Dynamic Pricing And Inventory Control With Fixed Ordering Cost And Incomplete Demand Information

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Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information

Author : Boxiao Chen
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information by : Boxiao Chen

Download or read book Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information written by Boxiao Chen and published by . This book was released on 2020 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the periodic review dynamic pricing and inventory control problem with fixed ordering cost. Demand is random and price dependent, and unsatisfied demand is backlogged. With complete demand information, the celebrated (s,S,p) policy is proved to be optimal, where s and S are the reorder point and order-up-to level for ordering strategy, and p, a function of on-hand inventory level, characterizes the pricing strategy. In this paper, we consider incomplete demand information and develop online learning algorithms whose average profit approaches that of the optimal (s,S,p) with a tight O ̃(√T) regret rate. A number of salient features differentiate our work from the existing online learning researches in the OM literature. First, computing the optimal (s,S,p) policy requires solving a dynamic programming (DP) over multiple periods involving unknown quantities, which is different from the majority of learning problems in operations management that only require solving single-period optimization questions. It is hence challenging to establish stability results through DP recursions, which we accomplish by proving uniform convergence of the profit-to-go function. The necessity of analyzing action-dependent state transition over multiple periods resembles the reinforcement learning question, considerably more difficult than existing bandit learning algorithms. Second, the pricing function p is of infinite dimension, and approaching it is much more challenging than approaching a finite number of parameters as seen in existing researches. The demand-price relationship is estimated based on upper confidence bound, but the confidence interval cannot be explicitly calculated due to the complexity of the DP recursion. Finally, due to the multi-period nature of (s,S,p) policies the actual distribution of the randomness in demand plays an important role in determining the optimal pricing strategy p, which is unknown to the learner a priori. In this paper, the demand randomness is approximated by an empirical distribution constructed using dependent samples, and a novel Wasserstein metric based argument is employed to prove convergence of the empirical distribution.

Dynamic Pricing With Infrequent Inventory Replenishments

Author : Boxiao Chen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Dynamic Pricing With Infrequent Inventory Replenishments by : Boxiao Chen

Download or read book Dynamic Pricing With Infrequent Inventory Replenishments written by Boxiao Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a joint pricing and inventory control problem where pricing can be adjusted more frequently, such as every period, than inventory ordering decisions, which are made every epoch that consists of multiple periods. This is motivated by many examples, especially for online retailers, where price is indeed much easier to change than inventory level, because changing the latter is subject to logistic and capacity constraints. In this setting, the retailer determines the inventory level at the beginning of each epoch and solves a dynamic pricing problem within each epoch with no further replenishment opportunities. The optimal pricing and inventory control policy is characterized by an intricate dynamic programming (DP) solution. We consider the situation where the demand-price function and the distribution of random demand noise are both unknown to the retailer, and the retailer needs to develop an online learning algorithm to learn those information and at the same time maximize total profit. We propose a learning algorithm based on least squares estimation and construction of an empirical noise distribution under a UCB framework and prove that the algorithm converges through the DP recursions to approach the optimal pricing and inventory control policy under complete demand information. The theoretical lower bound for convergence rate of a learning algorithm is proved based on the multivariate Van Trees inequality coupled with some structural DP analyses, and we show that the upper bound of our algorithm's convergence rate matches the theoretical lower bound.

Joint Pricing and Inventory Control with a Markovian Demand Model

Author : Rui Yin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Joint Pricing and Inventory Control with a Markovian Demand Model by : Rui Yin

Download or read book Joint Pricing and Inventory Control with a Markovian Demand Model written by Rui Yin and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the joint pricing and inventory control problem for a single product with a finite horizon and periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders and also incorporate capacity and service level constraints. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing strategies through numerical examples. The results indicate that it is more beneficial to implement the dynamic pricing strategy in a Markovian demand environment with a high fixed ordering cost or with high demand uncertainty.

Optimal Pricing and Inventory Control Policy in Periodic-Review Systems with Fixed Ordering Cost and Lost Sales

Author : Frank Chen
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Optimal Pricing and Inventory Control Policy in Periodic-Review Systems with Fixed Ordering Cost and Lost Sales by : Frank Chen

Download or read book Optimal Pricing and Inventory Control Policy in Periodic-Review Systems with Fixed Ordering Cost and Lost Sales written by Frank Chen and published by . This book was released on 2007 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies a periodic-review pricing and inventory control problem for a retailer, which faces stochastic price-sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s, S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty.

