916 resultados para over-generalization and under-generalization problems
Resumo:
La programmation par contraintes est une technique puissante pour résoudre, entre autres, des problèmes d’ordonnancement de grande envergure. L’ordonnancement vise à allouer dans le temps des tâches à des ressources. Lors de son exécution, une tâche consomme une ressource à un taux constant. Généralement, on cherche à optimiser une fonction objectif telle la durée totale d’un ordonnancement. Résoudre un problème d’ordonnancement signifie trouver quand chaque tâche doit débuter et quelle ressource doit l’exécuter. La plupart des problèmes d’ordonnancement sont NP-Difficiles. Conséquemment, il n’existe aucun algorithme connu capable de les résoudre en temps polynomial. Cependant, il existe des spécialisations aux problèmes d’ordonnancement qui ne sont pas NP-Complet. Ces problèmes peuvent être résolus en temps polynomial en utilisant des algorithmes qui leur sont propres. Notre objectif est d’explorer ces algorithmes d’ordonnancement dans plusieurs contextes variés. Les techniques de filtrage ont beaucoup évolué dans les dernières années en ordonnancement basé sur les contraintes. La proéminence des algorithmes de filtrage repose sur leur habilité à réduire l’arbre de recherche en excluant les valeurs des domaines qui ne participent pas à des solutions au problème. Nous proposons des améliorations et présentons des algorithmes de filtrage plus efficaces pour résoudre des problèmes classiques d’ordonnancement. De plus, nous présentons des adaptations de techniques de filtrage pour le cas où les tâches peuvent être retardées. Nous considérons aussi différentes propriétés de problèmes industriels et résolvons plus efficacement des problèmes où le critère d’optimisation n’est pas nécessairement le moment où la dernière tâche se termine. Par exemple, nous présentons des algorithmes à temps polynomial pour le cas où la quantité de ressources fluctue dans le temps, ou quand le coût d’exécuter une tâche au temps t dépend de t.
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A multistate molecular dyad containing flavylium and viologen units was synthesized and the pH dependent thermodynamics of the network completely characterized by a variety of spectroscopic techniques such as NMR, UV-vis and stopped-flow. The flavylium cation is only stable at acidic pH values. Above pH ≈ 5 the hydration of the flavylium leads to the formation of the hemiketal followed by ring-opening tautomerization to give the cis-chalcone. Finally, this last species isomerizes to give the trans-chalcone. For the present system only the flavylium cation and the trans-chalcone species could be detected as being thermodynamically stable. The hemiketal and the cis-chalcone are kinetic intermediates with negligible concentrations at the equilibrium. All stable species of the network were found to form 1 : 1 and 2 : 1 host : guest complexes with cucurbit[7]uril (CB7) with association constants in the ranges 10(5)-10(8) M(-1) and 10(3)-10(4) M(-1), respectively. The 1 : 1 complexes were particularly interesting to devise pH responsive bistable pseudorotaxanes: at basic pH values (≈12) the flavylium cation interconverts into the deprotonated trans-chalcone in a few minutes and under these conditions the CB7 wheel was found to be located around the viologen unit. A decrease in pH to values around 1 regenerates the flavylium cation in seconds and the macrocycle is translocated to the middle of the axle. On the other hand, if the pH is decreased to 6, the deprotonated trans-chalcone is neutralized to give a metastable species that evolves to the thermodynamically stable flavylium cation in ca. 20 hours. By taking advantage of the pH-dependent kinetics of the trans-chalcone/flavylium interconversion, spatiotemporal control of the molecular organization in pseudorotaxane systems can be achieved.
