<p> The optimal temperature policy with time is sought which maximizes the total amount of reaction in a fixed time in a tubular reactor with uniform temperature and decaying catalyst for a single reversible reaction.</p> <p> A numerical procedure together with theoretical developments is used to solve this problem for two kinetic models. The problem is treated in the format of Pontryagin's Maximum Principle.</p> <p> Computer listings are given in the Appendix for the following cases A) Optimal policy for irreversible reactions 8) Optimal policy for isothermal irreversible reactions C) Optimal policy for reversible reactions.</p> / Thesis / Master of Engineering (MEngr)

This thesis is of the three article format. All three articles contribute to the literature on optimal fiscal policy with exogeneous government expenditures and distortionary taxation following Lucas and Stokey (1983) and Aiyagari et al. (2002) (AMSS). The first article extends the framework of AMSS by modelling agents ex ante heterogeneous in deterministic labour productivity trends in an infinite-horizon production economy with incomplete markets. The government does not use transfers. When the productivities of different agents grow at different rates, there is a conflict over the timing of tax collection. This is explored in a two-period model. The infinite-horizon model with two agents (‘lowskilled’ and ‘high-skilled’) is used to quantitatively analyse the impact of productivity trends observed in recent decades on the optimal policy. The impact is significant. The model can contribute to explaining the increase in government debt in many advanced economies in recent decades. The optimal policy strongly depends on Pareto weights but welfare of the agents does not. Political economics implications are discussed. The second article analyses the impact of heterogeneous productivity trends on the optimal policy when the social planner can use transfers. There is now conflict over the timing and the level of taxation, and it is explored in a two-period model. The optimal policy is studied in the same environment as in the first article. For most Pareto weights, the change in the tax rate is less pronounced than in the model without transfers, but still greater than the expected change due to shocks. The optimal policy and the welfare of the agents strongly depend on Pareto weights. Policy implications are discussed. The optimal policy in the horizon of decades is significantly affected by even a modest heterogeneity in the growth rates of the agents. Solution methods common to all three articles are discussed. In the third article the closed economy model of AMSS is extended into an open economy setting with two countries. The government of each country finances its exogeneous stochastic expenditures by distortionary labour taxation, and issues one-period bonds. The Ramsey planner chooses policy for both countries, and a no-arbitrage condition on the return of bonds of the two countries restricts her choices. The optimal policy is quantitatively studied in a calibrated model with ex-ante identical countries and equal Pareto weights, and three settings are compared in terms of policy and welfare: autarky (closed economy), partial union (international borrowing allowed), and full union (transfers between governments allowed).

De nombreux retours de produits dus au recyclage et à la réutilisation des déchets se développent dans le but de préserver les ressources naturelles limitées de notre planète. Ces nouveaux flux interagissant avec les flux de production traditionnels, il est important de les piloter de façon à satisfaire au mieux les demandes des clients et minimiser l'encours dans la chaîne logistique. Nos travaux s'inscrivent dans cette démarche. Nous nous plaçons dans un contexte où la capacité de production est limitée et nous considérons un problème opérationnel de gestion des stocks et de la production intégrant des flux de retours. Nous modélisons trois problèmes de production et de stockage à temps continu, avec des capacités de production limitées, des délais aléatoires et des coûts linéaires. Le premier prenant en compte la probabilité qu'un produit puisse être réutilisé comme produit fini ou seulement comme produit semi-fini (par partie), le deuxième présentant un problème où la réutilisation d'un retour comme produit fini nécessite une étape de remise à neuf et le troisième modélisant un système où les clients préviennent à l'avance du renvoi potentiel de leurs produits. Outre la caractérisation des politiques optimales de gestion, une part importante de nos contributions réside dans l'évaluation des performances de différentes politiques heuristiques et l'étude de l'impact de la capacité de production sur celles-ci. Enfin, nous nous servons dans tout ce document d'outils permettant la caractérisation des politiques optimales. La dernière partie de ce document vise à développer ces outils et à permettre l'étude de l'effet des paramètres d'un système formulé en processus de décision Markovien sur la politique optimale de celui-ci. / Flows of returns due to recycling and reusing waste are developing in order to preserve the limited natural resources of our planet. These new flows interact with the traditional production flows. Therefore, in order to provide customers with the best service level and minimize the stock in the supply chain, the control of the return flows appears to be of highest importance. We address this problem by modeling a situation with a limited porduction capacity and we consider an operational production/inventory problem that incorporates flows of returns. We model three continuous-time production/inventory problems with limited produc- tion capacities, random lead times, and linear costs. In the first problem we take into account the probability that a product can be reused as a finished product or only as semi-finished product (by parts), in the second problem we include a step of remanufac- turing before reusing the returned product, and in the third problem we consider a system with product returns that are announced in advance by the customers. Apart from the caracterization of the optimal policies for these cases, the performance assessments of some heuristic policies and the study of the poduction capacity effect on these heuristic policies stand as main contributions. Throughout this work we have used existing tools to characterize optimal policies for different Markov decision processes. The last chapter aims to improve these tools and enable us to study the influence of several system parameters on its optimal policy.

This thesis is divided into two main parts. The first provides a novel analysis of dynamic optimal taxation under the assumption that individuals in an economy have ‘hidden’ idiosyncratic productivity levels. Specifically, it shows how to derive a complete set of optimality conditions characterising the solution to a problem of this kind. The method relies on constructing perturbations to the consumption-output allocations of agents in a manner that preserves all relevant incentive compatibility restrictions. We are able to use it to generalise the ‘inverse Euler condition’ to cases in which preferences are non-separable between consumption and labour supply, and to prove a number of novel results about optimal income and savings tax wedges. The second main part investigates a more general problem. When policymakers are constrained in their present choices by expectations of future outcomes a well-known time-inconsistency problem hinders optimal decision-making: the preferences of policymakers who exist at different points in time are not in agreement with one another, because of differences in the constraints faced by each. We present a new approach to determining policy in this setting, based on asking: What policy would be chosen by a decisionmaker who did not know the time period in which their choice was to be implemented? This is akin to designing institutions from behind a Rawlsian ‘veil of ignorance’. The theory is used to obtain qualitative policy prescriptions across a number of environments; these policies have several appealing properties that we outline.

Thesis advisor: Fabio Ghironi / My dissertation develops a set of tools for introducing heterogeneity into economic models in an analytically tractable way. Many models use the representative agent framework, which greatly simplifies macroeconomic aggregation but abstracts from the heterogeneity we see in the real world. In my research, I move away from the representative agent framework in two key ways. First, my work in international macroeconomics incorporates heterogeneity via idiosyncratic shocks across countries. Second, my work on financial frictions employs asymmetric information between lenders and borrowers. In both of these areas, my goal is to examine the implications of heterogeneity in the most tractable way possible. Crucially, these insights can be incorporated into the models currently used by academics and central banks for policy analysis. The first chapter of my dissertation, "Price Stability in Small Open Economies," joint work with Mikhail Dmitriev, studies the conduct of optimal monetary policy in a continuum of small open economies. We obtain a novel closed-form solution that does not restrict the elasticity of substitution between home and foreign goods to one. Using this global closed-form solution, we give an exact characterization of optimal monetary policy and welfare with and without international policy cooperation. We consider the cases of internationally complete asset markets and financial autarky, producer currency pricing and local currency pricing. Under producer currency pricing, it is always optimal to mimic the flexible-price equilibrium through a policy of price stability. Under local currency pricing, policy should fix the exchange rate. Even though countries have monopoly power, the continuum of small open economies implies that policymakers cannot affect world income. This inability to influence world income removes the incentive to deviate from price stability under producer currency pricing or a fixed exchange rate under local currency pricing, and prevents gains from international monetary cooperation in all cases examined. Our results contrast with those for large open economies, where interactions between home policy and world income drive optimal policy away from price stability or fixed exchange rates, and gains from cooperation are present. The second chapter of my dissertation, "The Optimal Design of a Fiscal Union'', joint work with Mikhail Dmitriev, examines the role of fiscal policy cooperation and financial market integration in an open economy setting, motivated by the recent crisis in the euro area. I show that the optimal design of a fiscal union is governed by the degree of substitutability between the export goods of different countries. When countries produce goods that are imperfect substitutes they should harmonize their income taxes to prevent large terms of trade externalities. On the other hand, when countries produce goods that are close substitutes, they should organize a contingent fiscal transfer scheme to insure against idiosyncratic shocks. The welfare gains from the optimal fiscal union are as high as 5\% of permanent consumption when countries are able to trade safe government bonds, and approach 20\% of permanent consumption when countries lose access to international financial markets. These gains are especially large for countries like Greece that produce highly substitutable export goods and who cannot raise funds on international financial markets to insure against downside risk. The results illustrate why federal currency unions such as the U.S., Canada and Australia, with income tax harmonization and built-in fiscal transfer arrangements, withstand asymmetric shocks across regions much better than the euro area, which lacks these ingredients at the moment. The third chapter of my dissertation, joint work with Mikhail Dmitriev, studies macro-financial linkages and the impact of financial frictions on real economic activity in some of my other work. Beginning with the Bernanke-Gertler-Gilchrist (1999) financial accelerator model, a large literature has shown that financial frictions amplify business cycles. Using this framework, Christiano, Motto and Rostagno (AER, 2013) show that shocks to financial frictions can explain business cycle fluctuations quite well. However, this literature relies on two ad hoc assumptions. When these assumptions are relaxed and agents have access to a broader set of lending contracts, the financial accelerator disappears, and shocks to financial frictions have little to no impact on the economy. In addition, under the ad hoc lending contract inflation targeting eliminates the financial accelerator. These results provide guidance for monetary policymakers and present a puzzle for macroeconomic theory. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

