Browsing by Subject "Markov Decision Process"

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    Essays on Sharing Economy
    (2017-06) Li, Xiang
    This thesis studies the product sharing manifestation of the sharing and on-demand economy. It consists of two essays, one on peer-to-peer (P2P) product sharing and the other on business-to-consumer (B2C) product sharing. The first essay describes an equilibrium model of P2P sharing or collaborative consumption, where individuals with varying usage levels make decisions about whether or not to own a product. Owners are able to generate income from renting their products to non-owners while non-owners are able to access these products through renting on as needed basis. We characterize equilibrium outcomes, including ownership and usage levels, consumer surplus, and social welfare. We compare each outcome in systems with and without collaborative consumption. Our findings indicate that collaborative consumption can result in either lower or higher ownership and usage levels, with higher ownership and usage levels more likely when the cost of ownership is high. Our findings also indicate that consumers always benefit from collaborative consumption, with individuals who, in the absence of collaborative consumption, are indifferent between owning and not owning benefitting the most. We study both profit maximizing and social welfare maximizing platforms and compare equilibrium outcomes under both in terms of ownership, usage, and social welfare. We find that a not-for-profit platform would always charge a lower price and, therefore, lead to lower ownership and usage than a for-profit platform. We also examine the robustness of our results by considering several extensions to our model. The second essay characterizes the optimal inventory repositioning policy for a class of B2C product sharing networks. We consider a B2C product sharing network with a fixed number of rental units distributed across multiple locations. The units are accessed by customers without prior reservation and on an on-demand basis. Customers are provided with the flexibility to decide on how long to keep a unit and where to return it. Because of the randomness in demand, rental periods and return locations, there is a need to periodically reposition inventory away from some locations and into others. In deciding on how much inventory to reposition and where, the system manager balances potential lost sales with repositioning costs. We formulate the problem into a Markov decision process and show that the problem in each period is one that involves solving a convex optimization problem. The optimal policy in each period can be described in terms of a well-specified region over the state space. Within this region, it is optimal not to reposition any inventory while, outside the region, it is optimal to reposition some inventory but only such that the system moves to a new state that is on the boundary of the no-repositioning region. We provide a simple check for when a state is in the no-repositioning region, which also allows us to compute the optimal policy more efficiently.
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    A Heterogeneous Markov Chain Model to Predict Pavement Deterioration and Optimize Repair Activities
    (2021-12) Matias de Oliveira, Jhenyffer Lorrany
    In an era where system needs exceed available funding across all infrastructure components, planners and decision makers need tools to make informed decisions about the value of assets, such as accurate models to predict pavement condition over time. This prediction is essential in pavement management systems (PMS) because it provides information that allows forecasting repair demands and optimizing life-cycle costs. Markov Chains have been proposed in the past as a tool for forecasting pavement performance and deterioration. A weakness of the traditional Markov Chain is that the conventional transition matrix has limited ability to account for site-specific variability. To address this problem, this dissertation proposes a combination of ordinal logistic regression and Markov Chains. The logistic regression models were found to bring two major improvements to the Markov model. First, the enhanced Markov transition probability matrix allows for site specific predictions because the models use specific characteristics of each pavement section. Second, the enhanced matrix offers additional benefits by allowing the comparison of several factors and the analysis of how each of them influences the pavement performance and deterioration, as well as providing an understanding of the interaction between these several external factors, such as district location, repair history, functional class, base thickness, speed limit and pavement thickness. Numerical examples are provided to demonstrate how the Markov Transition Matrix can be used to model future pavement deterioration. The final Markov probability matrix was also used to determine an optimal sequence of pavement repair activities.