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This thesis presents approximation algorithms for some NP-Hard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widely-believed complexity-theoretic assumption that P is not equal to NP, there are no efficient (i.e., polynomial-time) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an NP-Hard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing fault-tolerant networks. Two vertices u,v in a network are said to be k-edge-connected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are k-vertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning that even if a small number of edges and nodes fail, the remaining nodes will still be able to communicate. A brief description of some of our results is given below. We study the problem of building 2-vertex-connected networks that are large and have low cost. Given an n-node graph with costs on its edges and any integer k, we give an O(log n log k) approximation for the problem of finding a minimum-cost 2-vertex-connected subgraph containing at least k nodes. We also give an algorithm of similar approximation ratio for maximizing the number of nodes in a 2-vertex-connected subgraph subject to a budget constraint on the total cost of its edges. Our algorithms are based on a pruning process that, given a 2-vertex-connected graph, finds a 2-vertex-connected subgraph of any desired size and of density comparable to the input graph, where the density of a graph is the ratio of its cost to the number of vertices it contains. This pruning algorithm is simple and efficient, and is likely to find additional applications. Recent breakthroughs on vertex-connectivity have made use of algorithms for element-connectivity problems. We develop an algorithm that, given a graph with some vertices marked as terminals, significantly simplifies the graph while preserving the pairwise element-connectivity of all terminals; in fact, the resulting graph is bipartite. We believe that our simplification/reduction algorithm will be a useful tool in many settings. We illustrate its applicability by giving algorithms to find many trees that each span a given terminal set, while being disjoint on edges and non-terminal vertices; such problems have applications in VLSI design and other areas. We also use this reduction algorithm to analyze simple algorithms for single-sink network design problems with high vertex-connectivity requirements; we give an O(k log n)-approximation for the problem of k-connecting a given set of terminals to a common sink. We study similar problems in which different types of links, of varying capacities and costs, can be used to connect nodes; assuming there are economies of scale, we give algorithms to construct low-cost networks with sufficient capacity or bandwidth to simultaneously support flow from each terminal to the common sink along many vertex-disjoint paths. We further investigate capacitated network design, where edges may have arbitrary costs and capacities. Given a connectivity requirement R_uv for each pair of vertices u,v, the goal is to find a low-cost network which, for each uv, can support a flow of R_uv units of traffic between u and v. We study several special cases of this problem, giving both algorithmic and hardness results. In addition to Network Design, we consider certain Traveling Salesperson-like problems, where the goal is to find short walks that visit many distinct vertices. We give a (2 + epsilon)-approximation for Orienteering in undirected graphs, achieving the best known approximation ratio, and the first approximation algorithm for Orienteering in directed graphs. We also give improved algorithms for Orienteering with time windows, in which vertices must be visited between specified release times and deadlines, and other related problems. These problems are motivated by applications in the fields of vehicle routing, delivery and transportation of goods, and robot path planning.
Resumo:
This thesis is actually the composition of two separate studies aimed at further understanding the role of incomplete combustion products on atmospheric chemistry. The first explores the sensitivity of black carbon (BC) forcing to aerosol vertical location since BC has an increased forcing per unit mass when it is located above reflective clouds. We used a column radiative transfer model to produce globally-averaged values of normalized direct radiative forcing (NDRF) for BC over and under different types of clouds. We developed a simple column-weighting scheme based on the mass fractions of BC that are over and under clouds in measured vertical profiles. The resulting NDRF is in good agreement with global 3-D model estimates, supporting the column-weighted model as a tool for exploring uncertainties due to diversity in vertical distribution. BC above low clouds accounts for about 20% of the global burden but 50% of the forcing. We estimate maximum-minimum spread in NDRF due to modeled profiles as about 40% and uncertainty as about 25%. Models overestimate BC in the upper troposphere compared with measurements; modeled NDRF might need to be reduced by about 15%. Redistributing BC within the lowest 4 km of the atmosphere affects modeled NDRF by only about 5% and cannot account for very high forcing estimates. The second study estimated global year 2000 carbon monoxide (CO) emissions using a traditional bottom-up inventory. We applied literature-derived emission factors to a variety of fuel and technology combinations. Combining these with regional fuel use and production data we produced CO emissions estimates that were separable by sector, fuel type, technology, and region. We estimated year 2000 stationary source emissions of 685.9 Tg/yr and 885 Tg/yr if we included adopted mobile sources from EDGAR v3.2FT2000. Open/biomass burning contributed most significantly to global CO burden, while the residential sector, primarily in Asia and Africa, were the largest contributors with respect to contained combustion sources. Industry production in Asia, including brick, cement, iron and steel-making, also contributed significantly to CO emissions. Our estimates of biofuel emissions are lower than most previously published bottom-up estimates while our other fuel emissions are generally in good agreement. Our values are also universally lower than recently estimated CO emissions from models using top-down methods.
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Over the past 40 years, restorative justice (RJ) has slowly emerged as one of the most promising novelties within western contemporary penality, a relentlessly growing field of research able to inspire concrete actions within, outside or against many and diverse criminal justice systems. The Directive 2012/29/EU (i.e. Victims’ Directive) is just the last and most evident effort in this direction, with its emphasis on RJ as a victim service...
