Approximate Dynamic Programming and Stochastic Approximation Methods for Inventory Control and Revenue Management - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximate Dynamic Programming and Stochastic Approximation Methods for Inventory Control and Revenue Management write by Sumit Mathew Kunnumkal. This book was released on 2007. Approximate Dynamic Programming and Stochastic Approximation Methods for Inventory Control and Revenue Management available in PDF, EPUB and Kindle.
Sequential Inventory Control and Optimization Through Stochastic Approximation
Sequential Inventory Control and Optimization Through Stochastic Approximation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sequential Inventory Control and Optimization Through Stochastic Approximation write by Thomas R. Tower. This book was released on 1972. Sequential Inventory Control and Optimization Through Stochastic Approximation available in PDF, EPUB and Kindle. Optimal inventory policies are typically characterized by a stationary post-order inventory level S, which is the level up to which an order is placed including both inventory on hand and on order. Some Inventory systems have explicit solutions presented in the literature and others have solutions characterized by dynamic programming equations. All of these solutions require a knowledge of the distribution function for demand when it is a random variable. If one has no knowledge of the distribution function one is able to formulate certain stochastic approximation techniques which 'hone-in' on the optimal policy values using observations of demands and costs as they occur. These techniques all assume convergence in the mean square and with probability one to the optimal values. (Author).
Approximate Dynamic Programming
Approximate Dynamic Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximate Dynamic Programming write by Warren B. Powell. This book was released on 2007-10-05. Approximate Dynamic Programming available in PDF, EPUB and Kindle. A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.
A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System
A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System write by Rainer Quante. This book was released on 2010. A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System available in PDF, EPUB and Kindle. In this paper, we consider a make-to-stock production system with known exogenous replenishments and multiple customer classes. The objective is to maximize profit over the planning horizon by deciding whether to accept or reject a given order, in anticipation of more profitable future orders. What distinguishes this setup from classical airline revenue management problems is the explicit consideration of past and future replenishments and the integration of inventory holding and backlogging costs. If stock is on-hand, orders can be fulfilled immediately, backlogged or rejected. In shortage situations, orders can be either rejected or backlogged to be fulfilled from future arriving supply. The described decision problem occurs in many practical settings, notably in make-to-stock production systems, in which production planning is performed on a mid-term level, based on aggregated demand forecasts. In the short term, acceptance decisions about incoming orders are then made according to stock on-hand and scheduled production quantities. We model this problem as a stochastic dynamic program and characterize its optimal policy. It turns out that the optimal fulfillment policy has a relatively simple structure and is easy to implement. We evaluate this policy numerically and find that it systematically outperforms common current fulfillment policies, such as first-come-first-served and deterministic optimization.
Approximate Dynamic Programming for Weakly Coupled Markov Decision Processes with Perfect and Imperfect Information
Approximate Dynamic Programming for Weakly Coupled Markov Decision Processes with Perfect and Imperfect Information - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximate Dynamic Programming for Weakly Coupled Markov Decision Processes with Perfect and Imperfect Information write by Mahshid Salemi Parizi. This book was released on 2018. Approximate Dynamic Programming for Weakly Coupled Markov Decision Processes with Perfect and Imperfect Information available in PDF, EPUB and Kindle. A broad range of optimization problems in applications such as healthcare operations, revenue management, telecommunications, high-performance computing, logistics and transportation, business analytics, and defense, have the following form. Heterogeneous service requests arrive dynamically and stochastically over slotted time. A request may require multiple resources to complete. The decision-maker may collect a reward on successfully completing a service request, and may also incur costs for rejecting requests or for delaying service. The decision-maker's goal is to choose how to dynamically allocate limited resources to various service requests so as to optimize a certain performance-metric. Despite the prevalence of these problems, a majority of existing research focuses only on their stylized models. While such stylized models are often insightful, several experts have commented in recent literature reviews that their applicability is limited in practice. On the other hand, more realistic models of such problems are computationally difficult to solve owing to the curse of dimensionality. The research objective of this dissertation is to build Markov decision process (MDP) models of four classes of dynamic resource allocation problems under uncertainty, and then to develop algorithms for their approximate solution. Specifically, most MDP models in this dissertation will possess the so-called weakly coupled structure. That is, the MDP is composed of several sub-MDPs; the reward is additively separable and the transition probabilities are multiplicatively separable over these sub-MDPs; and the sub-MDPs are joined only via linking constraints on the actions they choose. The dissertation proposes mathematical