976 resultados para location-allocation problem


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This work proposes two optimization algorithms for the solution of the Berth Allocation Problem (PAB). Due to the economic development of the country, it became necessary for the improvement of means of transport, which mainly shipping. For this, you need a better system management port, you will receive a lot of ships carrying cargo. In this work the PAB is approached so that the goals are to reduce costs and time handling in ports. For this, we applied two computational techniques, genetic algorithms and optimization for cloud particles, to obtain the best results for this problem. The results obtained with each type of algorithm are compared to conclude which method is more efficient for the port system

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Pós-graduação em Engenharia Elétrica - FEIS

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Pós-graduação em Engenharia Elétrica - FEIS

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Pós-graduação em Engenharia Elétrica - FEIS

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Pós-graduação em Engenharia Elétrica - FEIS

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Das operative Torbelegungsproblem (TBP) z. B. an einem Distributions- oder Cross-dockingzentrum ist ein logistisches Problem, bei dem es gilt, an- und abfahrende Fahrzeuge zeitlich und räumlich so auf die Warenein- und -ausgangstore zu verteilen, dass eine mög-lichst kostengünstige Abfertigung ermöglicht wird. Bisherige Arbeiten, die sich mit dem TBP beschäftigen, lassen Aspekte der Kooperation außer Acht. Dieser Beitrag stellt ein Verfahren vor, durch das der Nachteil einseitig optimaler Torbelegungen überwunden werden kann. Dabei wird auf das Mittel der kombinatorischen Auktionen zurückgegriffen und das TBP als Allokationsproblem modelliert, bei dem Frachtführer um Bündel konsekutiver Einheitszeit-intervalle an den Toren konkurrieren. Mittels eines Vickrey-Clarke-Groves-Mechanismus wird einerseits die Anreizkompatibilität, andererseits die individuelle Rationalität des Auk-tionsverfahrens sichergestellt. Das Verfahren wurde in ILOG OPL Studio 3.6.1 implemen-tiert und die durch Testdaten gewonnenen Ergebnisse zeigen, dass die Laufzeiten gering genug sind, um das Verfahren für die operative (kurzfristige) Planung einzusetzen und so transportlogistische Prozesse für alle Beteiligten wirtschaftlicher zu gestalten.

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Growth codes are a subclass of Rateless codes that have found interesting applications in data dissemination problems. Compared to other Rateless and conventional channel codes, Growth codes show improved intermediate performance which is particularly useful in applications where partial data presents some utility. In this paper, we investigate the asymptotic performance of Growth codes using the Wormald method, which was proposed for studying the Peeling Decoder of LDPC and LDGM codes. Compared to previous works, the Wormald differential equations are set on nodes' perspective which enables a numerical solution to the computation of the expected asymptotic decoding performance of Growth codes. Our framework is appropriate for any class of Rateless codes that does not include a precoding step. We further study the performance of Growth codes with moderate and large size codeblocks through simulations and we use the generalized logistic function to model the decoding probability. We then exploit the decoding probability model in an illustrative application of Growth codes to error resilient video transmission. The video transmission problem is cast as a joint source and channel rate allocation problem that is shown to be convex with respect to the channel rate. This illustrative application permits to highlight the main advantage of Growth codes, namely improved performance in the intermediate loss region.

