Dynamic Pricing and Inventory Control with Learning

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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:

Dynamic Pricing and Inventory Control with Learning

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ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (368 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 1996 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

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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.

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

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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 With Infrequent Inventory Replenishments

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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.

Combined Dynamic Pricing and Inventory Control

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ISBN 13 : 9780599594609
Total Pages : pages
Book Rating : 4.5/5 (946 download)

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Book Synopsis Combined Dynamic Pricing and Inventory Control by :

Download or read book Combined Dynamic Pricing and Inventory Control written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Pricing and Inventory Control

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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.

Data Based Dynamic Pricing and Inventory Control with Censored Demand and Limited Price Changes

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ISBN 13 :
Total Pages : 61 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Data Based Dynamic Pricing and Inventory Control with Censored Demand and Limited Price Changes by : Boxiao Chen

Download or read book Data Based Dynamic Pricing and Inventory Control with Censored Demand and Limited Price Changes written by Boxiao Chen and published by . This book was released on 2020 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: A firm makes pricing and inventory replenishment decisions for a product over T periods to maximize its expected total profit. Demand is random and price sensitive, and unsatisfied demands are lost and unobservable (censored demand). The firm knows the demand process up to some parameters and needs to learn them through pricing and inventory experimentation. However, due to business constraints the firm is prevented from making frequent price changes, leading to correlated and dependent sales data. We develop data-driven algorithms by actively experimenting inventory and pricing decisions and construct maximum likelihood estimator with censored and correlated samples for parameter estimation. We analyze the algorithms using the T-period regret, defined as the profit loss of the algorithms over T periods compared with the clairvoyant optimal policy that knew the parameters a priori. For a so-called well-separated case, we show that the regret of our algorithm is O(T^{1/(m+1)}) when the number of price changes is limited by m >= 1, and is O( log T) when limited by beta log T for some positive constant beta>0; while for a more general case, the regret is O(T^{1/2}) when the underlying demand is bounded and O(T^{1/2} log T) when the underlying demand is unbounded. We further prove that our algorithm for each case is the best possible in the sense that its regret rate matches with the theoretical lower bound.

The Oxford Handbook of Pricing Management

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Publisher : OUP Oxford
ISBN 13 : 0191634263
Total Pages : 976 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis The Oxford Handbook of Pricing Management by : Özalp Özer

Download or read book The Oxford Handbook of Pricing Management written by Özalp Özer and published by OUP Oxford. This book was released on 2012-06-07 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Handbook of Pricing Management is a comprehensive guide to the theory and practice of pricing across industries, environments, and methodologies. The Handbook illustrates the wide variety of pricing approaches that are used in different industries. It also covers the diverse range of methodologies that are needed to support pricing decisions across these different industries. It includes more than 30 chapters written by pricing leaders from industry, consulting, and academia. It explains how pricing is actually performed in a range of industries, from airlines and internet advertising to electric power and health care. The volume covers the fundamental principles of pricing, such as price theory in economics, models of consumer demand, game theory, and behavioural issues in pricing, as well as specific pricing tactics such as customized pricing, nonlinear pricing, dynamic pricing, sales promotions, markdown management, revenue management, and auction pricing. In addition, there are articles on the key issues involved in structuring and managing a pricing organization, setting a global pricing strategy, and pricing in business-to-business settings.

Operationalizing Dynamic Pricing Models

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Publisher : Springer Science & Business Media
ISBN 13 : 3834961841
Total Pages : 363 pages
Book Rating : 4.8/5 (349 download)

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Book Synopsis Operationalizing Dynamic Pricing Models by : Steffen Christ

Download or read book Operationalizing Dynamic Pricing Models written by Steffen Christ and published by Springer Science & Business Media. This book was released on 2011-04-02 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steffen Christ shows how theoretic optimization models can be operationalized by employing self-learning strategies to construct relevant input variables, such as latent demand and customer price sensitivity.

