We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice to calculate optimal inventory level, would be very costly. Our algorithm uses quadratic splines to approximate the optimal cost function for this dynamic inventory problem and calculates the optimal inventory level and optimal cost.

<div>Intelligent machines, and more broadly, intelligent systems, are becoming increasingly common in the everyday lives of humans. Nonetheless, despite significant advancements in automation, human supervision and intervention are still essential in almost all sectors, ranging from manufacturing and transportation to disaster-management and healthcare. These intelligent machines<i> interact and collaborate</i> with humans in a way that demands a greater level of trust between human and machine. While a lack of trust can lead to a human's disuse of automation, over-trust can result in a human trusting a faulty autonomous system which could have negative consequences for the human. Therefore, human trust should be <i>calibrated </i>to optimize these human-machine interactions. This calibration can be achieved by designing human-aware automation that can infer human behavior and respond accordingly in real-time.</div><div><br></div><div>In this dissertation, I present a probabilistic framework to model and calibrate a human's trust and workload dynamics during his/her interaction with an intelligent decision-aid system. More specifically, I develop multiple quantitative models of human trust, ranging from a classical state-space model to a classification model based on machine learning techniques. Both models are parameterized using data collected through human-subject experiments. Thereafter, I present a probabilistic dynamic model to capture the dynamics of human trust along with human workload. This model is used to synthesize optimal control policies aimed at improving context-specific performance objectives that vary automation transparency based on human state estimation. I also analyze the coupled interactions between human trust and workload to strengthen the model framework. Finally, I validate the optimal control policies using closed-loop human subject experiments. The proposed framework provides a foundation toward widespread design and implementation of real-time adaptive automation based on human states for use in human-machine interactions.</div>

[pt] Tarifas comerciais podem ser usadas para auxiliar o Banco Central na estabilização da economia? Para responder essa pergunta construímos um modelo Novo Keynesiano de economia aberta com dois países onde as firmas têm poder de mercado suficientemente alto para definir preços diferentes para o mercado local e estrangeiro e obtemos a política monetária e tarifária ótima sob a existência de um limite inferior para a taxa nominal de juros. Fazendo um exercício numérico, analisamos duas situações: quando apenas um país se encontra em uma armadilha de liquidez e quando ambos os países se encontram presos em uma armadilha de liquidez global. Nossos resultados sugerem, que mesmo quando os dois países estão cooperando, a existência do limite inferior da taxa de juros nominal gera uma situação onde o uso ativo de tarifas comerciais pode aumentar o bem-estar da economia. / [en] Can trade tariffs be used to help the Central Bank stabilize the economic cycle? To answer that question we build a New Keynesian Open Economy model with two different countries and where firms have enough market power to set prices in both Home and Foreign markets and calculate the optimal monetary and tariff policy under the existence of a Zero Lower Bound on the nominal interest rate. We perform a numerical exercise to analyse two distinct situations: when only one country is restricted by the Zero Lower Bound and when both countries face this constraint. Our results suggest that the Zero Lower Bound creates a situation in which active use of trade tariffs can be optimal, even if countries are cooperating.