The Elements of Joint Learning and Optimization in Operations Management

Author : Xi Chen
Publisher : Springer Nature
ISBN 13 : 3031019261
Total Pages : 444 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Elements of Joint Learning and Optimization in Operations Management by : Xi Chen

Download or read book The Elements of Joint Learning and Optimization in Operations Management written by Xi Chen and published by Springer Nature. This book was released on 2022-09-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines recent developments in Operations Management, and focuses on four major application areas: dynamic pricing, assortment optimization, supply chain and inventory management, and healthcare operations. Data-driven optimization in which real-time input of data is being used to simultaneously learn the (true) underlying model of a system and optimize its performance, is becoming increasingly important in the last few years, especially with the rise of Big Data.

Integrating Dynamic Pricing and Inventory Control for Fresh-Agri Product Under Consumer Choice

Author : Hawking Wang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Integrating Dynamic Pricing and Inventory Control for Fresh-Agri Product Under Consumer Choice by : Hawking Wang

Download or read book Integrating Dynamic Pricing and Inventory Control for Fresh-Agri Product Under Consumer Choice written by Hawking Wang and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh-agri products (FAPs) with two-period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period, the retailer makes ordering decision for new FAP and sets regular and discount prices for new and old inventories, respectively. After demand realisation, the expired leftover is disposed and unexpired inventory is carried to the next period, for continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximise the total expected discount profit over the whole planning horizon. We present a price dependent, stochastic dynamic programming model taking into account zero lead-time, linear ordering costs, inventory holding and backlogging costs, as well as disposal cost. As the influence of the perishability, each customer selects his preferred choice based on the utility of product price and quality. By the way of constructing demand rate vector, the original formulation can be transferred to be jointly concave and tractable. Finally, we characterise the optimal policy and develop effective methods to solve the problem. We also conduct numerical studies to further characterise the optimal policy, and to evaluate the loss of efficiency under static policies when compared to the optimal dynamic policy.

Inventory Control

Author : Dieter Bartmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642871461
Total Pages : 271 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Inventory Control by : Dieter Bartmann

Download or read book Inventory Control written by Dieter Bartmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experts in operations research and developers of software application systems have been treading separate paths for many years. It is urgently necessary to reset this course so that the demanding requirements of variousCIM concepts can be realized. This is specially relevant for computer-based stock management. Both authors, with a number of years of practical experience behind them, have written this book with this objective in mind. The book shows how modern inventory control can be rationally structured with the help of OR. Two aspects are given importance:1) the necessary mathematical derivations are completely explained in detail so that the reader will be able to optimally handle a given situation with the help of the methods learned in this book, and 2) aside from the models, strong emphasis is given on numerical methods. Suitable algorithms are thoroughly explained for the more important cases.

Optimal Policies for Dynamic Pricing and Inventory Control with Nonparametric Censored Demands

Author : Boxiao Chen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Optimal Policies for Dynamic Pricing and Inventory Control with Nonparametric Censored Demands by : Boxiao Chen

Download or read book Optimal Policies for Dynamic Pricing and Inventory Control with Nonparametric Censored Demands written by Boxiao Chen and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the fundamental model in joint pricing and inventory replenishment control under the learning-while-doing framework, with T consecutive review periods and the firm not knowing the demand curve a priori. At the beginning of each period, the retailer makes both a price decision and an inventory order-up-to level decision, and collects revenues from consumers' realized demands while suffering costs from either holding unsold inventory items, or lost sales from unsatisfied customer demands. We make the following contributions to this fundamental problem as follows:1. We propose a novel inversion method based on empirical measures to consistently estimate the difference of the instantaneous reward functions at two prices, directly tackling the fundamental challenge brought by censored demands, without raising the order-up-to levels to unnaturally high levels to collect more demand information. Based on this technical innovation, we design bisection and trisection search methods that attain an O(T^{1/2}) regret, assuming the reward function is concave and only twice continuously differentiable.2. In the more general case of non-concave reward functions, we design an active tournament elimination method that attains O(T^{3/5}) regret, based also on the technical innovation of consistent estimates of reward differences at two prices.3. We complement the O(T^{3/5}) regret upper bound with a matching Omega(T^{3/5}) regret lower bound. The lower bound is established by a novel information-theoretical argument based on generalized squared Hellinger distance, which is significantly different from conventional arguments that are based on Kullback-Leibler divergence. This lower bound shows that no learning-while-doing algorithm could achieve O(T^{1/2}) regret without assuming the reward function is concave, even if the sales revenue as a function of demand rate or price is concave.Both the upper bound technique based on the "difference estimator" and the lower bound technique based on generalized Hellinger distance are new in the literature, and can be potentially applied to solve other inventory or censored demand type problems that involve learning.