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Advancements in cloud computing have enabled the proliferation of distributed applications, which require management and control of multiple services. However, without an efficient mechanism for scaling services in response to changing workload conditions, such as number of connected users, application performance might suffer, leading to violations of Service Level Agreements (SLA) and possible inefficient use of hardware resources. Combining dynamic application requirements with the increased use of virtualised computing resources creates a challenging resource Management context for application and cloud-infrastructure owners. In such complex environments, business entities use SLAs as a means for specifying quantitative and qualitative requirements of services. There are several challenges in running distributed enterprise applications in cloud environments, ranging from the instantiation of service VMs in the correct order using an adequate quantity of computing resources, to adapting the number of running services in response to varying external loads, such as number of users. The application owner is interested in finding the optimum amount of computing and network resources to use for ensuring that the performance requirements of all her/his applications are met. She/he is also interested in appropriately scaling the distributed services so that application performance guarantees are maintained even under dynamic workload conditions. Similarly, the infrastructure Providers are interested in optimally provisioning the virtual resources onto the available physical infrastructure so that her/his operational costs are minimized, while maximizing the performance of tenants’ applications. Motivated by the complexities associated with the management and scaling of distributed applications, while satisfying multiple objectives (related to both consumers and providers of cloud resources), this thesis proposes a cloud resource management platform able to dynamically provision and coordinate the various lifecycle actions on both virtual and physical cloud resources using semantically enriched SLAs. The system focuses on dynamic sizing (scaling) of virtual infrastructures composed of virtual machines (VM) bounded application services. We describe several algorithms for adapting the number of VMs allocated to the distributed application in response to changing workload conditions, based on SLA-defined performance guarantees. We also present a framework for dynamic composition of scaling rules for distributed service, which used benchmark-generated application Monitoring traces. We show how these scaling rules can be combined and included into semantic SLAs for controlling allocation of services. We also provide a detailed description of the multi-objective infrastructure resource allocation problem and various approaches to satisfying this problem. We present a resource management system based on a genetic algorithm, which performs allocation of virtual resources, while considering the optimization of multiple criteria. We prove that our approach significantly outperforms reactive VM-scaling algorithms as well as heuristic-based VM-allocation approaches.

