Optimal Ordering Policies for Stochastic Inventory Problems with Observed Information Delays PDF Download

Author: Alain Bensoussan
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Information delays exist in an inventory system when it takes time to collect, process, validate, and transmit inventory/demand data. A general framework is developed in this paper to describe information flows in an inventory system with information delays. We characterize the suffcient statistics for making optimal decisions. When the ordering cost is linear, the optimality of a state-dependent base-stock policy is established even when information flows are allowed to cross over time. Additional insights into the problem are obtained via a comparison between our models and the models with stochastic order lead times. We also show that inventory can substitute for information and vice versa.

Author: Alain Bensoussan
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Information delays exist when the most recent inventory information available to the Inventory Manager (IM) is dated. In other words, the IM observes only the inventory level that belongs to an earlier period. Such situations are not uncommon, and they arise when it takes a while to process the demand data and pass the results to the IM. We introduce dynamic information delays as a Markov process into the standard multiperiod stochastic inventory problem with backorders. We develop the concept of a reference inventory position. We show that this position observed delay and the age of this observation are sufficient statistics for finding the optimal order quantities. Furthermore, we establish that the optimal ordering policy is of state-dependent base-stock type with respect to the reference inventory position (or state-dependent (s, S) type if there is a fixed ordering cost). The optimal base stock and (s, S) levels depend on the magnitude of the latest observed delay and the age of this observation. Finally, we study the sensitivity of the optimal base stock and the optimal cost with respect to the sufficient statistics.

Author: Suresh P. Sethi
Publisher: Springer Nature
ISBN: 3030917452
Category : Business & Economics
Languages : en
Pages : 520

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Book Description
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.

Author: Alain Bensoussan
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an appropriate reference inventory position, which is a sufficient statistics for finding the optimal order quantity. We show that the optimal ordering policy is of base-stock type with respect to the reference inventory position and is of (s, S) type if there is also a fixed cost of ordering.

Author: Alain Bensoussan
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Under many circumstances, demand observations are often censored due to the lack of tracking lost sales caused by stockouts. To understand the impact of the lost sales information on the ordering decisions, a periodic-review inventory model is formulated in which only the sales information is obtained immediately upon the realization of the demand. This is equivalent to observing the demand when the sales are less than the available stock and to inferring that the demand is higher than the stock when there is a stockout. Subsequently, the lost sales information is obtained after a delay. In the resulting model, an optimal policy, if exists, reveals a very complex structure. By decomposing the derivative of the value function, we demonstrate two different roles of inventory in our model: satisfying the demand and extracting the demand information. We show that the optimal inventory levels under the delayed observation of the lost sales are always higher than those for which the demands are fully observed. Moreover, as illustrated in numerical examples, the optimal policy possesses a counterintuitive behavior with respect to the problem parameters. To understand the key drivers of the optimal decisions, we further compare the costs under different demand observations. Two important observations are made. First, a lower cost is obtained when the realized demand is observed than when the demand is only observed to be higher than the inventory level, and, furthermore, the cost difference represents the value of demand information. Second, while a higher inventory level induces a more accurate demand forecast, the value of exact demand observation is not monotone in the procurement cost. Consequently, the optimal ordering quantity is not always decreasing in the procurement cost.

Author: Rajan Suri
Publisher: Taylor & Francis
ISBN: 1351170740
Category : Business & Economics
Languages : en
Pages : 383

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Book Description
POLCA (Paired-cell Overlapping Loops of Cards with Authorization) is a card-based visual control system that manages the flow of jobs through the shop floor: at each operation, it controls which job should be worked on next to meet delivery targets. POLCA ensures that upstream operations use their capacity effectively by working on jobs that are needed downstream, while at the same time preventing excessive work-in-process (WIP) build-ups when bottlenecks appear unexpectedly. POLCA is particularly suited to companies manufacturing high-mix, low-volume and customized products. Such companies struggle with long lead times, late deliveries, and daily expediting to meet delivery dates. ERP systems are not designed to deal with this highly variable environment, and add-on software such as Finite Capacity Scheduling systems can require complex installation. Also, the Kanban system does not work well with low-volume or custom production. POLCA has delivered impressive results in such environments. It does not require any complex software implementation: it can be used without an ERP system or it can seamlessly complement an existing ERP system. This book: Provides a step-by-step roadmap on how to implement POLCA; invaluable for both companies that wish to implement POLCA as well as consultants and academics advising such companies. Explains the concepts in practical and easy-to-understand terms by showing detailed shop-floor examples. Includes more than 100 illustrations for understanding how POLCA works as well as for elaborating on details of the implementation steps. Contains case studies written by company owners and executives documenting their POLCA implementation process and the results achieved in various industries in six countries.

Author: Institute for Operations Research and the Management Sciences. National Meeting
Publisher:
ISBN:
Category : Industrial management
Languages : en
Pages : 480

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Book Description

Author: Tsan-Ming Choi
Publisher: Springer Science & Business Media
ISBN: 1461476399
Category : Business & Economics
Languages : en
Pages : 281

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Book Description
The Economic Order Quantity (EOQ) inventory model first appeared in 1913, and in its centennial, it is still one of the most important inventory models. Despite the abundance of both classical and new research results, there was (until now) no comprehensive reference source that provides the state-of-the-art findings on both theoretical and applied research on the EOQ and its related models. This edited handbook puts together all these interesting works and the respective insights into an edited volume. The handbook contains papers which explore both the deterministic and the stochastic EOQ-model based problems and applications. It is organized into three parts: Part I presents three papers that provide an introduction and review of various EOQ related models. Part II includes four technical analyses on single-echelon EOQ-model based inventory problems. Part III consists of five papers on applications of the EOQ model for multi-echelon supply chain inventory analysis.

Author: Rogemar S. Mamon
Publisher: Springer Science & Business Media
ISBN: 0387711635
Category : Business & Economics
Languages : en
Pages : 203

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Book Description
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.

Author: Mr.Sunil Sharma
Publisher: INTERNATIONAL MONETARY FUND
ISBN: 9781451859300
Category : Business & Economics
Languages : en
Pages : 0

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Book Description
This paper analyzes the stochastic inventory control problem when the demand distribution is not known. In contrast to previous Bayesian inventory models, this paper adopts a non-parametric Bayesian approach in which the firm’s prior information is characterized by a Dirichlet process prior. This provides considerable freedom in the specification of prior information about demand and it permits the accommodation of fixed order costs. As information on the demand distribution accumulates, optimal history-dependent (s,S) rules are shown to converge to an (s,S) rule that is optimal when the underlying demand distribution is known.