solution algorithms that can efficiently handle this class of models. The classical linearization approaches are first discussed and employed to the model at hand, and then a hybrid linearization-Benders decomposition technique is developed in order to separate the complicating variables from the non-complicating ones. As a third alternative, a modified Branch-and-Bound (B&B) algorithm is proposed where the branching, bounding and fathoming criteria differ from those of classical B&B algorithms previously established in the literature. Numerical experiments have shown that the proposed B&B algorithm outperforms the other two approaches for larger problem instances with savings in computational time amounting to 48%. The second part of this thesis extends the previous analysis to allow for the incorporation of internal as well as external sources of uncertainty associated with end customers’ demand and production capacity in the planning decisions. In such situations, the implementation of the model on a rolling horizon basis is a common business practice but it requires the repetitive solution of the model at the beginning of each time period. As such, viable approximations that result in a tractable number of binary and/or integer variables and generate only exact schedules are developed. Computational experiments suggest that a fair compromise between the quality of the solutions and substantial computational time savings is achieved via the employment of these approximate models. The dynamic nature of the operating environment can also be captured using the concept of fuzzy set theory (FST). The use of FST allows for the incorporation of the decision maker’s subjective judgment in the context of mathematical models through flexible mathematical programming (FMP) approach and possibilistic programming (PP) approach. In this work, both of these approaches are combined where the volatility in demand is reflected by a flexible constraint expressed by a fuzzy set having a triangular membership function, and the production capacity is expressed as a triangular fuzzy number. Numerical analysis illustrates the economical benefits obtained from using the fuzzy approach as compared to its deterministic counterpart

Modelo de p-medianas hierárquico e acessibilidade: análise dos hospitais públicos de Santa Catarina

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Produção, Florianópolis, 2016.A escassez de meios, na história da humanidade, sempre motivou a criação e o desenvolvimento de técnicas que melhorassem a efetividade de aplicação dos recursos. Em diversas áreas de atuação governamental é essencial saber onde posicionar as unidades de atendimento de forma a facilitar ao máximo o acesso de toda a população ao serviço. Considerando serviços de saúde, não somente valores econômicos estão envolvidos, mas principalmente a vida das pessoas. Os principais problemas envolvendo a localização de instalações de saúde incluem questões sobre planejamento de serviços, agendamento de recursos, logística, diagnóstico, tratamento e cuidados preventivos.O trabalho versa sobre um problema de localização que tem por objetivo reduzir a distância ponderada percorrida pelos usuários para acessar uma rede hierárquica pública de serviços, mantendo o nível de acessibilidade dos usuários a patamares aceitáveis. Para tal fim, utiliza-se um modelo matemático de análise locacional que traz em seu bojo um indicador de acessibilidade para avaliar a equidade para a população, sem perder de vista a eficiência do sistema.Propõe-se uma avaliação da rede pública do Sistema de Saúde do estado de Santa Catarina e a compara com a solução ótima do problema de p-medianas hierárquico não capacitado com demanda fixa. O indicador de acessibilidade proposto foi aplicado à distribuição de unidades de forma a permitir avaliar o grau de acessibilidade e de eficiência do sistema, e através de um algoritmo genético multiobjetivo novas e mais adequadas soluções foram produzidas e comparadas, buscando satisfazer simultaneamente equidade e eficiência.Em suma, o estudo permite gerar subsídios para melhor avaliar os impactos da política de distribuição dos sistemas de saúde. Sua aplicação visa resultar ganhos à sociedade em termos de qualidade no serviço prestado e eficiência na aplicação dos recursos, justificando estratégias a partir dos resultados obtidos que estabeleçam uma configuração no sistema de saúde mais próxima dos interesses dos usuários.Abstract : The stringency of resources, in mankind's history, always had driven the creation and development of techniques that aim to the maximal effectiveness use of resources. In many areas of governmental action, it is fundamental to know where to locate healthcare units in order to ease population accessing to medical services. The main awkwardnesses about locating health facilities include planning services, scheduling, logistics, diagnosis, treatment and preventive care. Concerning health services, not only economic values are involved, but, above all things, human lives.This work deals with a location problem which targets to curb the weighted distance traveled by users to access a public hierarchical network services, maintaining the level of accessibility within acceptable levels. For this purpose, a location mathematical model that assess equity through an accessibility indicator is applied, in order to improve efficiency meanwhile keeping accessibility to the system.An assessment of the public health system in the state of Santa Catarina network is proposed and portrait against to the optimal solution of the fixed demand unconstrained p-median hierarchical problem. The proposed accessibility indicator had been applied to the spreading healthcare units to make possible to gauge the degree of accessibility and efficiency of the system. Last but not least a multi-objective genetic algorithm was implemented aiming to provide and compare new and appropriate solutions, which searches simultaneously satisfying equity and efficiency.In short, this study paves ways to generate data and arguments to better assess the impacts of the distribution policy of health systems. Its application could lead gains to society in terms of quality in service and efficiency in application of resources, and justifies strategies to settle, resettle and augment the healthcare network system, directing investments to the interest of the users