Strategic network design has significant impacts on the operational performance of transportation and telecommunications industries. The corresponding networks are typically characterized by a multicommodity ow structure where a commodity is defined by a unique origin-destination pair and an associated amount of ow. In turn, multicommodity network design and hub location models are commonly employed when designing strategic networks in transportation and telecommunications applications. In this dissertation, these two modeling approaches are integrated and generalized to address important requirements in network design for truckload transportation and long-distance telecommunications networks. To this end, we first introduce a cost effective relay network design model and then extend this base model to address the specific characteristics of these applications. The base model determines relay point (RP) locations where the commodities are relayed from their origins to destinations. In doing this, we explicitly consider distance constraints for the RP-RP and nonRPRP linkages. In truckload transportation, a relay network (RP-network) can be utilized to decrease drivers' driving distances and keep them within their domiciles. This can potentially help alleviate the high driver turnover problem. In this case, the percentage circuitry, load-imbalance, and link-imbalance constraints are incorporated into the base model to control related performance metrics that are affected by the distance constraints. When compared to the networks from other modeling approaches, the RP-network is more effective in controlling drivers' tour lengths and capable of controlling the empty mileage to low levels without adding a large amount of additional travel distance. In telecommunications, an RP-network can be beneficial in long-distance data transfers where the signals' delity must be improved/regenerated at RPs along their travel paths. For this setting, we extend the base model to include fixed link setup costs and capacities. From our computational results, our models provide better network configuration that is cost effective and facilitates a better service quality (shorter delays and better connectivity). Concerning methodology, we develop effcient exact solution algorithms based on Benders decomposition, Lagrangean decomposition, and Lagrangean relaxation. The performance of the typical solution frameworks are enhanced via numerous accelerating techniques to allow the solution of large-sized instances in reduced solution times. The accelerating techniques and solution approaches are transferable to other network design problem settings with similar characteristics.

The goal of this dissertation is to study optimization models that integrate location, production, inventory and transportation decisions for industrial products and apply the knowledge gained to develop supply chains for agricultural products (biomass). We estimate unit cost for the whole biomass-to-biofuels’ supply chain which is the per gallon cost for biofuels up till it reaches the markets. The unit cost estimated is the summation of location, production, inventory holding, and transportation costs. In this dissertation, we focus on building mathematical models for designing and managing the biomass-to-biofuels’ supply chains. The computational complexity of the developed models makes it advisable to use heuristic solution procedures. We develop a Lagrangean decomposition heuristic. In our heuristic, we divide the problem into two sub-problems, sub-problem 1 is a transportation problem and sub-problem 2 is a combination of a capacitated facility location and production planning problem. Subproblem 2 is further divided by commodities. The algorithm is tested for a number of different scenarios. We also develop a decision support system (DSS) for the biomass-to-biofuels’ supply chain. In our DSS, the main problem is divided into four easy-to-solve supply chain problems. These problems were determined based on our knowledge of supply chain and discussions with the experts from the biomass and biofuels’ sector. The DSS is coded using visual basic applications (VBA) for Excel and has a simple user interface which assists the user in running different types of supply chain problems and provides results in form of reports which are easy to understand.