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The main theme of this thesis is the social, economic and political response of a single community to economic dislocation in the interwar years. The community under consideration is Clydebank., The thesis is divided into several parts. Part I establishes the development of the burgh and considers the physical framework of the community, mainly in the years before 1919. The town's characteristics are examined in terms of population structure and development between the world wars. In the last part of this section there is a review of the economic structure of the burgh and changes occurring in it between 1919 and 1939. In Part II consideration is given to the actual extent and form of the unemployment affecting Clydebank at this time, and comparison is made with other communities and geographic/economic areas. Attention is then focussed more narrowly on the actual individuals suffering unemployment in the burgh during the 1930s, in an attempt to personalise the experience of the unemployed. Part III reviews central and local government responses to the situation in which Clydebank found itself oetween 1919 and 1939. Central government policies discussed include unemployment insurance, public works, the Special Areas legislation, assistance in the construction of the 534 "Queen Mary" and the direction of financial support to areas of particular need. Amongst local authority actions described are additional local support for the poor, public works, efforts to attract new industry to the town, attempts to deal with the housing problem which was particularly acute at times of high unemployment and measures to maintain health standards in the community. In Part IV the responses of the community to unemployment and government policies are detailed. The burgh's commercial sector is surveyed as are developments in leisure provision, religion, temperance and crime, and local politics. A number of individual responses are also given consideration such as migration, commuting, changes in birth and marriage rates and suicide.
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This dissertation seeks to discern the impact of social housing on public health in the cities of Glasgow, Scotland and Baltimore, Maryland in the twentieth century. Additionally, this dissertation seeks to compare the impact of social housing policy implementation in both cities, to determine the efficacy of social housing as a tool of public health betterment. This is accomplished through the exposition and evaluation of the housing and health trends of both cities over the course of the latter half of the twentieth century. Both the cities of Glasgow and Baltimore had long struggled with both overcrowded slum districts and relatively unhealthy populations. Early commentators had noticed the connection between insanitary housing and poor health, and sought a solution to both of these problems. Beginning in the 1940s, housing reform advocates (self-dubbed ‘housers') pressed for the development of social housing, or municipally-controlled housing for low-income persons, to alleviate the problems of overcrowded slum dwellings in both cities. The impetus for social housing was twofold: to provide affordable housing to low-income persons and to provide housing that would facilitate healthy lives for tenants. Whether social housing achieved these goals is the crux of this dissertation. In the immediate years following the Second World War, social housing was built en masse in both cities. Social housing provided a reprieve from slum housing for both working-class Glaswegians and Baltimoreans. In Baltimore specifically, social housing provided accommodation for the city’s Black residents, who found it difficult to occupy housing in White neighbourhoods. As the years progressed, social housing developments in both cities faced unexpected problems. In Glasgow, stable tenant flight (including both middle class and skilled artisan workers)+ resulted in a concentration of poverty in the city’s housing schemes, and in Baltimore, a flight of White tenants of all income levels created a new kind of state subsidized segregated housing stock. The implementation of high-rise tower blocks in both cities, once heralded as a symbol of housing modernity, also faced increased scrutiny in the 1960s and 1970s. During the period of 1940-1980, before policy makers in the United States began to eschew social housing for subsidized private housing vouchers and community based housing associations had truly taken off in Britain, public health professionals conducted academic studies of the impact of social housing tenancy on health. Their findings provide the evidence used to assess the second objective of social housing provision, as outlined above. Put simply, while social housing units were undoubtedly better equipped than slum dwellings in both cities, the public health investigations into the impact of rehousing slum dwellers into social housing revealed that social housing was not a panacea for each city’s social and public health problems.