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Abstract The proliferation of wireless sensor networks and the variety of envisioned applications associated with them has motivated the development of distributed algorithms for collaborative processing over networked systems. One of the applications that has attracted the attention of the researchers is that of target localization where the nodes of the network try to estimate the position of an unknown target that lies within its coverage area. Particularly challenging is the problem of estimating the target’s position when we use received signal strength indicator (RSSI) due to the nonlinear relationship between the measured signal and the true position of the target. Many of the existing approaches suffer either from high computational complexity (e.g., particle filters) or lack of accuracy. Further, many of the proposed solutions are centralized which make their application to a sensor network questionable. Depending on the application at hand and, from a practical perspective it could be convenient to find a balance between localization accuracy and complexity. Into this direction we approach the maximum likelihood location estimation problem by solving a suboptimal (and more tractable) problem. One of the main advantages of the proposed scheme is that it allows for a decentralized implementation using distributed processing tools (e.g., consensus and convex optimization) and therefore, it is very suitable to be implemented in real sensor networks. If further accuracy is needed an additional refinement step could be performed around the found solution. Under the assumption of independent noise among the nodes such local search can be done in a fully distributed way using a distributed version of the Gauss-Newton method based on consensus. Regardless of the underlying application or function of the sensor network it is al¬ways necessary to have a mechanism for data reporting. While some approaches use a special kind of nodes (called sink nodes) for data harvesting and forwarding to the outside world, there are however some scenarios where such an approach is impractical or even impossible to deploy. Further, such sink nodes become a bottleneck in terms of traffic flow and power consumption. To overcome these issues instead of using sink nodes for data reporting one could use collaborative beamforming techniques to forward directly the generated data to a base station or gateway to the outside world. In a dis-tributed environment like a sensor network nodes cooperate in order to form a virtual antenna array that can exploit the benefits of multi-antenna communications. In col-laborative beamforming nodes synchronize their phases in order to add constructively at the receiver. Some of the inconveniences associated with collaborative beamforming techniques is that there is no control over the radiation pattern since it is treated as a random quantity. This may cause interference to other coexisting systems and fast bat-tery depletion at the nodes. Since energy-efficiency is a major design issue we consider the development of a distributed collaborative beamforming scheme that maximizes the network lifetime while meeting some quality of service (QoS) requirement at the re¬ceiver side. Using local information about battery status and channel conditions we find distributed algorithms that converge to the optimal centralized beamformer. While in the first part we consider only battery depletion due to communications beamforming, we extend the model to account for more realistic scenarios by the introduction of an additional random energy consumption. It is shown how the new problem generalizes the original one and under which conditions it is easily solvable. By formulating the problem under the energy-efficiency perspective the network’s lifetime is significantly improved. Resumen La proliferación de las redes inalámbricas de sensores junto con la gran variedad de posi¬bles aplicaciones relacionadas, han motivado el desarrollo de herramientas y algoritmos necesarios para el procesado cooperativo en sistemas distribuidos. Una de las aplicaciones que suscitado mayor interés entre la comunidad científica es la de localization, donde el conjunto de nodos de la red intenta estimar la posición de un blanco localizado dentro de su área de cobertura. El problema de la localization es especialmente desafiante cuando se usan niveles de energía de la seal recibida (RSSI por sus siglas en inglés) como medida para la localization. El principal inconveniente reside en el hecho que el nivel de señal recibida no sigue una relación lineal con la posición del blanco. Muchas de las soluciones actuales al problema de localization usando RSSI se basan en complejos esquemas centralizados como filtros de partículas, mientas que en otras se basan en esquemas mucho más simples pero con menor precisión. Además, en muchos casos las estrategias son centralizadas lo que resulta poco prácticos para su implementación en redes de sensores. Desde un punto de vista práctico y de implementation, es conveniente, para ciertos escenarios y aplicaciones, el desarrollo de alternativas que ofrezcan un compromiso entre complejidad y precisión. En esta línea, en lugar de abordar directamente el problema de la estimación de la posición del blanco bajo el criterio de máxima verosimilitud, proponemos usar una formulación subóptima del problema más manejable analíticamente y que ofrece la ventaja de permitir en¬contrar la solución al problema de localization de una forma totalmente distribuida, convirtiéndola así en una solución atractiva dentro del contexto de redes inalámbricas de sensores. Para ello, se usan herramientas de procesado distribuido como los algorit¬mos de consenso y de optimización convexa en sistemas distribuidos. Para aplicaciones donde se requiera de un mayor grado de precisión se propone una estrategia que con¬siste en la optimización local de la función de verosimilitud entorno a la estimación inicialmente obtenida. Esta optimización se puede realizar de forma descentralizada usando una versión basada en consenso del método de Gauss-Newton siempre y cuando asumamos independencia de los ruidos de medida en los diferentes nodos. Independientemente de la aplicación subyacente de la red de sensores, es necesario tener un mecanismo que permita recopilar los datos provenientes de la red de sensores. Una forma de hacerlo es mediante el uso de uno o varios nodos especiales, llamados nodos “sumidero”, (sink en inglés) que actúen como centros recolectores de información y que estarán equipados con hardware adicional que les permita la interacción con el exterior de la red. La principal desventaja de esta estrategia es que dichos nodos se convierten en cuellos de botella en cuanto a tráfico y capacidad de cálculo. Como alter¬nativa se pueden usar técnicas cooperativas de conformación de haz (beamforming en inglés) de manera que el conjunto de la red puede verse como un único sistema virtual de múltiples antenas y, por tanto, que exploten los beneficios que ofrecen las comu¬nicaciones con múltiples antenas. Para ello, los distintos nodos de la red sincronizan sus transmisiones de manera que se produce una interferencia constructiva en el recep¬tor. No obstante, las actuales técnicas se basan en resultados promedios y asintóticos, cuando el número de nodos es muy grande. Para una configuración específica se pierde el control sobre el diagrama de radiación causando posibles interferencias sobre sis¬temas coexistentes o gastando más potencia de la requerida. La eficiencia energética es una cuestión capital en las redes inalámbricas de sensores ya que los nodos están equipados con baterías. Es por tanto muy importante preservar la batería evitando cambios innecesarios y el consecuente aumento de costes. Bajo estas consideraciones, se propone un esquema de conformación de haz que maximice el tiempo de vida útil de la red, entendiendo como tal el máximo tiempo que la red puede estar operativa garantizando unos requisitos de calidad de servicio (QoS por sus siglas en inglés) que permitan una decodificación fiable de la señal recibida en la estación base. Se proponen además algoritmos distribuidos que convergen a la solución centralizada. Inicialmente se considera que la única causa de consumo energético se debe a las comunicaciones con la estación base. Este modelo de consumo energético es modificado para tener en cuenta otras formas de consumo de energía derivadas de procesos inherentes al funcionamiento de la red como la adquisición y procesado de datos, las comunicaciones locales entre nodos, etc. Dicho consumo adicional de energía se modela como una variable aleatoria en cada nodo. Se cambia por tanto, a un escenario probabilístico que generaliza el caso determinista y se proporcionan condiciones bajo las cuales el problema se puede resolver de forma eficiente. Se demuestra que el tiempo de vida de la red mejora de forma significativa usando el criterio propuesto de eficiencia energética.