programming-based and simulation-based approximate dynamic programming methods for their solution. Performance of these methods is compared against one-another and against heuristic resource allocation policies. An outline of this dissertation is described below. Chapter 1 investigates a class of scheduling problems where dynamically and stochastically arriving appointment requests are either rejected or booked for future slots. A customer may cancel an appointment. A customer who does not cancel may fail to show up. The planner may overbook appointments to mitigate the detrimental effects of cancellations and no-shows. A customer needs multiple renewable resources. The system receives a reward for providing service; and incurs costs for rejecting requests, appointment delays, and overtime. Customers are heterogeneous in all problem parameters. The chapter provides a weakly coupled MDP formulation of these problems. Exact solution of this MDP is intractable. An approximate dynamic programming method rooted in Lagrangian relaxation, affine value function approximation, and constraint generation is applied to this weakly coupled MDP. This method is compared with a myopic scheduling heuristic on 1800 problem instances. These numerical experiments show that there was a statistically significant difference in the performance of the two methods in 77% of these instances. Of these statistically significant instances, the Lagrangian method outperformed the myopic method in 97% instances. Chapter 2 focuses on a class of non-preemptive scheduling problems, where a decision-maker stochastically and dynamically receives requests to work on heterogeneous projects over discrete time. The projects are comprised of precedence-constrained tasks that require multiple resources with limited availabilities. Incomplete projects are held in virtual queues with finite capacities. When a queue is full, an arriving project must be rejected. The projects differ in their stochastic arrival patterns; completion rewards; rejection, waiting and operating costs; activity-on-node networks and task durations; queue capacities; and resource requirements. The decision-maker's goal is to choose which tasks to start in each time-slot to maximize the infinite-horizon discounted expected profit. The chapter provides a weakly coupled MDP formulation of such dynamic resource-constrained project scheduling problems (DRCPSPs). Unfortunately, existing mathematical programming-based approximate dynamic programming techniques (similar to those in Chapter 1) are computationally tedious for DRCPSPs owing to their exceedingly large scale and complex combinatorial structure. Therefore, the chapter applies a simulation-based policy iteration method that uses least-squares fitting to tune the parameters of a value function approximation. The performance of this method is numerically compared against a myopic scheduling heuristic on 480 randomly generated problem instances. These numerical experiments show that the difference between the two methods statistically significant in about 60%of the instances. The approximate policy iteration method outperformed the myopic heuristic in 74% of these statistically significant instances. In Chapters 1 and 2, the decision-maker is assumed to know all parameters that describe the weakly coupled MDPs. Chapter 3 investigates an extension where the decision-maker only has imperfect information about the weakly coupled MDP. Rather than only focusing on weakly coupled MDPs that arise in specific applications as in Chapters 1 and 2, Chapter 3 works with general weakly coupled MDPs. Two different scenarios with imperfect information are studied. In the first case, the transition probabilities for each subproblem are unknown to the decision-maker. In particular, these transition probabilities are parameterized, and the decision-maker does not know the values of these parameters. The decision-maker begins with prior probabilistic beliefs about these parameters and updates these beliefs using Bayes' Theorem as the state evolution is observed. This yields a Bayes-adaptive weakly coupled MDP formulation whose exact solution is intractable. Computationally tractable approximate dynamic programing methods that combine semi-stochastic certainty equivalent control or Thompson sampling with Lagrangian relaxation are proposed. These ideas are applied to a class of dynamic stochastic resource allocation problems and numerical results are presented.In the second case, the decision-maker cannot observe the actual state of the system, but only receives a noisy signal about it. The decision-maker thus needs to probabilistically infer the actual state. This yields a partially observable weakly coupled MDP formulation whose exact solution is also intractable. Computationally tractable approximate dynamic programming methods rooted in semi-stochastic certainty equivalent control and Thompson sampling are again proposed. These ideas are applied to a restless multi-armed bandit problem and numerical results are presented. Chapter 4 investigates a class of sequential auction design problems under imperfect information. There, the resource corresponds to the seller's inventory on hand, which is to be allocated to dynamically and stochastically arriving buyers' requests (bids). In particular, the seller needs to decide lot-sizes in a sequential, multi-unit auction setting, where bidder demand and bid distributions are not known in their entirety. The chapter formulates a Bayes-adaptive MDP to study a profit maximization problem in this scenario. The number of bidders is Poisson distributed with a Gamma prior on its mean, and the bid distribution is categorical with a Dirichlet prior. The seller updates these beliefs using data collected over auctions while simultaneously making lot-sizing decisions until all inventory is depleted. Exact solution of this Bayes-adaptive MDP is intractable. The chapter proposes three approximation methods (semi-stochastic certainty equivalent control, knowledge gradient, and Thompson sampling) and compares them via numerical experiments.