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Metal-organic frameworks (MOFs) have attracted significant attention during the past decade due to their high porosity, tunable structures, and controllable surface functionalities. Therefore many applications have been proposed for MOFs. All of them however are still in their infancy stage and have not yet been brought into the market place. In this thesis, the background of the MOF area is first briefly introduced. The main components and the motifs of designing MOFs are summarized, followed by their synthesis and postsynthetic modification methods. Several promising application areas of MOFs including gas storage and separation, catalysis and sensing are reviewed. The current status of commercialization of MOFs as new chemical products is also summarized. Examples of the design and synthesis of two new MOF structures Eu(4,4′,4′′,4′′′-(porphine-5,10,15,20-tetrayl)tetrakis(benzoic acid))·2H2O∙xDMF and Zn4O(azobenzene-4,4’-dicarboxylic acid)3∙xNMP are described. The first one contains free-base porphyrin centers and the second one has azobenzene components. Although the structures were synthesized as designed, unfortunately they did not possess the expected properties. The research idea to use MOFs as template materials to synthesize porous polymers is introduced. Several methods are discussed to grow PMMA into IRMOF-1 (Zn4O(benzene-1,4-dicarboxylate)3, IR stands for isoreticular) structure. High concentration of the monomers resulted in PMMA shell after MOF digestion while with low concentration of monomers no PMMA was left after digestion due to the small iii molecular weight. During the study of this chapter, Kitagawa and co-workers published several papers on the same topic, so this part of the research was terminated thereafter. Many MOFs are reported to be unstable in air due to the water molecules in air which greatly limited their applications. By incorporating a number of water repelling functional groups such as trifluoromethoxy group and methyl groups in the frameworks, the water stability of MOFs are shown to be significantly enhanced. Several MOFs inculding Banasorb-22 (Zn4O(2-trifluoromethoxybenzene-1,4-dicarboxylate)3), Banasorb-24 (Zn4O(2, 5-dimethylbenzene-1,4-dicarboxylate)3) and Banasorb-30 (Zn4O(2-methylbenzene-1,4-dicarboxylate)3) were synthesized and proved to have isostructures with IRMOF-1. Banasorb-22 was stable in boiling water steam for one week and Banasorb-30’s shelf life was over 10 months under ambient condition. For comparison, IRMOF-1’s structure collapses in air after a few hours to several days. Although MOF is a very popular research area nowadays, only a few studies have been reported on the mechanical properties of MOFs. Many of MOF’s applications involve high pressure conditions, so it is important to understand the behavior of MOFs under elivated pressures. The mechanical properties of IRMOF-1 and a new MOF structure Eu2(C12N2O4H6)3(DEF)0.87(H2O)2.13 were studied using diamond anvil cells at Advanced Photon Source. IRMOF-1 experienced an irriversible phase transtion to a nonporous phase followed by amorphization under high pressure. Eu2(C12N2O4H6)3(DEF)0.87(H2O)2.13 showed reversible compression under pressure up to 9.08GPa.
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This dissertation mainly focuses on coordinated pricing and inventory management problems, where the related background is provided in Chapter 1. Several periodic-review models are then discussed in Chapters 2,3,4 and 5, respectively. Chapter 2 analyzes a deterministic single-product model, where a price adjustment cost incurs if the current selling price is changed from the previous period. We develop exact algorithms for the problem under different conditions and find out that computation complexity varies significantly associated with the cost structure. %Moreover, our numerical study indicates that dynamic pricing strategies may outperform static pricing strategies even when price adjustment cost accounts for a significant portion of the total profit. Chapter 3 develops a single-product model in which demand of a period depends not only on the current selling price but also on past prices through the so-called reference price. Strongly polynomial time algorithms are designed for the case without no fixed ordering cost, and a heuristic is proposed for the general case together with an error bound estimation. Moreover, our illustrates through numerical studies that incorporating reference price effect into coordinated pricing and inventory models can have a significant impact on firms' profits. Chapter 4 discusses the stochastic version of the model in Chapter 3 when customers are loss averse. It extends the associated results developed in literature and proves that the reference price dependent base-stock policy is proved to be optimal under a certain conditions. Instead of dealing with specific problems, Chapter 5 establishes the preservation of supermodularity in a class of optimization problems. This property and its extensions include several existing results in the literature as special cases, and provide powerful tools as we illustrate their applications to several operations problems: the stochastic two-product model with cross-price effects, the two-stage inventory control model, and the self-financing model.