The purpose of this work aims to develop and explore a nonlinear multiperiod petroleum refinery model based on a real-world model. Due to the inherent complexity and interconnected nature of petroleum refineries, various studies are implemented to describe the multiperiod model. The model is based around maximizing the profit of a petroleum refinery, starting from the crude inputs through the crude distillation unit, to the intermediate product processing through various unit operations, and finally to the blending of the final products. The model begins as a single period model, and is re-formulated as a multiperiod model by incorporating intermediate product tanks and dividing the model into partitions. In solving the multiperiod model, the termination criteria for convergence was varied in order to investigate the effect on the solution; it was found that it is acceptable to terminate at a relaxed tolerance due to minimal differences in solution. Several case studies, defined as deviations from normal operation, are implemented in order to draw comparisons between the real-world model and the model studied in this thesis. The thesis model, solved by CONOPT and IPOPT, resulted in significant gains over the real-world model. Next, a Lagrangean decomposition scheme was implemented in an attempt to decrease computation times. The decomposition was unable to find feasible solutions for the subproblems, as the nonlinear and nonconvex nature of the problem posed difficulty in finding feasibilities. However, in the case of a failed decomposition, the point where the decomposition ends may be used as an initial guess to solve the full space problem, regardless of feasibility of the subproblems. It was found that running the decomposition fewer times provided better initial guesses due to lower constraint violations from the infeasibilities, and then combined with the shorter decomposition time resulted in faster computation times. / Thesis / Master of Applied Science (MASc) / Petroleum refineries consist of complex units that serve a certain purpose, such as separating components of a mixed stream or blending intermediate products, in order to create final commercial products, e.g. gasoline and diesel. Due to the complexity and interconnectivity in a refinery, it is difficult to determine the optimal mode of operation. Thus, by formulating the refinery in mathematical form, optimization techniques may be used to find optimal operation. Furthermore, optimization problems can be formulated in a multiperiod fashion, where the problem is repeated over a set time horizon in partitions. The advantage is a higher detail in the operation of the refinery but this comes at a cost of higher computation time. In this work, a multiperiod refinery is formulated and studied by exploring model size, computation times, comparison of solvers, and solution strategies such as decomposition.

In this study, a Lagrangean heuristic based on Lagrangean relaxation and subgradient optimization is proposed for the two-stage modular capacitated facility location problem. The objective is to minimize the cost of locating and operating plants and warehouses, plus the cost of transporting goods at both echelons to satisfy the demand of customers. The difference of our study from the two-stage capacitated facility location problem is the existence of multiple capacity levels as a candidate for each plant in the problem. Each capacity level has a minimum production capacity which has to be satisfied to open the relevant capacity level. Obviously, a single capacity level can be selected for an opened facility location. In the second echelon, the warehouses are capacitated and have unique fixed and variable costs for opening and operating. Multiple sourcing is allowed in both transportation echelons. Firstly, we develop a mixed integer linear programming model for the two-stage modular capacitated facility location problem. Then we develop a Lagrangean heuristic to solve the problem efficiently. Our Lagrangean heuristic consists of three main components: Lagrangean relaxation, subgradient optimization and a primal heuristic. Lagrangean relaxation is employed for obtaining the lower bound, subgradient optimization is used for updating the Lagrange multipliers at each iteration, and finally a three-stage primal heuristic is created for generating the upper bound solutions. At the first stage of the upper bound heuristic, global feasibility of the plants and warehouses is inspected and a greedy heuristic is executed, if there is a global infeasibility. At the next stage, an allocation heuristic is used to assign customers to warehouses and warehouses to plants sequentially. At the final stage of the upper bound heuristic, local feasibilities of the plants are investigated and infeasible capacity levels are adjusted if necessary. In order to show the efficiency of the developed heuristic, we have tested our heuristic on 280 problem instances generated randomly but systematically. The results of the experiments show that the developed heuristic is efficient and effective in terms of solution quality and computational effort especially for large instances.