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El objetivo del presente trabajo es determinar la localización óptima de una planta de producción de 30.000 m3/año de bioetanol a partir de tubérculos de pataca (Helianthus tuberosus L.) cultivada en regadío, en tierras de barbecho de la Cuenca Hidrográfica del Duero (CH Duero). Inicialmente se elaboró, a partir de datos bibliográficos, un modelo de producción de pataca en base a una ecuación de regresión que relaciona datos experimentales de rendimientos de variedades tardías con variables agroclimáticas. Así se obtuvo una función de producción basada en la cantidad de agua disponible (precipitación efectiva + dosis de riego) y en la radiación global acumulada en el periodo brotación‐senescencia del cultivo. A continuación se estima la superficie potencial de cultivo de pataca en la CH Duero a partir de la superficie arable en regadío cartografiada por el Sistema de Ocupación del Suelo (SIOSE), a la cual se le aplican, en base a los requerimientos del cultivo, unas restricciones climáticas, edafológicas, topográficas y logísticas mediante el uso de Sistemas de Información Geográfica (SIG). La proporción de superficie de regadío restringida se cuantifica a escala municipal con el fin de calcular la superficie de barbecho en regadío apta para el cultivo de pataca. A partir de las bases de datos georreferenciadas de precipitación, radiación global, y la dotación de agua para el riego de cultivos no específicos establecida en el Plan Hidrológico de la Cuenca del Duero a escala comarcal, se estimó la producción potencial de tubérculos de pataca sobre la superficie de barbecho de regadío según el modelo de producción elaborado. Así, en las 53.360 ha de barbecho en regadío aptas para el cultivo de pataca se podrían producir 3,8 Mt de tubérculos al año (80 % de humedad) (761.156 t ms/año) de los que se podría obtener 304.462 m3/año de bioetanol, considerando un rendimiento en la transformación de 12,5 kg mf/l de etanol. Se estiman los costes de las labores de cultivo de pataca así como los costes de la logística de suministro a una planta de transformación considerando una distancia media de transporte de 25 km, en base a las hojas de cálculo de utilización de aperos y maquinaria agrícola oficiales del Ministerio de Agricultura, Alimentación y Medio Ambiente (MAGRAMA). Considerando el balance de costes asociados a la producción de bioetanol (costes de transformación, distribución y transporte del producto, costes estructurales de la planta, ahorro de costes por la utilización de las vinazas generadas en el proceso como fertilizante y un beneficio industrial), se ha estimado que el coste de producción de bioetanol a partir de tubérculos de pataca asciende a 61,03 c€/l. Se calculan los beneficios fiscales para el Estado por el cultivo de 5.522 ha de pataca que suministren la materia prima necesaria para una planta de bioetanol de 30.000 m3/año, en concepto de cotizaciones a la Seguridad Social de los trabajadores, impuestos sobre el valor añadido de los productos consumidos, impuesto sobre sociedades y ahorro de las prestaciones por desempleo. Se obtuvieron unos beneficios fiscales de 10,25 c€ por litro de bioetanol producido. El coste de producción de bioetanol depende del rendimiento de tubérculos por hectárea y de la distancia de transporte desde las zonas de producción de la materia prima hasta la planta. Se calculó la distancia máxima de transporte para que el precio de coste del bioetanol producido sea competitivo con el precio de mercado del bioetanol. Como resultado se determinó que el precio del bioetanol (incluido un beneficio industrial del 15%) de la planta sería igual o inferior al precio de venta en el mercado (66,35 c€/l) con una distancia máxima de transporte de 25 km y un rendimiento mínimo del cultivo de 60,1 t mf/ha. Una vez conocido el área de influencia de la planta según la distancia de transporte máxima, se determinó la localización óptima de la planta de producción de bioetanol mediante un proceso de ubicación‐asignación realizado con SIG. Para ello se analizan los puntos candidatos a la ubicación de la planta según el cumplimiento de unos requerimientos técnicos establecidos (distancia a fuentes de suministro eléctrico y de recursos hídricos, distancia a estaciones de ferrocarril, distancia a núcleos urbanos y existencia de Espacios Naturales Protegidos) que minimizan la distancia de transporte maximizando la cantidad de biomasa disponible según la producción potencial estimada anteriormente. Por último, la superficie destinada al cultivo de pataca en el área de influencia de la planta se determina en base a un patrón de distribución del cultivo alrededor de una agroindustria. Dicho patrón se ha obtenido a partir del análisis del grado de ocupación del cultivo de la remolacha en función de la distancia de transporte a la planta azucarera de Miranda de Ebro (Burgos). El patrón resultante muestra que la relación entre el grado de ocupación del suelo por el cultivo y la distancia de transporte a la planta siguen una ecuación logística. La localización óptima que se ha obtenido mediante la metodología descrita se ubica en el municipio leonés de El Burgo Ranero, donde la producción potencial de tubérculos de pataca en la superficie de barbecho situada en un radio de acción de 25 km es de 375.665 t mf/año, superando las 375.000 t mf requeridas anualmente por la planta de bioetanol. ABSTRACT Jerusalem artichoke (Helianthus tuberosus L.) is a harsh crop with a high potential for biomass production. Its main use is related to bioethanol production from the carbohydrates, inulin mainly, accumulated in its tubers at the end of the crop cycle. The aerial biomass could be used as solid biofuel to provide energy to the bioethanol production process. Therefore, Jerusalem artichoke is a promising crop as feedstock for biofuel production in order to achieve the biofuels consumption objectives established by the Government of Spain (PER 2011‐2020 and RDL 4/2013) and the European Union (Directive 2009/28/EC). This work aims at the determination of the optimal location for a 30,000 m3/year bioethanol production plant from Jerusalem artichoke tubers in the Duero river basin. With this purpose, a crop production model was developed by means of a regression equation that relates experimental yield data of late Jerusalem artichoke varieties with pedo‐climatic parameters from a bibliographic data matrix. The resulting crop production model was based on the crop water availability (including effective rainfall and irrigation water supplied) and on global radiation accumulated in the crop emergence‐senescence period. The crop potential cultivation area for Jerusalem artichoke in the Duero basin was estimated using the georeferenced irrigated arable land from the “Sistema de Ocupación del Suelo” (SIOSE) of Spain. Climatic, soil, slope and logistic restrictions were considered by means of Geographic Information Systems (GIS). The limited potential growing area was then applied to a municipality scale in order to calculate the amount of fallow land suitable for Jerusalem artichoke production. Rainfall and global radiation georeferenced layers as well as data of irrigation water supply for crop production (established within the Duero Hydrologic Plan) were use to estimate the potential production of Jerusalem artichoke tubers in the suitable fallow land according to the crop production model. As a result of this estimation, there are 53,360 ha of fallow land suitable for Jerusalem artichoke production in the Duero basin, where 3.8 M t fm/year could be produced. Considering a bioethanol processing yield of 12.5 kg mf per liter of bioethanol, the above mentioned tuber potential production could be processed in 304,462 m3/year of bioethanol. The Jerusalem crop production costs and the logistic supply costs (considering an average transport distance of 25 km) were estimated according to official agricultural machinery cost calculation sheets of the Minister of Agriculture of Spain (MAGRAMA). The bioethanol production cost from Jerusalem artichoke tubers was calculated considering bioethanol processing, transport and structural costs, industrial profits as well as plant cost savings from the use of vinasses as fertilizer. The resulting bioetanol production cost from Jerusalem artichoke tubers was 61.03 c€/l. Additionally, revenues for the state coffers regarding Social Security contributions, added value taxes of consumed raw materials, corporation tax and unemployment benefit savings due to the cultivation of 5,522 ha of Jerusalem artichoke for the 30.000 m3/year bioethanol plant supply were calculated. The calculated revenues amounted to 10.25 c€/l. Bioethanol production cost and consequently the bioethanol plant economic viability are strongly related to the crop yield as well as to road transport distance from feedstock production areas to the processing plant. The previously estimated bioethanol production cost was compared to the bioethanol market price in order to determine the maximum supply transport distance and the minimum crop yield to reach the bioethanol plant economic viability. The results showed that the proposed plant would be economically viable at a maximum transport distance of 25 km and at a crop yield not less than 60.1 t fm/ha. By means of a GIS location‐allocation analysis, the optimal bioethanol plant location was determined. Suitable candidates were detected according to several plant technical requirements (distance to power and water supply sources, distance to freight station, and distance to urban areas and to Natural Protected Areas). The optimal bioethanol plant location must minimize the supply transport distance whereas it maximizes the amount of available biomass according to the previously estimated biomass potential production. Lastly, the agricultural area around the bioethanol plant finally dedicated to Jerusalem artichoke cultivation was planned according to a crop distribution model. The crop distribution model was established from the analysis of the relation between the sugar beet (Beta vulgaris L.) cropping area and the road transport distance from the sugar processing plant of Miranda de Ebro (Burgos, North of Spain). The optimal location was situated in the municipality of ‘El Burgo Ranero’ in the province of León. The potential production of Jerusalem artichoke tubers in the fallow land within 25 km distance from the plant location was 375,665 t fm/year, which exceeds the amount of biomass yearly required by the bioethanol plant.