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This thesis investigates the effectiveness of Corporate Governance (CG) reforms in Pakistan. Using a sample of 160 Pakistani firms from 2003 to 2013 and governance data collected manually from the annual reports, this thesis investigates seven closely related and important corporate issues that are related to the compliance of governance rules. Specifically, it aims to : (i) investigate the degree of CG compliance with 2002 Pakistani Code of CG (PCCG); (ii) determine whether the introduction of 2002 PCCG has improved Pakistani CG practices; (iii) investigate the determinants of CG compliance and disclosure for Pakistani listed firms; (iv) test the nexus between CG compliance with the 2002 PCCG and firms’ cost of capital (COC); (v) investigate the impact of different individual CG mechanisms on listed firms COC; (vi) examine how different ownership structures impact on firms’ COC; and (vii) analyse relationship between CG structures and Cost of Equity (COE) as well as Cost of Debt (COD) for Pakistani listed firms. These empirical investigations report some important results. First, the reported findings suggest that Pakistani firms have responded positively to governance disclosure requirements over the eleven year period from 2003 to 2013. The results also show that the introduction of the PCCG in 2002 has improved CG standards by Pakistani listed firms. Second, the reported results related to the determinants of CG compliance demonstrate that significant and positive association between institutional, government and foreign ownership with CG compliance. However, findings relating to the determinants of CG compliance show a negative and significant association between board size and block ownership with CG compliance and disclosure. The study finds no significant relationship between director ownership, audit firm size and the presence of female board members with the constructed Pakistan Corporate Governance Index (PCGI). Third, the investigation on the relationship between CG and COC report a significantly negative nexus between PCGI and firms’ COC. The investigation on the association between ownership structures and COC report a negative and significant nexus between block ownership with firms’ COC. Further, a number of robustness analyses performed in this study suggest that the empirical results reported in this study are generally robust to the alternative CG variables, alternative COC variables and potential endogeneity problems.
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Background: Under nutrition is a problem of severe magnitude in low income countries like Nigeria. Adolescent school children might also be vulnerable. The dearth of data hinders planning of school health and nutrition programmes for school children. Objective: To determine the prevalence of stunting, thinness; vitamin A and iron deficiencies among adolescent students in Nsukka urban, Nigeria and to determine factors that are associated with these nutritional problems. Methods: A total of 400 participants were randomly selected from 717 students aged 12 – 18 years in 3 randomly selected secondary schools. Questionnaires, anthropometric measurements, and blood analyses were the data collection methods employed. Results: The prevalence of stunting was 33.3% and thinness 31.0%. Neither overweight nor obesity was observed. While 64.0% were anaemic; 44.0% had vitamin A deficiency (VAD). A total of 48.0% had both anaemia and stunting, 42% had VAD + thinness; while 40% had anaemia + VAD. Household income was a predictor of vitamin A status. Children from medium/ high income households had higher odds of having VAD than those from low income households (AOR=0.14; 95% CI=0.031, 0.607; P=0.009). Household income (AOR=0.12; 95% CI=0.021, 0.671; P=0.016), and age (AOR=0.09; 95% CI=0.014, 0.587; P=0.012) were independent determinants of height-for-age status. Conclusion: Among urban adolescent students in Nigeria, stunting, thinness, anaemia and VAD were problems of public health significance. Age and household monthly income played major roles.
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Safe operation of unmanned aerial vehicles (UAVs) over populated areas requires reducing the risk posed by a UAV if it crashed during its operation. We considered several types of UAV risk-based path planning problems and developed techniques for estimating the risk to third parties on the ground. The path planning problem requires making trade-offs between risk and flight time. Four optimization approaches for solving the problem were tested; a network-based approach that used a greedy algorithm to improve the original solution generated the best solutions with the least computational effort. Additionally, an approach for solving a combined design and path planning problems was developed and tested. This approach was extended to solve robust risk-based path planning problem in which uncertainty about wind conditions would affect the risk posed by a UAV.
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In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck.
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We present a general multistage stochastic mixed 0-1 problem where the uncertainty appears everywhere in the objective function, constraints matrix and right-hand-side. The uncertainty is represented by a scenario tree that can be a symmetric or a nonsymmetric one. The stochastic model is converted in a mixed 0-1 Deterministic Equivalent Model in compact representation. Due to the difficulty of the problem, the solution offered by the stochastic model has been traditionally obtained by optimizing the objective function expected value (i.e., mean) over the scenarios, usually, along a time horizon. This approach (so named risk neutral) has the inconvenience of providing a solution that ignores the variance of the objective value of the scenarios and, so, the occurrence of scenarios with an objective value below the expected one. Alternatively, we present several approaches for risk averse management, namely, a scenario immunization strategy, the optimization of the well known Value-at-Risk (VaR) and several variants of the Conditional Value-at-Risk strategies, the optimization of the expected mean minus the weighted probability of having a "bad" scenario to occur for the given solution provided by the model, the optimization of the objective function expected value subject to stochastic dominance constraints (SDC) for a set of profiles given by the pairs of threshold objective values and either bounds on the probability of not reaching the thresholds or the expected shortfall over them, and the optimization of a mixture of the VaR and SDC strategies.
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Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions.