Control variation as a source of uncertainty

Orientador: João Bosco Ribeiro do ValDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho apresenta a caracterização teórica e a estratégia de controle para sistemas estocásticos em tempo discreto onde a variação da ação de controle aumenta a incerteza sobre o estado (sistemas VCAI). Este tipo de sistema possui várias aplicações práticas, como em problemas de política monetária, medicina e, de forma geral, em problemas onde um modelo dinâmico completo do sistema é complexo demais para ser conhecido. Utilizando ferramentas da análise de funções não suaves, mostra-se para um sistema VCAI multidimensional que a convexidade é uma invariante da função valor da Programação Dinâmica quando o custo por estágio é convexo. Esta estratégia indica a existência de uma região no espaço de estados onde a ação ótima de controle é de não variação (denominada região de não-variação), estando de acordo com a natureza cautelosa do controle de sistemas subdeterminados. Adicionalmente, estudou-se algoritmos para a obtenção da política ótima de controle para sistemas VCAI, com ênfase no caso mono-entrada avaliado através de uma função custo quadrática. Finalmente, os resultados obtidos foram aplicados no problema da condução da política monetária pelo Banco Central.Abstract: This dissertation presents a theoretical framework and the control strategy for discrete-time stochastic systems for which the control variations increase state uncertainty (CVIU systems). This type of system model can be useful in many practical situations, such as in monetary policy problems, medicine and biology, and, in general, in problems for which a complete dynamic model is too complex to be feasible. The optimal control strategy for a multidimensional CVIU system associated with a convex cost functional is devised using dynamic programming and tools from nonsmooth analysis. Furthermore, this strategy points to a region in the state space in which the optimal action is of no variation (the region of no variation), as expected from the cautionary nature of controlling underdetermined systems. Numerical strategies for obtaining the optimal policy in CVIU systems were developed, with focus on the single-input input case evaluated through a quadratic cost functional. These results are illustrated through a numerical example in economics.MestradoAutomaçãoMestre em Engenharia Elétric

Inventory Management in a Consumer Electronics Closed-Loop Supply Chain

The goal of this paper is to describe, model, and optimize inventory in a reverse logistics system that supports the warranty returns and replacements for a consumer electronic device. The context and motivation for this work stem from a collaboration with an industrial partner, a Fortune 100 company that sells consumer electronics. The reverse logistics system is a closed-loop supply chain: failed devices are returned for repair and refurbishing; this inventory is then used to serve warranty claims or sold through a side sales channel. Managing inventory in this system is challenging because of the short life cycle of these devices and the rapidly declining value for the inventory. We examine an inventory model that captures these dynamics. We characterize the structure of the optimal policy for this problem for stochastic demand and introduce an algorithm to calculate optimal sell-down levels. We also provide a closed-form policy for the deterministic version of the problem, and we use this policy as a certainty-equivalent approximation to the stochastic optimal policy. Finally, using numerical experiments, we analyze the sensitivity of this system to changes in various parameters, and we also evaluate the performance of the certainty-equivalent approximation using data from our industrial partner. Keywords: inventory management; closed-loop supply chains; reverse logistics; sustainabilit

Traceability Technology Adoption in Supply Chain Networks

Modern traceability technologies promise to improve supply chain management by simplifying recalls, increasing visibility, or verifying sustainable supplier practices. Initiatives developing traceability technologies - and who hope to make their technologies the industry standard - must choose the least-costly set of firms to target as early adopters. This choice is challenging because firms are part of supply chains interlinked in complex networks, yielding an inherent supply chain effect: benefits obtained from traceability are conditional on technology adoption by a (potentially large) subset of firms in a product's supply chain. We prove that the problem of selecting the least-costly set of early adopters in a supply chain network is hard to solve and even approximate within a polylogarithmic factor. Nevertheless, we provide a novel linear programming-based algorithm to identify the least-costly set of early adopters. The algorithm is fixed-parameter tractable in the supply chain network's treewidth, a parameter which we show to be low in real-world supply chain networks. The algorithm also enables us to derive easily-computable bounds on the optimal cost of selecting early adopters as well as key managerial insights about which type of firm to select

Warranty Matching in a Consumer Electronics Closed-Loop Supply Chain

Problem definition: We examine a dynamic assignment problem faced by a large wireless service provider (WSP) that is a Fortune 100 company. This company manages two warranties: (i) a customer warranty that the WSP offers its customers and (ii) an original equipment manufacturer (OEM) warranty that OEMs offer the WSP. The WSP uses devices refurbished by the OEM as replacement devices, and hence their warranty operation is a closed-loop supply chain. Depending on the assignment the WSP uses, the customer and OEM warranties might become misaligned for customer-device pairs, potentially incurring a cost for the WSP. Academic/practical relevance: We identify, model, and analyze a new dynamic assignment problem that emerges in this setting called the warranty matching problem. We introduce a new class of policies, called farsighted policies, which can perform better than myopic policies. We also propose a new heuristic assignment policy, the sampling policy, which leads to a near-optimal assignment. Our model and results are motivated by a real-world problem, and our theory-guided assignment policies can be used in practice; we validate our results using data from our industrial partner. Methodology: We formulate the problem of dynamically assigning devices to customers as a discrete-time stochastic dynamic programming problem. Because this problem suffers from the curse of dimensionality, we propose and analyze a set of reasonable classes of assignment policies. Results: The performance metric that we use for a given assignment policy is the average time that a replacement device under a customer warranty is uncovered by an OEM warranty. We show that our assignment policies reduce the average uncovered time and the expected number of out-of-OEM-warranty returns by more than 75% in comparison with our industrial partner’s current assignment policy. We also provide distribution-free bounds for the performance of a myopic assignment policy and of random assignment, which is a proxy for the WSP’s current policy. Managerial implications: Our results indicate that, in closed-loop supply chains, being completely farsighted might be better than being completely myopic. Also, policies that are effective in balancing short-term and long-term costs can be simple and effective, as illustrated by our sampling policy. We describe how the performance of myopic and farsighted policies depend on the size and length of inventory buildup

Revenue Management with Repeated Customer Interactions

Motivated by online advertising, we model and analyze a revenue management problem where a platform interacts with a set of customers over a number of periods. Unlike traditional network revenue management, which treats the interaction between platform and customers as one-shot, we consider stateful customers who can dynamically change their goodwill toward the platform depending on the quality of their past interactions. Customer goodwill further determines the amount of budget that they allocate to the platform in the future. These dynamics create a trade-off between the platform myopically maximizing short-term revenues, versus maximizing the long-term goodwill of its customers to collect higher future revenues. We identify a set of natural conditions under which myopic policies that ignore the budget dynamics are either optimal or admit parametric guarantees; such simple policies are particularly desirable since they do not require the platform to learn the parameters of each customer dynamic and only rely on data that is readily available to the platform. We also show that, if these conditions do not hold, myopic and finite look-ahead policies can perform arbitrarily poorly in this repeated setting. From an optimization perspective, this is one of a few instances where myopic policies are optimal or have parametric performance guarantees for a dynamic program with nonconvex dynamics. We extend our model to the cases where supply varies over time and where customers may not interact with the platform in every period.The research of the third author was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant

Meta-analysis of radiocesium contamination data in Japanese cedar and cypress forests over the period 2011–2017

International audienceSince Fukushima accident, dozens of field studies have been conducted in order to quantify and understand the behaviour of atmospheric radiocesium (137Cs) fallouts in contaminated forests of Fukushima and neighbouring prefectures. In this paper, we carry out a detailed review of data acquired over 2011–2017 in Japanese cedar and cypress plantations, focusing on aerial tree organs, soil layers and tree-to-soil depuration fluxes. To enable comparison and reinforce the consistency between sites, radiological measurements were normalized by the deposit and interpolated onto the same spatio-temporal frame. Despite some (poorly explained) residual variability, we derived a “mean” pattern by log-averaging data among sites. These “mean” results were analysed with the help of a simple mass-balance approach and discussed in the light of post-Fukushima literature. We demonstrated that the activity levels and dynamics in all compartments were consistent and generally well reproduced by the mass balance approach, for values of the interception fraction between 0.7 and 0.85. The analysis indicated that about 5% of the initial deposit remained in the aerial vegetation after 6 years, more than two thirds of intercepted 137Cs being transferred to the soil due to throughfall. The simulations indicated that foliar uptake might have contributed between 40% and 100% to the activity transferred to stem wood. The activity concentration in canopy organs rapidly decreased in the first few months then more slowly, according to an effective half-life of about 1.6 years. The activity level in the organic layer peaked in summer 2011 then decreased according to an effective half-life of 2.2 years. After a rapid increase in 2011, the contamination of mineral horizons continued to increase more slowly, 85% of 137Cs incoming through the organic layer being retained in the 0–5 cm layer according to a mean residence time longer than in the upper layer (7 against 1.5 years)

Bayesian inference of biomass growth characteristics for sugi (C. japonica) and hinoki (C. obtusa) forests in self-thinned and managed stands

International audienceBackground: Forests are an important sink for atmospheric carbon and could release that carbon upon deforestation and degradation. Knowing stand biomass dynamic of evergreen forests has become necessary to improve current biomass production models. The different growth processes of managed forests compared to self-managed forests imply an adaptation of biomass prediction models. Methods: In this paper we model through three models the biomass growth of two tree species (Japanese cedar, Japanese cypress) at stand level whether they are managed or not (self-thinning). One of them is named self-thinned model which uses a specific self-thinning parameter a and adapted to self-managed forests and an other model is named thinned model adapted to managed forests. The latter is compared to a Mitscherlich model. The self-thinned model takes into account the light competition between trees relying on easily observable parameters (e.g. stand density). A Bayesian inference was carried out to determine parameters values according to a large database collected. Results: In managed forest, Bayesian inference results showed obviously a lackof identifiability of Mitscherlich model parameters and a strong evidence for the thinned model in comparison to Mitscherlich model. In self-thinning forest, the results of Bayesian inference are in accordance with the self-thinning 3/2 rule (a = 1.4). Structural dependence between stand density and stand yield in self-thinned model allows to qualifying the expression of biological time as a function of physical time and better qualify growth and mortality rate. Relative mortality rate is 2.5 times more important than relative growth rate after about 40 years old. Stand density and stand yield can be expressed as function of biological time, showing that yield is independent of initial density. Conclusions: This paper addressed stand biomass dynamic models of evergreen forests in order to improve biomass growth dynamic assessment at regional scale relying on easily observable parameters. These models can be used to dynamically estimate forest biomass and more generally estimate the carbon balance and could contribute to a better understanding of climate change factors

Transfert de radionucléides dans les sols forestiers : influence de la nature de la contamination

