Download or read book Data Driven Approximation Schemes for Joint Pricing and Inventory Control Models written by Hanzhang Qin and published by . This book was released on 2019 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Near optimal Data driven Approximation Schemes for Joint Pricing and Inventory Control Models written by Hanzhang Qin (S. M.) and published by . This book was released on 2018 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis studies the classical multi-period joint pricing and inventory control problem in a data-driven setting. In the problem, a retailer makes periodic decisions of the prices and inventory levels of an item that the retailer wishes to sell. The objective is to match the inventory level with a random demand that depends on the price in each period, while maximizing the expected profit over finite horizon. In reality, the demand functions or the distribution of the random noise are usually unavailable, whereas past demand data are relatively easy to collect. A novel data-driven nonparametric algorithm is proposed, which uses the past demand data to solve the joint pricing and inventory control problem, without assuming the parameters of the demand functions and the noise distributions are known. Explicit sample complexity bounds are given, on the number of data samples needed to guarantee a near-optimal profit. A simulation study suggests that the algorithm is efficient in practice.

Download or read book Research Handbook on Inventory Management written by Jing-Sheng J. Song and published by Edward Elgar Publishing. This book was released on 2023-08-14 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive Handbook provides an overview of state-of-the-art research on quantitative models for inventory management. Despite over half a century’s progress, inventory management remains a challenge, as evidenced by the recent Covid-19 pandemic. With an expanse of world-renowned inventory scholars from major international research universities, this Handbook explores key areas including mathematical modelling, the interplay of inventory decisions and other business decisions and the unique challenges posed to multiple industries.

Download or read book Sampling Based Approximation Schemes for Capacitated Stochastic Inventory Control Models written by Wang Chi Cheung and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the classical multi-period capacitated stochastic inventory control problems in a data-driven setting. Instead of assuming full knowledge of the demand distributions, we assume that the demand distributions can only be accessed through drawing random samples. Such data-driven models are ubiquitous in practice, where the cumulative distribution functions of the underlying random demand are either unavailable or too complicated to work with. We apply the Sample Average Approximation (SAA) method to the capacitated inventory control problem and establish an upper bound on the number of samples needed for the SAA method to achieve a near-optimal expected cost, under any level of required accuracy and pre-specified confidence probability. The sample bound is polynomial in the number of time periods as well as the confidence and accuracy parameters. Moreover, the bound is independent of the underlying demand distributions. However, the SAA requires solving the SAA problem, which is #P-hard. Thus, motivated by the SAA analysis, we propose a randomized polynomial time approximation scheme which also uses polynomially many samples. Finally, we establish a lower bound on the number of samples required to solve this data-driven newsvendor problem to near-optimality.

Download or read book Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand written by Boxiao Chen and published by . This book was released on 2020 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a joint pricing and inventory control problem in which the customer's response to selling price and the demand distribution are not known a priori. Unsatisfied demand is lost and unobserved, and the only available information for decision-making is the observed sales data (a.k.a. censored demand). Conventional approaches, such as stochastic approximation, online convex optimization, and continuum-armed bandit algorithms, cannot be employed since neither the realized values of the profit function nor its derivatives are known. A major challenge of this problem lies in that the estimated profit function constructed from observed sales data is multimodal in price. We develop a nonparametric spline approximation based learning algorithm. The algorithm separates the planning horizon into a disjoint exploration phase and an exploitation phase. During the exploration phase, the price space is discretized, and each price is offered an equal number of periods together with a pre-specified target inventory level. Based on the sales data collected on these prices, a spline approximation of the demand-price function is constructed, and then the corresponding surrogate optimization problem is solved on a sparse grid to obtain a pair of recommended price and target inventory level. During the exploitation phase, the algorithm implements the recommended strategies. We establish a (nearly) square-root regret rate, which (almost) matches the theoretical lower bound.

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.

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.

Download or read book Iterative Algorithms for a Joint Pricing and Inventory Control Problem with Nonlinear Demand Functions written by Anupam Mazumdar (S. M.) and published by . This book was released on 2009 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: Price management, production planning and inventory control are important determinants of a firm's profitability. The intense competition brought about by rapid innovation, lean manufacturing time and the internet revolution has compelled firms to adopt a dynamic strategy that involves complex interplay between pricing and production decisions. In this thesis we consider some of these problems and develop computationally efficient algorithms that aim to tackle and optimally solve these problems in a finite amount of time. In the first half of the thesis we consider the joint pricing and inventory control problem in a deterministic and multiperiod setting utilizing the popular log linear demand model. We develop four algorithms that aim to solve the resulting profit maximization problem in a finite amount of time. The developed algorithms are then tested in a variety of settings ranging from small to large instances of trial data. The second half of the thesis deals with setting prices effectively when the customer demand is assumed to follow the multinomial logit demand model, which is the most popular discrete choice demand model. The profit maximization problem (even in the absence of constraints) is non-convex and hard to solve. Despite this fact we develop algorithms that compute the optimal solution efficiently. We test the algorithms we develop in a wide variety of scenarios from small to large customer segment, with and without production/inventory constraints. The last part of the thesis develops solution methods for the joint pricing and inventory control problem when costs are linear and demand follows the multinomial logit model.

