In this study, an operational (short term) flexibility management approach is proposed for make-to-order companies with flexible shops. Order Review and Release (ORR) techniques and typical Flexible Manufacturing System (FMS) decisions are combined in this method. The proposed method prepares a shop environment by allocating process and routing flexibility types at different levels to the shop in each production cycle. Variety, volume, and criticality of the part types in the pool and the anticipated orders constitute the main inputs for flexibility allocation. A flexibility management policy is introduced and determination of the proper policy is realized with the integrated utilization of mathematical programming and simulation modeling. An experimental study is performed to investigate the effects of proposed method on a hypothetical flexible shop. Results show that with an appropriate policy, periodical and online flexibility management can be an effective tool to cope with uncertainty in demand if combined with ORR techniques.

In this research, the focus is on improving a designer's capability to determine near-optimal sizes of components for a given system architecture. Component sizing is a hard problem to solve because of the presence of competing objectives, requirements from multiple disciplines, and the need for finding a solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, this research introduces advances in the following two areas: a.) Formulating a component sizing problem in a manner that is convenient to designers and b.) Solving the component sizing problem in an efficient manner so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal. In particular, an acausal, algebraic, equation-based, declarative modeling approach is taken to solve component sizing problems efficiently. This is because global optimization algorithms exist for algebraic models and the computation time is considerably less as compared to the optimization of dynamic simulations. In this thesis, the mathematical programming language known as GAMS (General Algebraic Modeling System) and its associated global optimization solvers are used to solve component sizing problems efficiently. Mathematical programming languages such as GAMS are not convenient for formulating component sizing problems and therefore the Systems Modeling Language developed by the Object Management Group (OMG SysML ) is used to formally capture and organize models related to component sizing into libraries that can be reused to compose new models quickly by connecting them together. Model-transformations are then used to generate low-level mathematical programming models in GAMS that can be solved using commercial off-the-shelf solvers such as BARON (Branch and Reduce Optimization Navigator) to determine the component sizes that satisfy the requirements and objectives imposed on the system. This framework is illustrated by applying it to an example application for sizing a hydraulic log splitter.

In the last decade, market pressures for greater variety of products forced a gradual shift from continuous manufacturing to batch manufacturing in various industries. Consequently batch scheduling problems have attracted the attention of researchers in production and operations management. This thesis addresses the scheduling of parallel non-identical batch processors in the presence of dynamic job arrivals, incompatible job-families and non-identical job sizes. This problem abstracts the scheduling of heat-treatment furnace operations of castings in a steel foundry. The problem is of considerable interest in this sector as a large proportion of the total production time is spent in heat treatment processing. This problem is also encountered in other industrial settings such as burn-in operation in the final testing stage of semiconductor manufacturing, and manufacturing of steel, ceramics, aircraft parts, footwear, etc. A detailed literature review and personal communications with experts revealed that this class of batch scheduling problems have not been addressed hitherto. A major concern in the management of foundries is to maximize throughput and reduce flow time and work-in-process inventories. Therefore we have chosen the primary scheduling objective to be the utilization of batch processors and as secondary objectives the minimization of overall flow time and weighted average waiting time per job. This formulation can be considered as an extension of problems studied by DOBSON AND NAMBINADOM (1992), UZSOY (1995), ZEE et a/. (1997) and MEHTA AND UZSOY (1998). Our effort to carefully catalogue the large number of variants of deterministic batch scheduling problems led us to the development of a taxonomy and notation. Not surprisingly, we are able to show that our problem is NP-hard and is therefore in the company of many scheduling problems that are difficult to solve. Initially two heuristic algorithms, one a mathematical programming based heuristic algorithm (MPHA) and the other a greedy heuristic algorithm were developed. Due to the computational overheads in the implementation of MPHA when compared with the greedy heuristic, we chose to focus on the latter as the primary scheduling methodology. Preliminary experimentation led us to the observation that the performance of greedy heuristics depends critically on the selection of job-families. So eight variants of the greedy heuristic that differ mainly in the decision