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

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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 Pricing and Inventory Control for Multiple Products

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ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Dynamic Pricing and Inventory Control for Multiple Products by : Dimitris Bertsimas

Download or read book Dynamic Pricing and Inventory Control for Multiple Products written by Dimitris Bertsimas and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: A periodical multi-product pricing and inventory control problem with applications to production planning and airline revenue management is studied. The objective function of the single-period model is shown to be convex for certain types of demand distributions, thus tractable for large instances. A heuristic is proposed to solve the more complex multi-period problem, which is an interesting combination of linear and dynamic programming. Numerical experiments and theoretical bounds on the optimal expected revenue suggest that the extent to which a dynamic policy based on a stochastic model will outperform a simple static policy based on a deterministic model depends on the level of demand variability as measured by the coefficient of variation.

The Elements of Joint Learning and Optimization in Operations Management

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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.

Dynamic Pricing and Inventory Management in the Presence of Online Reviews

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ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Dynamic Pricing and Inventory Management in the Presence of Online Reviews by : Nan Yang

Download or read book Dynamic Pricing and Inventory Management in the Presence of Online Reviews written by Nan Yang and published by . This book was released on 2018 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the joint pricing and inventory management problem in the presence of online customer reviews. Customers who purchase the product may post reviews that would influence future customers' purchasing behaviors. Under the common practice of customer-generated reviews on e-commerce platforms, rigorous investigation of their operational implications offers valuable insights and guidance for both the research community and practitioners. We develop a stochastic joint pricing and inventory management model to characterize the optimal policy in the presence of online reviews. We show that a rating-dependent base-stock/list-price policy is optimal. Interestingly, the inventory dynamics of the firm do not influence the optimal policy as long as the initial inventory is below the initial base-stock level. Hence, we can reduce the dynamic program that characterizes the optimal policy to one with a single-dimensional state-space (the aggregate net rating). The presence of online reviews gives rise to the trade-off between generating current profits and inducing future demands, thus having several important implications upon the firm's operations decisions. First, online reviews drive the firm to deliver a better service and attract more customers to post a review. Hence, the safety-stock and base-stock levels are higher in the presence of online reviews. Second, the evolution of the aggregate net rating process follows a mean-reverting pattern: When the current rating is low (resp. high), it has an increasing (resp. decreasing) trend in expectation. Third, although myopic profit optimization leads to significant optimality losses in the presence of online reviews, balancing the current profits and near-future demands suffices to exploit the network effect induced by online reviews. We propose a dynamic look-ahead heuristic policy that well leverages this idea and achieves small optimality gaps which decay exponentially in the length of the look-ahead time-window.

Dynamic Pricing and Learning Under The Effect of Inventory Scarcity

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

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Book Synopsis Dynamic Pricing and Learning Under The Effect of Inventory Scarcity by : Mengyan Zhu

Download or read book Dynamic Pricing and Learning Under The Effect of Inventory Scarcity written by Mengyan Zhu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revealing inventory scarcity messages to customers to trigger scarcity effect is an important and widely adopted way to promote sales in online platforms. Under such circumstances, the demand is affected by both price and scarcity messages. In this article, we study the joint dynamic pricing and learning problem under the inventory scarcity effect. Specifically, we consider three popular scarcity messages: partially revealed, fully revealed, and mixedly revealed inventory information, and we design passive learning algorithms with/without forced learning steps to learn unknown parameters in the demand function with a planning horizon consisting of many independent selling seasons. The main challenge is that there is always a strictly positive probability of no learning in one selling season, since the change of inventory status is not fully under control. To balance the learning speed and regret in this setting, we introduce the idea of endogenous and forced learning cycles, and design indices to determine when to conduct forced learning steps. Furthermore, to increase the success learning probability, we design learning steps by grouping two selling seasons together based on the MDP structure for the optimal pricing policy, which is quite different from the scenario without inventory scarcity effect. As a result, our methods have $O( log^2 T)$ regret bounds in all cases. Moreover, numerical experiments show that ignoring the scarcity effect will cause significant revenue loss. We also provide insights on when the seller should choose pure passive learning method or passive learning methods with forced learning steps. Our work sheds light on the practice of online retailing in the presence of inventory scarcity effect.