Download or read book Asymptotic Optimality of Constant Order Policies in Joint Pricing and Inventory Control Models written by Xin Chen and published by . This book was released on 2019 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a traditional joint pricing and inventory control problem with lead times, which has been extensively studied in the literature but is notoriously difficult to solve due to the complex structure of the optimal policy. In this work, rather than analyzing the optimal policy, we propose a class of so-called constant-order dynamic pricing policies, which are quite different from base-stock heuristics, the primary focus in the existing literature. Under such a policy, a constant-order amount of new inventory is ordered every period and a pricing decision is made based on the on-hand inventory. The policy is independent of the lead time and does not suffer from the curse of dimensionality. We prove that the best constant-order dynamic pricing policy is asymptotically optimal as the lead time grows large, which is exactly the setting in which the problem becomes computationally intractable due to the curse of dimensionality. As a main methodological contribution, we implement the so-called vanishing discount factor approach and establish the convergence to a long-run average random yield inventory model with zero lead time and ordering capacities by its discounted counterpart as the discount factor goes to one, non-trivially extending the previous results in Federgruen and Yang (2014) that analyze a similar model but without capacity constraints.

Download or read book Linear Programming based Subgradient Algorithm for Joint Pricing and Inventory Control Problems written by Tingting Rao and published by . This book was released on 2008 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is important for companies to manage their revenues and -reduce their costs efficiently. These goals can be achieved through effective pricing and inventory control strategies. This thesis studies a joint multi-period pricing and inventory control problem for a make-to-stock manufacturing system. Multiple products are produced under shared production capacity over a finite time horizon. The demand for each product is a function of the prices and no back orders are allowed. Inventory and production costs are linear functions of the levels of inventory and production, respectively. In this thesis, we introduce an iterative gradient-based algorithm. A key idea is that given a demand realization, the cost minimization part of the problem becomes a linear transportation problem. Given this idea, if we knew the optimal demand, we could solve the production problem efficiently. At each iteration of the algorithm, given a demand vector we solve a linear transportation problem and use its dual variables in order to solve a quadratic optimization problem that optimizes the revenue part and generates a new pricing policy. We illustrate computationally that this algorithm obtains the optimal production and pricing policy over the finite time horizon efficiently. The computational experiments in this thesis use a wide range of simulated data. The results show that the algorithm we study in this thesis indeed computes the optimal solution for the joint pricing and inventory control problem and is efficient as compared to solving a reformulation of the problem directly using commercial software. The algorithm proposed in this thesis solves large scale problems and can handle a wide range of nonlinear demand functions.

Download or read book Joint Pricing and Inventory Control Under Reference Price Effects written by Lisa Gimpl-Heersink and published by Peter Lang Pub Incorporated. This book was released on 2009 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we address the problem of simultaneously determining a pricing and inventory replenishment strategy under reference price effects. This reference price effect models the fact that consumers not only react sensitively to the current price, but also to deviations from a reference price formed on the basis of past purchases. Immediate effects of price reductions on profits have to be weighted against the resulting losses in future periods. By providing an analytical analysis and numerical simulations we study how the additional dynamics of the consumers' willingness to pay affect an optimal pricing and inventory control model and whether a simple policy such as a base-stock-list-price policy holds in such a setting.

Download or read book Joint Pricing and Inventory Control with Substitutable Products written by Ahmet Kuyumcu and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Joint Pricing and Inventory Management with Strategic Customers written by Yiwei Chen and published by . This book was released on 2018 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a model wherein the seller sells a product to customers over an infinite horizon. At each time, the seller decides a set of purchase options offered to customers and the inventory replenishment quantity. Each purchase option specifies a price and a product delivery time. Customers are infinitesimal and arrive to the system with a constant rate. Customer product valuations are heterogenous and follow a stationary distribution. A customer's arrival time and product valuation are his private information. Customers are forward looking, i.e., they strategize their purchasing times. A customer incurs delay disutility from postponing to place an order and waiting for the product delivery. A customer's delay disutility rate is perfectly and positively correlated with his valuation. The seller has zero replenishment lead time. The seller incurs fixed ordering cost and inventory holding cost. The seller seeks a joint pricing, delivery and inventory policy that maximizes her long-run average profit. Through a tractable upper bound constructed by solving a mechanism design problem, we derive an optimal joint pricing, delivery and inventory policy, which is a simple cyclic policy. We also extend our policy to a stochastic setting and establish its asymptotic optimality.

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.

Download or read book Data Driven Dynamic Pricing and Inventory Management of an Omni Channel Retailer in an Uncertain Demand Environment written by Shiyu Liu and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, omni-channel retailing has become immensely popular among both retailers and consumers. In this approach, retailers often leverage their brick-and-mortar stores to fulfill online orders, leading to the need for simultaneous decision-making on replenishment and inventory rationing. This inventory strategy presents significant complexities in traditional dynamic pricing and inventory management problems, particularly in unpredictable market environments. Therefore, we have developed a dynamic pricing, replenishment, and rationing model for omni-channel retailers using a two-level partially observed Markov decision process to visualize the dynamic process. We design a deep reinforcement learning algorithm, called Maskable LSTM-Proximal Policy Optimization (ML-PPO), which integrates the current observations and future predictions as input to the agent and uses the invalid action mask to guarantee the allowable actions. Our simulation experiments have demonstrated the ML-PPO's efficiency in maximizing retailer profit and service level, along with its generalized ability to tackle dynamic pricing and inventory management problems.

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.