on "job-family selection" were proposed. These eight heuristics are basically two sets {Al, A2, A3, A4} and the modified (MAI, MA2, MA3, MA4}, which differ only on how the "job-family" index, weighted shortest processing time, is computed. For evaluating the performance of the eight heuristics, computational experiments were carried out. The analysis of the experimental data is presented in two perspectives. The goal of the first perspective was to evaluate the absolute quality of the solutions obtained by the proposed heuristic algorithms when compared with estimated optimal solutions. The second perspective was to compare the relative performance of the proposed heuristics. The test problems generated were designed to reflect real-world scheduling problems that we have observed in the steel-casting industry. Three important problem parameters for the test set generation are the number of jobs [n], job-priority [P], and job-family [F]. We considered 5 different levels for n, 2 different levels for P and 2 different levels for F. The test set reflects (i) the size of the jobs vary uniformly (ii) there are two batch processors and (iii) five incompatible job-families with different processing times. 15 problem instances were generated for each level of (n, P, and F). Out of many procedures available in the literature for estimating optimal value for combinatorial optimization problems, we used the procedure based on Weibull distribution as discussed in Rardin and Uzsoy (2001). For each problem instance of the randomly generated 300 problem instances, 15 feasible solutions (i.e., the average utilization of batch processors (AUBP)) were obtained using "random decision rule for first two stages and using a "best-fit heuristic' for the last stage of the scheduling problem. These 15 feasible solutions were used to estimate the optimal value. The generated 15 feasible solutions are expected to provide the estimated optimal value of the problem instance with a very high probability. Both average performance and worst-case performance of the heuristics indicated that, the heuristic algorithms A3 and A4, on the average yielded better utilization than the estimated optimal value. This indicates that the Weibull-based technique may have yielded conservative estimates of the optimal value. Further, the other heuristic algorithms found inferior solutions when compared with the estimated optimal value. But the deviations were very small. From this, we may infer that all the proposed heuristic algorithms are acceptable. The relative evaluation of heuristics was in terms of both computational effort and the quality of the solution. For the heuristics, it was clear that the computational burden is low enough on the average to run all the proposed heuristics on each problem instance and select the best solution. Also, it is observed that any algorithm from the first set of {Al, A2, A3, and A4} takes more computational time than any one from the second set {MAI, MA2, MA3, and MA4}. Regarding solution quality, the following inferences were made: ٭ In general the heuristic algorithms are sensitive to the choice of problem factors with respect to all the scheduling objectives. ٭ The three algorithms A3, MA4 and MAI are observed to be superior with respect to the scheduling objectives: maximizing average utilization of batch processors (AUBP), minimization of overall flow time (OFT) and minimizing weighted average waiting time (WAWT) respectively. Further, the heuristic algorithm MAI turns out to be the best choice if we trade-off all three objectives AUBP, OFT and WAWT. Finally we carried out simple sensitivity analyses experiments in order to understand the influence of some parameters of the scheduling on the performance of the heuristic algorithms. These were related to one at a time changes in (1) job-size distribution, (2) capacities of batch processors and (3) processing time of job-families. From the analyses it appears that there is an influence of changes in these input parameters. The results of the sensitivity analyses can be used to guide the selection of a heuristic for a particular combination of input parameters. For example, if we have to pick a single heuristic algorithm, then MAI is the best choice when considering the performance and the robustness indicated by the sensitivity analysis. In summary, this thesis examined a problem arising in the scheduling of heat-treatment operations in the steel-casting industry. This problem was abstracted to a class of deterministic batch scheduling problems. We analyzed the computational complexity of this problem and showed that it is NP-hard and therefore unlikely to admit a scalable exact method. Eight variants of a fast greedy heuristic were designed to solve the scheduling problem of interest. Extensive computational experiments were carried out to compare the performance of the heuristics with estimated optimal values (using the Weibull technique) and also for relative effectiveness and this showed that the heuristics are capable of consistently obtaining near-estimated) optimal solutions with very low computational burden for the solution of large scale problems. Finally, a comprehensive sensitivity analysis was carried out to study the influence of a few parameters, by changing them one at a time, on the performance of the heuristic algorithms. This type of analysis gives users some confidence in the robustness of the proposed heuristics.