International audienceL'accident de la centrale nucléaire de Fukushima Daiichi (FDNPP), survenu en mars 2011, a relâché dans l’environnement entre 380 et 800 PBq, dont 30% se sont répandus dans les écosystèmes terrestres japonais1. En raison de sa demi-vie (30,1 ans), le 137Cs est à ce jour le radionucléide majoritairement présent dans l’environnement. Dans ces régions montagneuses, les forêts, occupent près de 75% des territoires les plus contaminés2.Du fait de la persistance de leur niveau de contamination élevé, les forêts sont particulièrement étudiées afin de déterminer le risque de contamination secondaire des écosystèmes situés en aval par ruissellement/érosion hydriques. Après contamination des milieux forestiers, deux phases consécutives peuvent être distinguées3 : (1) une phase post-accidentelle «immédiate» d’une durée inférieure à 3 ans, caractérisée par la redistribution rapide des dépôts initiaux entre les arbres et le sol résultant des processus de dépuration (lessivage de la canopée, chute de litière, ruissellement le long des troncs) puis (2) l’atteinte d’un état « d’équilibre apparent» caractérisée par la stabilisation des transferts entre le sol et les arbres dont l’ampleur est contrôlée principalement par l’absorption racinaire. Le taux d’interception par la canopée ainsi que sa cinétique de dépuration influencent fortement la dynamique de redistribution du 137Cs dans les couches de sol et donc l’évolution de la disponibilité de cet élément pour le transfert aux espèces forestières (arbres, champignons,…). La proportion des dépôts au sol de nature liquide (pluie contaminée non interceptée, pluviolessivage) ou solide (chutes de litières) n’est pas constante dans le temps, avec une forte prédominance apports liquides juste après l’accident qui s’estompe dans le temps. Bien que ces différentes cinétiques de dépôts soient prises en compte dans les modèles4,5,6, leur disponibilité au transfert est considérée comme identique à de rares exceptions près 7,8. Or, la disponibilité aux transferts dans les sols est un paramètre clé dans la redistribution du 137Cs au sein des écosystèmes influençant fortement leur gestion à long terme. In Situ, à partir de prélèvements de sol il est impossible de distinguer le 137Cs provenant des dépôts liquides de celui provenant des dépôts solides sous forme de litières ou de leurs formes dégradées. Pour pouvoir déterminer la disponibilité aux transferts de ces différentes natures des dépôts, une expérimentation en milieu contrôlé a été réalisée. Des litières de cèdres japonais ou de chênes contaminées par du 137Cs, prélevées in situ, ou une solution contaminée en137Cs ont été mélangés à des sols, non contaminés, collectés dans les forêts de conifères et de feuillus de Fukushima. Ces mélanges ont ensuite été incubés en laboratoire pendant plus d’un an afin d’évaluer si la disponibilité environnementale du 137Cs dépendait de la nature de la contamination et évoluait dans le temps. Lors de cette étude, les capacités d’extraction du 137Cs par de l’eau et par une solution d’acétate d’ammonium (1 M) ont été déterminées à différents temps d’incubation. Les résultats montrent que la fraction de 137Cs extractible à l'eau était inférieure à 1% pour un apport liquide de 137Cs et inférieure à la limite de détection pour un apport sous forme solide. La fraction de 137Cs extractible à l’acétate d’ammonium diminuait de façon exponentielle de ≈ 55% à ≈ 30% pour l’apport sous forme liquide alors qu’aucune évolution n’était observée pour l’apport sous forme solide pour lequel seule la nature de la litière avait un impact (cèdre japonais ≈ 2% ; chêne ≈ 15%)9. Ce résultat montre clairement que la disponibilité du 137Cs dépend de la nature de la contamination et suggère que dans les écosystèmes forestiers contaminés, la fraction de 137Cs du sol provenant des dépôts humides (dépôts directs ou provenant du pluviolessivage de la canopée ou des troncs) est plus disponible que celle provenant des dépôts solides résultant des chutes de litière. Du fait de la variation dans le temps de la proportion solide/liquide des dépôts, une disponibilité plus importante du 137Cs est attendue en phase post accidentelle immédiate en comparaison de celle attendue à plus long terme. L’intégration de ces variations de disponibilité environnementale en fonction de la nature du dépôt semble donc être une piste intéressante pour raffiner les modèles de distribution du 137Cs dans les sols forestiers pour différentes échelles de temps.1. Steinhauser, G., Brandl, A. & Johnson, T. E. Comparison of the Chernobyl and Fukushima nuclear accidents: A review of the environmental impacts. Science of the Total Environment, 470–471, 800–817 (2014).2. Yoshihara, T., Matsumura, H., Hashida, S.-N. & Nagaoka, T. Radiocesium contaminations of 20 wood species and the corresponding gamma-ray dose rates around the canopies at 5 months after the Fukushima nuclear power plant accident. Journal of Environmental Radioactivity 115, 60–68 (2013).3. Calmon, P., Thiry, Y., Zibold, G., Rantavaara, A. & Fesenko, S. Transfer parameter values in temperate forest ecosystems: A review. Journal of Environmental Radioactivity 100, 757–766 (2009).4. Hashimoto, S., Matsuura, T., Nanko, K., Linkov, I., Shaw, G. and Kaneko, S. Predicted spatio-temporal dynamics of radiocesium deposited onto forests following the Fukushima nuclear accident. Scientific Reports, 3, 2564 (2013).5. Thiry, Y., Albrecht, A., Tanaka, T.Development and assessment of a simple ecological model (TRIPS) for forests contaminated by radiocesium fallout. Journal of Environmental Radioactivity, 190-191, pp. 149-159 (2018).6. Nishina, K., Hayashi, S. Modeling radionuclide Cs and C dynamics in an artificial forest ecosystem in Japan FoRothCs ver1.0, frontiers in Environmental Science, 2015-061 (2015).7. Ota, M., Nagai H., Koarashi, J. Modeling dynamics of 137Cs in forest surface environments: Application to a contaminated forest site near Fukushima and assessment of potential impacts of soil organic matter interactions, Science of The Total Environment, 551–552, 590-604 (2016).8. Gonze, M-A., Calmon, P., Hurtevent, P., Coppin, F., Nicoulaud, V., Application du modèle TREE4 au transfert de 137Cs dans les forêts de conifères à Fukushima. Rapport PSE-ENV/2018-00071 (2018).9. Teramage, M.T., Carasco, L., Orjollet, D., Coppin, F. The impact of radiocesium input forms on its extractability in Fukushima forest soils. Journal of Hazardous Materials, 349,. 205-214 (2018)