Dynamic Pricing and Inventory Management

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ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.:/5 (958 download)

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Book Synopsis Dynamic Pricing and Inventory Management by : Renyu Philip Zhang

Download or read book Dynamic Pricing and Inventory Management written by Renyu Philip Zhang and published by . This book was released on 2016 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop the models and methods to study the impact of some emerging trends in technology, marketplace, and society upon the pricing and inventory policy of a firm. We focus on the situation where the firm is in a dynamic, uncertain, and (possibly) competitive market environment. The market trends of particular interest to us are: (a) social networks, (b) sustainability concerns, and (c) customer behaviors. The two main running questions this dissertation aims to address are: (a) How these emerging market trends would influence the operations decisions and profitability of a firm; and (b) What pricing and inventory strategies a firm could use to leverage these trends. We also develop an effective comparative statics analysis method to address these two questions under different market trends. Overall, our results suggest that the current market trends of social networks, sustainability concerns, and customer behaviors have significant and interesting impact upon the operations policy of a firm, and that the firm could adopt some innovative pricing and inventory strategies to exploit these trends and substantially improve its profit. Our main findings are: (a) Network externalities (the monopoly setting). We find that network externalities prompt a firm to face the tradeoff between generating current profits and inducing future demands when making the price and inventory decisions, so that it should increase the base-stock level, and to decrease [increase] the sales price when the network size is small [large]. Our extensive numerical experiments also demonstrate the effectiveness of the heuristic policies that leverage network externalities by balancing generating current profits and inducing demands in the near future. (Chapter 2.) (b) Network externalities (the dynamic competition setting). In a competitive market with network externalities, the competing firms face the tradeoff between generating current profits and winning future market shares (i.e., the exploitation-induction tradeoff). We characterize the pure strategy Markov perfect equilibrium in both the simultaneous competition and the promotion-first competition. We show that, to balance the exploitation-induction tradeoff, the competing firms should increase promotional efforts, offer price discounts, and improve service levels. The exploitation-induction tradeoff could be a new driving force for the fat-cat effect (i.e., the equilibrium promotional efforts are higher under the promotion-first competition than those under the simultaneous competition). (Chapter 3.) (d) Trade-in remanufacturing. We show that, with the adoption of the very commonly used trade-in remanufacturing program, the firm may enjoy a higher profit with strategic customers than with myopic customers. Moreover, trade-in remanufacturing creates a tension between firm profitability and environmental sustainability with strategic customers, but benefits both the firm and the environment with myopic customers. We also find that, with either strategic or myopic customers, the socially optimal outcome can be achieved by using a simple linear subsidy and tax scheme. The commonly used government policy to subsidize for remanufacturing alone, however, does not induce the social optimum in general. (Chapter 4.) (d) Scarcity effect of inventory. We show that the scarcity effect drives both optimal prices and order-up-to levels down, whereas increased operational flexibilities (e.g., the inventory disposal and inventory withholding opportunities) mitigate the demand loss caused by high excess inventory and increase the optimal order-up-to levels and sales prices. Our extensive numerical studies also demonstrate that dynamic pricing leads to a much more significant profit improvement with the scarcity effect of inventory than without. (Chapter 5.) (e) Comparative statics analysis method. We develop a comparative statics method to study a general joint pricing and inventory management model with multiple demand segments, multiple suppliers, and stochastically evolving market conditions. Our new method makes componentwise comparisons between the focal decision variables under different parameter values, so it is capable of performing comparative statics analysis in a model where part of the decision variables are non-monotone, and it is well scalable. Hence, our new method is promising for comparative statics analysis in other operations management models. (Chapter 6.)

Inventory-Based Dynamic Pricing with Costly Price Adjustment

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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.