Ο Ακέραιος Προγραμματισμός είναι κλάδος του Γραμμικού Μαθηματικού Προγραμματισμού, και αποτελεί τμήμα της συνδιαστικής βελτιστοποίησης. Στόχος της χρήσης του είναι η βελτιστοποίηση συστημάτων παραγωγής ή διοίκησης. Ο Ακέραιος Προγραμματισμός χρησιμοποιείται για την επίλυση πρακτικών προβλημάτων, όπως: • Χρονοδιαγράμματα (Scheduling) • Σχεδιασμός παραγωγής • Παράλληλη εκτέλεση εργασιών • Τηλεπικοινωνίες Μπορεί να φαίνεται ότι τα προβλήματα ακεραίου προγραμματισμού είναι εύκολο να λυθούν. Παρ’όλ’αυτά, κάτι τέτοιο δεν ισχύει, διότι οι αστρονομικά μεγάλοι ακέραιοι αριθμοί, καθώς επίσης και η στρογγυλοποίηση και αφαίρεση μη ακεραίων λύσεων από ένα πρόβλημα γραμμικού προγραμματισμού οδηγούν σε προβλήματα και λανθασμένα συμπεράσματα. Οι κυριότερες τεχνικές Ακεραίου Προγραμματισμού είναι οι εξής: • Μέθοδος κλάδου και φραγής (Branch and Bound) • Τεχνικές περιορισμού του εφικτού χώρου (Cutting Planes) • Μέθοδοι απαρίθμησης • Διαμεριστικοί αλγόριθμοι • Αλγόριθμοι βασισμένοι στη θεωρία ομάδων (Gomory) Η προπτυχιακή αυτή διπλωματική εργασία έχει στόχο να παρουσιάσει δύο από αυτές τις τεχνικές λεπτομερώς, την μέθοδο κλάδου και φραγής και τεχνικές περιορισμού του εφικτού χώρου, και να κάνει κατανοητή τη χρησιμότητα των αλγορίθμων αυτών μέσα από παραδείγματα που αφορούν προβλήματα ακέραιου προγραμματισμού. / Integer Programming is a branch of Linear Mathematical Programming, and is part of the combinatorial optimization. The purpose of using the system optimization of production or administration. The Integer Programming is used to solve practical problems, such as: • Timelines (Scheduling) • Production Design • Parallel execution of works • Telecommunications It may seem that the integer programming problems are easy to solve. However, this is not true, because the astronomically large integers, as well as rounding and removing non-integer solutions of a linear programming problem lead to problems and false conclusions. The main technical Integer Programming are: • branch and bound method (Branch and Bound) • Technical limitations of feasible region (Cutting Planes) • Methods of enumeration • Diameristikoi algorithms • Algorithms based on the theory of groups (Gomory) Undergraduate this thesis aims to present two of these techniques in detail, the branch and bound method and techniques to reduce the feasible region, and make understandable the usefulness of these algorithms through examples involving integer programming problems.

No description available.

Disertaciniame darbe išplėtota vieninga tamprių-plastinių prisitaikančių sistemų optimizavimo su stiprumo, standumo ir klumpamosios galios sąlygomis, taikant ekstreminius energinius principus, matematinio programavimo teoriją, šiuolaikines kompiuterines technologijas ir sąsajas su projektavimo standartais, metodika. Darbe parodyta, kad prisitaikomumo teorija yra bendriausias metodinis įrankis skirtas statybinių konstrukcijų skaičiavimui nuo įvairių apkrovų, įgalinantis išvengti detalios apkrovimo istorijos nagrinėjimo. Disertaciją sudaro įvadas, penkeri skyriai, rezultatų apibendrinimas, naudotos literatūros ir autoriaus publikacijų disertacijos tema sąrašai ir keturi priedai. Įvadiniame skyriuje aptariama tiriamoji problema, darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, darbo rezultatų praktinė reikšmė, ginamieji teiginiai. Įvado pabaigoje pristatomos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimų konferencijose sąrašas bei disertacijos struktūra. Pirmasis skyrius skirtas literatūros apžvalgai. Jame atlikta prisitaikančių konstrukcijų optimizavimo metodų apžvalga, išryškinta būtinybė pasitelkti sąsajas tarp teorinių optimizavimo metodų ir projektavimo standartų. Antrajame skyriuje aptariama konstrukcijų diskretizacija, sudaryti patobulinti projektinio ir patikrinamojo uždavinių matematiniai modeliai. Trečiajame skyriuje parodyta sąsaja tarp statybos inžinerijoje... [toliau žr. visą tekstą] / The optimization methodology of shakedow structures evaluating strength, stiffness and stability constraints and unifying extremum energy principles, mathematical programming theory, stat-of-the-art computer technologies and design standards was developed in the dissertation. There are shown in the work that shakedown theory is a generalized tool for calculation of civil engineering structures under different loading conditions that avoid detailed investigation of loading history. The dissertation consists of six parts including Introduction, 5 chapters, Conclusions, References and 4 Annexes. The introduction reveals the investigated problem, importance of the thesis and the object of research and describes the purpose and tasks of the paper, research methodology, scientific novelty, the practical significance of results examined in the paper and defended statements. The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made presentations in conferences and defining the structure of the dissertation. Chapter 1 revises used literature. The optimization methods of shakedown structures are reviewed and a demand of linkage between theoretical optimization methods and standards is highlighted. Chapter 2 describes the discretization of structures, the mathematical models for improved design and check problems was created. In the Chapter 3 the equivalence between load combinations of civil engineering... [to full text]

Šio darbo pagrindinis tikslas yra suprojektuoti ir realizuoti debesų kompiuterijos paslaugą internetinei matematinio programavimo ir modeliavimo sistemai, kuri galėtų pakeisti šios sistemos kompiliavimo ir vykdymo serverinę dalį. Šiam tikslui pasiekti buvo nagrinėjama debesies kompiuterijos samprata. Atlikta debesies platformų analizė bei jų palyginimas tarpusavyje. Taip pat apžvelgti debesų kompiuterijos paslaugų tipai. Identifikuojamos ir nagrinėjamos problemos kurios iškilo projektuojant ir realizuojant debesų kompiuterijos paslaugą. Sukurta debesų kompiuterijos paslauga galinti pakeisti šio metu internetinėje matematinio programavimo ir modeliavimo sistemoje naudojama kompiliavimo ir vykdymo modulį. / The purpose of this work is to develop Cloud Computing service for Online Mathematical Programming and Simulation system, which can replace currently used compilation and execution server. To achieve this goal there was analysed Cloud Computing concept. Also Cloud Computing service types were reviewed. Moreover Cloud platforms there were analysed and compared to each other. Identified and analysed problems, which were raised in development process. Also was developed Cloud Computing Service which can replace currently used compiling and execution module in Online Mathematical Programming and Simulation system.

Abstract The removal of overlying waste rock in open pit mines to dumps is conventionally undertaken by draglines or by trucks and shovels, or by a combination of these. Waste rock dumps are the largest remnant structures of open cut mining operations and can absorb a large proportion of the mine operating costs. If the dumps are not properly developed they can be excessively expensive and can become a major safety risk and environmental hazard. There are many examples worldwide where poor design and construction of waste rock dumps have resulted in failures causing considerable loss of life and widespread damage, or have resulted in erosion and seepage that have led to severe environmental pollution. The proper design and scheduling of waste rock dumps and haul routes can significantly reduce costs, minimise the possibility of failures, and avoid harming the environment. This Thesis is limited to the consideration of trucks and shovels for waste rock haulage in open cut mining operations. It describes the development and application of a waste rock dump scheduling model using the Operations Research technique of Mixed-Integer Linear Programming, implemented in the mathematical modelling language AMPL. The model focuses on minimising the haulage cost for each block of waste rock taken from the open pit and placed in the dump. Allowance is made for the selective placement of benign and reactive waste rock, based on an open pit block model that delineates benign and reactive waste rock. The formulation requires input data including the xyz-coordinates of the block model for the open pit, information on whether the waste rock blocks are benign or reactive, the proposed time scheduling of waste rock haulage from the open pit, unit haulage costs, and the geometry of the waste rock dump, including the delineation of the zones that are benign and those that are reactive. The model was successfully tested by using both simple test data and actual mine site data. The application of the model to a simple case confirmed that it produces results that meet the Objective Function in producing an optimal haulage time and cost, and meets the various Constraints imposed. This model for scheduling the removal of waste rock from open cut mining operations with trucks and shovels will require further research and testing and, because the results are generated in a numerical format, there will also be a need to convert them to a graphical format to facilitate their interpretation. Ultimately, it will have the potential to provide a relatively low-cost scheduling tool that meets operators’ economic, safety and environmental goals.

sensíveis têm requerido elevados níveis de confiabilidade dos sistemas de distribuição de energia. Em meio a este cenário, a proliferação de geradores distribuídos conectados próximos às cargas evidencia o surgimento de um novo paradigma na produção e utilização da energia elétrica. No entanto, muitos problemas decorrem do fato de que os sistemas de distribuição não foram projetados para incorporar unidades geradoras de energia. A estratégia completa de controle e proteção é definida sob o pressuposto do fluxo unidirecional de potência nos alimentadores. Um dos conflitos mais imediatos que surgem com a penetração da geração distribuída é relacionado ao sistema de proteção, resultado da alteração na magnitude das correntes de falta. Algumas consequências são a perda da sensibilidade e da coordenação da proteção. Se contornados estes problemas, a geração distribuída tem potencial para exercer impacto positivo sobre a confiabilidade, em especial no suporte ao restabelecimento da carga em situações de contingência. Tendo em vista estes fatores, a metodologia proposta adota uma perspectiva multicriterial para otimizar o desempenho dos sistemas de distribuição na presença da geração distribuída. Os indicadores SAIDI, SAIFI e MAIFI são formulados como modelos de otimização que possibilitam a adequação do sistema de proteção às condições operacionais impostas pela geração distribuída. Dentre os aspectos considerados incluem-se a alocação, a seletividade e a coordenação dos dispositivos de proteção. A alocação de chaves de manobras para reconfiguração do alimentador é a estratégia adotada para maximizar o efeito positivo da geração distribuída sobre a confiabilidade. As soluções dos modelos definem os locais de instalação dos dispositivos de proteção e manobras, e os ajustes dos religadores de forma independente para as unidades de fase e terra. A minimização simultânea dos indicadores é formulada como um problema de Programação Linear Inteira Mista por Metas, visando o balanço ótimo entre a redução das interrupções momentâneas e sustentadas nos sistemas de distribuição. Os modelos analíticos dos indicadores são solucionados utilizando um pacote de otimização de uso geral, baseado no método de Branch-and-Bound. A metodologia é avaliada a partir de um estudo de caso, considerando níveis crescentes de penetração da geração distribuída em um alimentador de distribuição real. Os modelos matemáticos são aplicados em cenários distintos de operação do sistema, associados à diferentes restrições econômicas. Os resultados possibilitam a avaliação do impacto da geração distribuída no restabelecimento e na proteção do sistema de forma independente. / The increasing automation of industrial processes and the sensitivity of electronic loads have required high levels of power distribution system’s reliability. In this scenario, the widespread use of distributed generators connected near the loads shows the emergence of a new paradigm in electric energy production and application. However, many problems arise from the fact that the distribution systems were not designed to deal with power generating units. The complete control and protection strategy is defined under the assumption of radial power flow. One of the most immediate conflicts that arise with the penetration of distributed generation is related to the protection system, a result of the change in fault currents magnitude. Some consequences are loss of protection coordination and sensitivity. By addressing these problems, distributed generation has the potential to have a positive impact on distribution reliability, especially in supporting load restoration during system’s contingencies. Considering these factors, the proposed methodology uses a multi-criteria approach to optimize the overall performance of distribution systems in the presence of distributed generation. The reliability indices SAIDI, SAIFI and MAIFI are formulated as optimization models that allow adequacy of the protection system in relation to the operating conditions imposed by distributed generation. The aspects considered include the allocation, selectivity and coordination of protective devices. The allocation of sectionalizing switches for feeder restoration is the strategy to maximize the positive impact of distributed generation on the system reliability. The model solutions provide the protective devices and switches locations, as well as reclosers’ settings for phase and ground units, independently. Reliability indices minimization is formulated as a Mixed Integer Linear Goal Programming problem, in order to establish the optimal trade-off between reducing momentary and sustained interruptions in distribution systems. The analytical models are solved using a general-use optimization package based on the Branch-and-Bound method. The methodology is evaluated through a case study considering increasing levels of distributed generation penetration on a real distribution feeder. The proposed mathematical models are applied in different scenarios of system operation and under different economic constraints. The results allow the evaluation of the impact of distributed generation on restoration and protection of the test system.

sensíveis têm requerido elevados níveis de confiabilidade dos sistemas de distribuição de energia. Em meio a este cenário, a proliferação de geradores distribuídos conectados próximos às cargas evidencia o surgimento de um novo paradigma na produção e utilização da energia elétrica. No entanto, muitos problemas decorrem do fato de que os sistemas de distribuição não foram projetados para incorporar unidades geradoras de energia. A estratégia completa de controle e proteção é definida sob o pressuposto do fluxo unidirecional de potência nos alimentadores. Um dos conflitos mais imediatos que surgem com a penetração da geração distribuída é relacionado ao sistema de proteção, resultado da alteração na magnitude das correntes de falta. Algumas consequências são a perda da sensibilidade e da coordenação da proteção. Se contornados estes problemas, a geração distribuída tem potencial para exercer impacto positivo sobre a confiabilidade, em especial no suporte ao restabelecimento da carga em situações de contingência. Tendo em vista estes fatores, a metodologia proposta adota uma perspectiva multicriterial para otimizar o desempenho dos sistemas de distribuição na presença da geração distribuída. Os indicadores SAIDI, SAIFI e MAIFI são formulados como modelos de otimização que possibilitam a adequação do sistema de proteção às condições operacionais impostas pela geração distribuída. Dentre os aspectos considerados incluem-se a alocação, a seletividade e a coordenação dos dispositivos de proteção. A alocação de chaves de manobras para reconfiguração do alimentador é a estratégia adotada para maximizar o efeito positivo da geração distribuída sobre a confiabilidade. As soluções dos modelos definem os locais de instalação dos dispositivos de proteção e manobras, e os ajustes dos religadores de forma independente para as unidades de fase e terra. A minimização simultânea dos indicadores é formulada como um problema de Programação Linear Inteira Mista por Metas, visando o balanço ótimo entre a redução das interrupções momentâneas e sustentadas nos sistemas de distribuição. Os modelos analíticos dos indicadores são solucionados utilizando um pacote de otimização de uso geral, baseado no método de Branch-and-Bound. A metodologia é avaliada a partir de um estudo de caso, considerando níveis crescentes de penetração da geração distribuída em um alimentador de distribuição real. Os modelos matemáticos são aplicados em cenários distintos de operação do sistema, associados à diferentes restrições econômicas. Os resultados possibilitam a avaliação do impacto da geração distribuída no restabelecimento e na proteção do sistema de forma independente. / The increasing automation of industrial processes and the sensitivity of electronic loads have required high levels of power distribution system’s reliability. In this scenario, the widespread use of distributed generators connected near the loads shows the emergence of a new paradigm in electric energy production and application. However, many problems arise from the fact that the distribution systems were not designed to deal with power generating units. The complete control and protection strategy is defined under the assumption of radial power flow. One of the most immediate conflicts that arise with the penetration of distributed generation is related to the protection system, a result of the change in fault currents magnitude. Some consequences are loss of protection coordination and sensitivity. By addressing these problems, distributed generation has the potential to have a positive impact on distribution reliability, especially in supporting load restoration during system’s contingencies. Considering these factors, the proposed methodology uses a multi-criteria approach to optimize the overall performance of distribution systems in the presence of distributed generation. The reliability indices SAIDI, SAIFI and MAIFI are formulated as optimization models that allow adequacy of the protection system in relation to the operating conditions imposed by distributed generation. The aspects considered include the allocation, selectivity and coordination of protective devices. The allocation of sectionalizing switches for feeder restoration is the strategy to maximize the positive impact of distributed generation on the system reliability. The model solutions provide the protective devices and switches locations, as well as reclosers’ settings for phase and ground units, independently. Reliability indices minimization is formulated as a Mixed Integer Linear Goal Programming problem, in order to establish the optimal trade-off between reducing momentary and sustained interruptions in distribution systems. The analytical models are solved using a general-use optimization package based on the Branch-and-Bound method. The methodology is evaluated through a case study considering increasing levels of distributed generation penetration on a real distribution feeder. The proposed mathematical models are applied in different scenarios of system operation and under different economic constraints. The results allow the evaluation of the impact of distributed generation on restoration and protection of the test system.