O trabalho apresentado nesta dissertação é referente ao estudo da evacuação de pessoas, mais especificamente, a evacuação predial faseada. O objetivo é determinar, para instâncias de até 25 andares, os instantes de liberação de cada grupo de pessoas, a fim de minimizar o tempo total de evacuação do edifício. No entanto, a determinação destes instantes deve considerar o risco ao qual os diferentes grupos estão submetidos, priorizando a evacuação do andar afetado. Além disso, os conflitos de diferentes grupos por espaço nas rotas de evacuação também devem ser evitados, já que, são nessas situações que acontecem grande parte dos acidentes. Para atingir tal objetivo, foi elaborado um modelo matemático de programação linear inteira. Devido à alta complexidade do modelo, fez-se necessária a aplicação de métodos heurísticos para a obtenção de soluções. Dessa maneira, foram desenvolvidas uma heurística de busca baseada em GRASP e uma heurística lagrangeana. Apesar da heurística lagrangeana atestar a qualidade da solução (a partir da comparação do resultado obtido com o limitante inferior), a heurística de busca mostrou-se mais adequada para o problema, pois forneceu resultados de qualidade com pouco esforço computacional. / This dissertation studies the evacuation of people, more specifically, building phased evacuation. The objective of this study is to determine, for buildings of up to 25 floors, in which instants each group of people has to be released, in order to minimize the total evacuation time. Furthermore, the determination of these instants has to consider the risk to which each group of people is submitted, thus the affected floor has to be the first group to be released. In addition, conflicts for space between groups should be avoided, since such situations increase the occurrences of accidents. To achieve this goal, an integer linear programming model was designed. Due to the high complexity of the model, it was necessary to apply heuristics to obtain solutions for some instances. Therefore, a search heuristic based on GRASP and a lagrangian heuristic were developed. Despite the fact that the lagrangian heuristic attests to the quality of the solution (when it is compared to the lower bound), the search heuristic was considered more suitable for this problem because it provided quality results with lower computational efforts.

While the concept of regional organization (regionalization) of perinatal care aimed at reducing perinatal mortality has remained at the agenda of developed countries since 1970&rsquo / s, Turkey is one of the countries that does not have such a system yet. In this study, a three-level hierarchical location-allocation model is developed for the regionalization of perinatal care in an attempt to have a better distribution of maternal and perinatal health care services in Turkey. Since the mathematical model developed is difficult to solve in a reasonable time, we propose three heuristic approaches: top-down, modified top-down and Lagrangean relaxation based heuristics. These heuristics are computationally tested on a set of problem instances for networks ranging from 10 to 737 vertices. A significant result is that Lagrangean relaxation based heuristic outperforms the other two heuristics in terms of solution quality. In most of the test problems, the modified top-down heuristic outperforms the top-down heuristic in terms of solution quality. Using the proposed approaches, we solve a real life problem corresponding to the Eastern and South Eastern Anatolian Regions (the East Region) of Turkey.

In this study, we consider a capacity allocation problem in flexible manufacturing systems. We assume time and tool magazine capacities on the Numerical Controlled (NC) machines and limited number of available tools. Our problem is to allocate the available capacity of the NC machines to the required demand of the operations, so as to maximize the total weight of operation assignments. We formulate the problem as a Mixed Integer Linear Program and show that it is NP-hard in the strong sense. We solve the moderate-sized problems optimally by the available Integer Programming software. We also develop Lagrangean relaxation based upper bounds and several heuristic procedures. Our computational results have revealed that the Lagrangean upper bounds are very close to optimal solutions and the heuristic procedures produce near optimal solutions in very small solution times even when the problem sizes are large.