Dynamic Pricing and Inventory Control

Author : Elodie Adida
Publisher : VDM Publishing
ISBN 13 : 9783836421430
Total Pages : 288 pages
Book Rating : 4.4/5 (214 download)

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Book Synopsis Dynamic Pricing and Inventory Control by : Elodie Adida

Download or read book Dynamic Pricing and Inventory Control written by Elodie Adida and published by VDM Publishing. This book was released on 2007 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: (cont.) We introduce and study a solution method that enables to compute the optimal solution on a finite time horizon in a monopoly setting. Our results illustrate the role of capacity and the effects of the dynamic nature of demand. We then introduce an additive model of demand uncertainty. We use a robust optimization approach to protect the solution against data uncertainty in a tractable manner, and without imposing stringent assumptions on available information. We show that the robust formulation is of the same order of complexity as the deterministic problem and demonstrate how to adapt solution method. Finally, we consider a duopoly setting and use a more general model of additive and multiplicative demand uncertainty. We formulate the robust problem as a coupled constraint differential game. Using a quasi-variational inequality reformulation, we prove the existence of Nash equilibria in continuous time and study issues of uniqueness. Finally, we introduce a relaxation-type algorithm and prove its convergence to a particular Nash equilibrium (normalized Nash equilibrium) in discrete time.

Optimization and Inventory Management

Author : Nita H. Shah
Publisher : Springer Nature
ISBN 13 : 9811396981
Total Pages : 470 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Optimization and Inventory Management by : Nita H. Shah

Download or read book Optimization and Inventory Management written by Nita H. Shah and published by Springer Nature. This book was released on 2019-08-31 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses inventory models for determining optimal ordering policies using various optimization techniques, genetic algorithms, and data mining concepts. It also provides sensitivity analyses for the models’ robustness. It presents a collection of mathematical models that deal with real industry scenarios. All mathematical model solutions are provided with the help of various optimization techniques to determine optimal ordering policy. The book offers a range of perspectives on the implementation of optimization techniques, inflation, trade credit financing, fuzzy systems, human error, learning in production, inspection, green supply chains, closed supply chains, reworks, game theory approaches, genetic algorithms, and data mining, as well as research on big data applications for inventory management and control. Starting from deterministic inventory models, the book moves towards advanced inventory models. The content is divided into eight major sections: inventory control and management – inventory models with trade credit financing for imperfect quality items; environmental impact on ordering policies; impact of learning on the supply chain models; EOQ models considering warehousing; optimal ordering policies with data mining and PSO techniques; supply chain models in fuzzy environments; optimal production models for multi-items and multi-retailers; and a marketing model to understand buying behaviour. Given its scope, the book offers a valuable resource for practitioners, instructors, students and researchers alike. It also offers essential insights to help retailers/managers improve business functions and make more accurate and realistic decisions.

Inventory-Based Dynamic Pricing with Costly Price Adjustment

Author : Wen Chen
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Inventory-Based Dynamic Pricing with Costly Price Adjustment by : Wen Chen

Download or read book Inventory-Based Dynamic Pricing with Costly Price Adjustment written by Wen Chen and published by . This book was released on 2014 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study an average-cost stochastic inventory control problem in which the firm can replenish inventory and adjust price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size -- An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time-average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory-based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.

Demand Forecasting and Inventory Control

Author : Colin Lewis
Publisher : Routledge
ISBN 13 : 113634683X
Total Pages : 172 pages
Book Rating : 4.1/5 (363 download)

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Book Synopsis Demand Forecasting and Inventory Control by : Colin Lewis

Download or read book Demand Forecasting and Inventory Control written by Colin Lewis and published by Routledge. This book was released on 2012-05-23 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical book covers the forecasting- and inventory control methods used in commercial, retail and manufacturing companies. Colin Lewis explains the theory and practice of current demand forecasting methods, the links between forecasts produced as a result of analysing demand data and the various methods by which this information, together with cost information on stocked items, is used to establish the controlling parameters of the most commonly used inventory control systems. The demand forecasting section of the book concentrates on the family of short-term forecasting models based on the exponentially weighted average and its many variants and also a group of medium-term forecasting models based on a time series, curve fitting approach. The inventory control sections investigate the re-order level policy and re-order cycle policy and indicate how these two processes can be operated at minimum cost while offering a high level of customer service.

Dynamic Pricing and Inventory Control for Perishable Products Under Uncertain and Time Dependent Demand

Author : Halit Bayer
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Dynamic Pricing and Inventory Control for Perishable Products Under Uncertain and Time Dependent Demand by : Halit Bayer

Download or read book Dynamic Pricing and Inventory Control for Perishable Products Under Uncertain and Time Dependent Demand written by Halit Bayer and published by . This book was released on 2016 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Revenue and Inventory Management Models

Author : Yifeng Liu
Publisher :
ISBN 13 :
Total Pages : 127 pages
Book Rating : 4.:/5 (889 download)

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Book Synopsis Dynamic Revenue and Inventory Management Models by : Yifeng Liu

Download or read book Dynamic Revenue and Inventory Management Models written by Yifeng Liu and published by . This book was released on 2014 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective pricing and inventory controls are very important for the success of a company, especially in an environment with many uncertainties such as random demand and fluctuating cost. In this work, we first consider pure dynamic pricing. Indeed, we consider three cases: markup in which price can only go up, markdown in which price can only go down, and reversible pricing in which price can go either direction. We also consider a joint pricing and inventory control model in which the raw material price evolves as a Markov process. For this model, we suppose production is make-to-order, so that the conversion from raw material to finished product is carried out only when demand arrives. For the pure pricing model, we establish the optimality of threshold-like policies. We also develop efficient and numerically stable algorithms. For the make-to-order joint inventory-pricing model, we demonstrate the optimality of a base-stock-list-price policy. In addition, we identify conditions under which policy parameters would exhibit monotone trends. Moreover, we showed the significant benefit of adopting cost-dependent base-stock list-price policy.

Dynamic Pricing and Inventory Control with Learning

Author : Nicholas C. Petruzzi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (535 download)

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Book Synopsis Dynamic Pricing and Inventory Control with Learning by : Nicholas C. Petruzzi

Download or read book Dynamic Pricing and Inventory Control with Learning written by Nicholas C. Petruzzi and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Effectiveness of a Simple Policy for Coordinating Inventory Control and Pricing Strategies

Author : Zhibo Sun (S.M.)
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (76 download)

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Book Synopsis The Effectiveness of a Simple Policy for Coordinating Inventory Control and Pricing Strategies by : Zhibo Sun (S.M.)

Download or read book The Effectiveness of a Simple Policy for Coordinating Inventory Control and Pricing Strategies written by Zhibo Sun (S.M.) and published by . This book was released on 2010 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the effectiveness of an (s, S, p) policy relative to an (s, S, A, p) policy in a single product, periodic review, finite horizon model with stochastic multiplicative demand and fixed ordering cost, in which an (s, S, A, p) policy is optimal. An extensive numerical study shows that empirically an (s, S, p) policy is highly effective relative to an (s, S, A, p) policy. We also formulate two alternative benchmark policies and find that the (s, S, p) policy is superior in terms of profit. In addition, we propose an efficient algorithm with simulated annealing and modified binary search to determine the (s, S, p) policy for the model.

Single Period Inventory Control and Pricing

Author : Emel Arikan
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.:/5 (128 download)

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Book Synopsis Single Period Inventory Control and Pricing by : Emel Arikan

Download or read book Single Period Inventory Control and Pricing written by Emel Arikan and published by . This book was released on 2018 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The price-setting newsvendor model is used to address the single period joint pricing and inventory control problem. The objective is to set the optimal price and replenishment quantity of a single product in order to maximize the expected profit. Products with a short selling season and relatively long replenishment lead times such as fashion goods are the most relevant application areas of the model. The focus of the work is the generalization of the model with respect to the modeling of uncertainty in demand. The author presents an analytical and empirical study which compares different demand models with a more flexible model based on price and inventory optimization. She concludes that using a general model can increase the profits significantly.