The average cost of operating a queueing network depends on several factors such as the complexity of the network and the service policy used. Approximate linear programming (ALP) is a method that can be used to compute an accurate lower bound on the optimal average cost as well as generate policies to be used in operating the network. These average cost solutions and policies are dependent on the type of basis function used in the ALP. In this paper, the ALP average cost solutions and policies are analyzed for twelve networks with four different types of basis functions (quadratic, linear, pure exponential, and mixed exponential). An approximate bound on the optimality gap between the ALP average cost solution and the optimal average cost solution is computed for each system, and the size of this bound is determined relative to the ALP average cost solution. Using the same set of networks, the performance of ALP generated policies are compared to the performance of the heuristic policies first-buffer-first-served (FBFS), last-buffer-first-served (LBFS), highest-queue-first-served (HQFS), and random-queue-first-served (RQFS). In general, ALP generated average cost solutions are considerably smaller than the simulated average cost under the corresponding policy, and therefore the approximate bounds on the optimality gaps are quite large. This bound increases with the complexity of the queueing network. Some ALP generated policies are not stabilizing policies for their corresponding networks, especially those produced using pure exponential and mixed exponential basis functions. For almost all systems, at least one of the heuristic policies results in mean average cost less than or nearly equal to the smallest mean average cost of all ALP generated policies in simulation runs. This means that generally there exists a heuristic policy which can perform as well as or better than any ALP generated policy. In conclusion, a useful bound on the optimality gap between the ALP average cost solution and the optimal average cost solution cannot be computed with this method. Further, heuristic policies, which are more computationally tractable than ALP generated policies, can generally match or exceed the performance of ALP generated policies, and thus computing such policies is often unnecessary for realizing cost benefits in queueing networks. / text

This dissertation includes three chapters. The first chapter studies the question of whether countries with different fiscal capacity should optimally have different ex-ante minimum bank capital requirements. In an environment with endogenously incomplete markets and overinvestment because of moral hazard and pecuniary externalities, I show that countries with larger fiscal capacity should have lower minimum ex-ante bank capital requirements. I also show that, in addition to the minimum capital requirement, regulators in countries with a concentrated financial sector and large fiscal capacity (which are also countries with strong moral hazard) should impose a limit on the amount of liquidity pledged by financial institutions in a crisis state (for example, restrict the amount of put options/CDS contracts sold by financial institutions). The second chapter studies the welfare implications of a concentrated, imperfectly competitive banking sector, which faces a bank net worth constraint in a small open economy (SOE) environment. There are two standard sources of inefficiency --- pecuniary externalities, which lead to overinvestment, and a standard monopolistic underinvestment force. I show that the optimal policy instruments include subsidies on firm borrowing costs in certain periods and capital account controls in others, which is a good proxy for the behavior of emerging markets. For every country, there exists a financial sector with a particular banking sector concentration, for which the inefficiencies offset each other and no government intervention is required in some periods. Furthermore, this paper documents a novel theoretical result --- the interaction between future binding bank net worth constraints and dynamic (future) underinvestment could lead to ex-ante overinvestment even in economies with a single monopolistic bank where there are no pecuniary externalities. The last third chapter, which is coauthored with Kenneth Rogoff, evaluates a new class of exchange rate forecasting studies, which claim that structural models are getting closer to being able to forecast exchange rates at short horizons. We argue that misinterpretation of some new out-of-sample tests for nested models, over-reliance on asymptotic test statistics, and failure to sufficiently check robustness to alternative time windows have led many studies to overstate even the relatively thin positive results that have been found. / Economics

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / The present research seeks to show the importance of applying process management techniques and food safety norms in the operational processes of the supply chain to know the meaning and the need for an integrated hybrid model. The article reviews the sugarcane distillery sector of Peru and its main operational problems. Based on the literature reviewed and discussed with academics who have knowledge of the food supply chain, an integrated hybrid model was developed to help any distillery with lower levels of competitiveness than its competitors in other sectors, such as pisco, applying techniques of process management and food safety to increase the efficiency of liquor distilleries. The findings confirm that distilleries can increase their efficiency, thanks to the higher performance of their operations after their alignment with the integrated model. / Revisión por pares

Inventory management and production control problem of a dealer operating in a decentralized spare parts network is analyzed in this dissertation. Spare parts network is assumed to be formed of two dealers and the problem of a dealer is considered under the assumption that the other dealer has a known policy. These dealers collaborate through inventory and service pooling. Furthermore, the dealers collaborate through sharing information on the net inventory status. Upon demand arrival, a dealer may request a part from the other dealer, in which case a payment is made. Under this competitive and collaborative environment, the optimal operating policy of an individual dealer is characterized under full information. Through computational analysis, the conditions under which the dealer under consideration is most profitable are identified. Finally, by comparing dierent pooling strategies and several information availability levels, the benefit of information sharing is quantified.

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