DIAS, Fábio Carlos Sousa. Algoritmos para o problema de localização simples baseados nas formulações clássica e canônica. 2008. 89 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2008. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-11T15:12:03Z No. of bitstreams: 1 2008_dis_fcsdias.pdf: 533140 bytes, checksum: 547c9cf8d771e2646884c423f5a39936 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-15T15:32:35Z (GMT) No. of bitstreams: 1 2008_dis_fcsdias.pdf: 533140 bytes, checksum: 547c9cf8d771e2646884c423f5a39936 (MD5) / Made available in DSpace on 2016-07-15T15:32:35Z (GMT). No. of bitstreams: 1 2008_dis_fcsdias.pdf: 533140 bytes, checksum: 547c9cf8d771e2646884c423f5a39936 (MD5) Previous issue date: 2008 / In this work, we study the Simple Plant Location Problem (SPLP). Using its classical mathematical programming formulation and another recently proposed formulation, we develop several algorithms to …nd lower and upper bounds for the problem as well as branch-and-bound algorithms. With the classical formulation, such bounds are obtained via the data correction method and dominance criteria between …xed and transportation costs. We propose a projection of this formulation that has shown to be computationally atractive. Using the new formulation, we propose and prove the correctness of several iterative procedures that attempt to …nd an optimal solution to the problem by solving a sequence of parametric sub-problems, each one obtained by removing some variables and constraints of the original formulation. At each iteration of this process, we can obtain lower and upper bounds. We also apply Lagrangean relaxation to this new formulation in order to get other bounds. We consider several possibilities of relaxing the constraints. In addition, we develop branch-and-bound algorithms based on both formulations and the obtained bounds. We evaluate the computational e¢ ciency of all proposed algorithms with hard test instances from the literature. Computational results are reported and comparisons with other algorithms from the literature are carried out. / Neste trabalho, estudamos o problema de localização simples (SPLP - Simple Plant Location Problem). Usando a formulação matemática clássica e uma outra formulação proposta recentemente, desenvolvemos vários algoritmos para encontrar limites inferiores e superiores, bem como algoritmos tipo branch-and-bound. Com a formulação clássica, tais limites são obtidos utilizando o método de correção de dados e critérios de dominância entre os custos …xos e de transporte. Propomos uma projeção dessa formulação, que se mostrou computacionalmente atrativa. Usando a nova formulação propomos e mostramos a corretude de vários procedimentos iterativos que procuram encontrar uma solução para o problema, resolvendo uma seqüência de subproblemas paramétricos obtidos com a remoção de variáveis e restrições da formulação original. Em cada iteração desse processo, podemos gerar limites inferiores e superiores. Aplicamos ainda relaxação lagrangeana a essa nova formulação para obter outros limites. Analisamos várias possibilidades de relaxação das restrições. Desenvolmento também algoritmos branch-and-bound baseados em ambas as formulações e nos limites obtidos. Avaliamos a e…ciência computacional de todos os algoritmos com instâncias de teste difíceis, disponíveis na literatura. Resultados computacionais e comparações com outros algoritmos da literatura são reportados.

O trabalho apresentado nesta dissertação é referente ao estudo da evacuação de pessoas, mais especificamente, a evacuação predial faseada. O objetivo é determinar, para instâncias de até 25 andares, os instantes de liberação de cada grupo de pessoas, a fim de minimizar o tempo total de evacuação do edifício. No entanto, a determinação destes instantes deve considerar o risco ao qual os diferentes grupos estão submetidos, priorizando a evacuação do andar afetado. Além disso, os conflitos de diferentes grupos por espaço nas rotas de evacuação também devem ser evitados, já que, são nessas situações que acontecem grande parte dos acidentes. Para atingir tal objetivo, foi elaborado um modelo matemático de programação linear inteira. Devido à alta complexidade do modelo, fez-se necessária a aplicação de métodos heurísticos para a obtenção de soluções. Dessa maneira, foram desenvolvidas uma heurística de busca baseada em GRASP e uma heurística lagrangeana. Apesar da heurística lagrangeana atestar a qualidade da solução (a partir da comparação do resultado obtido com o limitante inferior), a heurística de busca mostrou-se mais adequada para o problema, pois forneceu resultados de qualidade com pouco esforço computacional. / This dissertation studies the evacuation of people, more specifically, building phased evacuation. The objective of this study is to determine, for buildings of up to 25 floors, in which instants each group of people has to be released, in order to minimize the total evacuation time. Furthermore, the determination of these instants has to consider the risk to which each group of people is submitted, thus the affected floor has to be the first group to be released. In addition, conflicts for space between groups should be avoided, since such situations increase the occurrences of accidents. To achieve this goal, an integer linear programming model was designed. Due to the high complexity of the model, it was necessary to apply heuristics to obtain solutions for some instances. Therefore, a search heuristic based on GRASP and a lagrangian heuristic were developed. Despite the fact that the lagrangian heuristic attests to the quality of the solution (when it is compared to the lower bound), the search heuristic was considered more suitable for this problem because it provided quality results with lower computational efforts.

This dissertation addresses the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second approach is Lagrangean decomposition. We present numerical results for a process network planning problem and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly. To further generalize this work, we also propose a graph-theory algorithm for non-anticipativity constraint reduction in problems with arbitrary scenario sets. Finally, in a break from the rest of the thesis, we present the basics of stochastic programming for non-expert users.