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The use of residual biomass for energy purposes is of great interest in isolated areas like Majorca for waste reduction, energy sufficiency and renewable energies development. In addition, densification processes lead to easy-to-automate solid biofuels which additionally have higher energy density. The present study aims at (i) the estimation of the potential of residual biomass from woody crops as well as from agri-food and wood industries in Majorca, and (ii) the analysis of the optimal location of potential pellet plants by means of a GIS approach (location-allocation analysis) and a cost evaluation of the pellets production chain. The residual biomass potential from woody crops in Majorca Island was estimated at 35,874 metric tons dry matter (t DM) per year, while the wood and agri-food industries produced annually 21,494 t DM and 2717 t DM, respectively. Thus, there would be enough resource available for the installation of 10 pellet plants of 6400 t·year−1 capacity. These plants were optimally located throughout the island of Mallorca with a maximum threshold distance of 28 km for biomass transport from the production points. Values found for the biomass cost at the pellet plant ranged between 57.1 €·t−1 and 63.4 €·t−1 for biomass transport distance of 10 and 28 km. The cost of pelleting amounted to 56.7 €·t−1; adding the concepts of business fee, pellet transport and profit margin (15%), the total cost of pelleting was estimated at 116.6 €·t−1. The present study provides a proposal for pellet production from residual woody biomass that would supply up to 2.8% of the primary energy consumed by the domestic and services sector in the Balearic Islands.

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Hearings held Jan. 26, 1956 - Feb. 5, 1960, pursuant to Senate resolution 18, 84th Cong. [and others] volume 8 has also special subtitle : The finale phase of the Committee's inquiry with reference to overall television allocations.

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The paper identifies the structural restrictions on preferences required for them to exhibit both translation homotheticity in particular direction and radial homotheticity. The results are illustrated by an application to an asset allocation problem in the absence of riskless asset.

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One of the most pressing issues facing the global conservation community is how to distribute limited resources between regions identified as priorities for biodiversity conservation(1-3). Approaches such as biodiversity hotspots(4), endemic bird areas(5) and ecoregions(6) are used by international organizations to prioritize conservation efforts globally(7). Although identifying priority regions is an important first step in solving this problem, it does not indicate how limited resources should be allocated between regions. Here we formulate how to allocate optimally conservation resources between regions identified as priorities for conservation - the 'conservation resource allocation problem'. Stochastic dynamic programming is used to find the optimal schedule of resource allocation for small problems but is intractable for large problems owing to the curse of dimensionality(8). We identify two easy- to- use and easy- to- interpret heuristics that closely approximate the optimal solution. We also show the importance of both correctly formulating the problem and using information on how investment returns change through time. Our conservation resource allocation approach can be applied at any spatial scale. We demonstrate the approach with an example of optimal resource allocation among five priority regions in Wallacea and Sundaland, the transition zone between Asia and Australasia.

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It is indisputable that printed circuit boards (PCBs) play a vital role in our daily lives. With the ever-increasing applications of PCBs, one of the crucial ways to increase a PCB manufacturer’s competitiveness in terms of operation efficiency is to minimize the production time so that the products can be introduced to the market sooner. Optimal Production Planning for PCB Assembly is the first book to focus on the optimization of the PCB assembly lines’ efficiency. This is done by: • integrating the component sequencing and the feeder arrangement problems together for both the pick-and-place machine and the chip shooter machine; • constructing mathematical models and developing an efficient and effective heuristic solution approach for the integrated problems for both types of placement machines, the line assignment problem, and the component allocation problem; and • developing a prototype of the PCB assembly planning system. The techniques proposed in Optimal Production Planning for PCB Assembly will enable process planners in the electronics manufacturing industry to improve the assembly line’s efficiency in their companies. Graduate students in operations research can familiarise themselves with the techniques and the applications of mathematical modeling after reading this advanced introduction to optimal production planning for PCB assembly.