Stochastic Inventory Control with Partial Demand Observability
Stochastic Inventory Control with Partial Demand Observability

Author: Olga L. Ortiz

Publisher:

Published: 2008

Total Pages:

ISBN-13:

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This dissertation focuses on issues associated with the value of information in models of sequential decision making under uncertainty. All of these issues are motivated by inventory management problems. First, we study the effect of the accuracy of inventory counts on system performance when using a zero-memory controller in an inventory system that is modeled as a partially observed Markov decision process (POMDP). We derive conditions for which improving the accuracy of inventory counts will either (i) improve system performance, (ii) degrade system performance or (iii) will not affect system performance. With a computational study, we determine the range of profitability impacts that result from inaccurate inventory counts when using reasonable zero-memory control policies. Second, we assess the value of demand observation quality in an inventory system with Markovian demand and lost sales. Again, the POMDP serves as a problem model, and we develop computationally tractable suboptimal algorithms to enable the computation of effective lower bounds on system profitability when demand observations are noise-corrupted. We then extend our results toconsider the effects that product substitution has on system performance. We show that systems with low demand variability, high holding cost levels, and high levels of substitution benefit more from demand bservability than systems with high demand variability, low holding cost levels, and low levels of substitution. Third, to enhance our understanding of sequential inventory control with substitutable products, we analyze a two-item inventory problem with known deterministic primary demand, but stochastic one-way substitution. We model this problem as a MDP and show that a decision rule that minimizes the single period cost function, when applied at every decision epoch over the infinite horizon, is an optimal policy for the infinite horizon problem. A definition of increased substitutability is presented, and it is shown that increased substitutability never increases optimal expected total discounted cost.

Optimal Control Theory
Optimal Control Theory

Author: Suresh P. Sethi

Publisher: Springer Nature

Published: 2022-01-03

Total Pages: 520

ISBN-13: 3030917452

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This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.

Advanced Mathematical Tools for Automatic Control Engineers: Volume 2
Advanced Mathematical Tools for Automatic Control Engineers: Volume 2

Author: Alexander S. Poznyak

Publisher: Elsevier

Published: 2009-08-13

Total Pages: 568

ISBN-13: 0080914039

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Advanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers. The book is divided into four main parts. Part I discusses the fundamentals of probability theory, covering probability spaces, random variables, mathematical expectation, inequalities, and characteristic functions. Part II addresses discrete time processes, including the concepts of random sequences, martingales, and limit theorems. Part III covers continuous time stochastic processes, namely Markov processes, stochastic integrals, and stochastic differential equations. Part IV presents applications of stochastic techniques for dynamic models and filtering, prediction, and smoothing problems. It also discusses the stochastic approximation method and the robust stochastic maximum principle. Provides comprehensive theory of matrices, real, complex and functional analysis Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications Contains worked proofs of all theorems and propositions presented

Two-sided Singular Control of an Inventory with Unknown Demand Trend
Two-sided Singular Control of an Inventory with Unknown Demand Trend

Author: Salvatore Federico

Publisher:

Published: 2021

Total Pages:

ISBN-13:

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We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly controlled in both an upward and downward direction. We first derive the equivalent separated problem under full information, with state-space components given by the Brownian motion and the filtering estimate of its unknown drift, and we then completely solve this latter problem. Our approach uses the transition amongst three different but equivalent problem formulations, links between two-dimensional bounded-variation stochastic control problems and games of optimal stopping, and probabilistic methods in combination with refined viscosity theory arguments. We show substantial regularity of (a transformed version of) the value function, we construct an optimal control rule, and we show that the free boundaries delineating (transformed) action and inaction regions are bounded globally Lipschitz continuous functions. To our knowledge this is the first time that such a problem has been solved in the literature.

Hidden Markov Models in Finance
Hidden Markov Models in Finance

Author: Rogemar S. Mamon

Publisher: Springer Science & Business Media

Published: 2007-04-26

Total Pages: 203

ISBN-13: 0387711635

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A number of methodologies have been employed to provide decision making solutions globalized markets. Hidden Markov Models in Finance offers the first systematic application of these methods to specialized financial problems: option pricing, credit risk modeling, volatility estimation and more. The book provides tools for sorting through turbulence, volatility, emotion, chaotic events – the random "noise" of financial markets – to analyze core components.