The newsvendor problem under multiplicative background risk

This note studies the single-period newsvendor problem when the newsvendor faces a multiplicative neutral independent background risk in an expected utility framework. It is shown that multiplicative risk vulnerability is a sufficient condition to guarantee a decrease in the optimal order. A weaker sufficient condition which has more interpretability is also provided and discussed. This result sheds light on situations where exchange, tax or inflation rates risks, which apply multiplicatively to the final wealth, are at work

Optimal Pricing and order quantity strategies for a firm offering multiple products facing customers cannibalization and random market demand

This paper studies a firm’s profitability problem offering its products into different market segments at differentiated prices. In order to improve the firms’ profitability the firm needs to decide the prices and order quantities allocations for each market segment. In perfect market segmentation, it is assumed that the customers do not cannibalize between market segments. Whereas, in the case of imperfect market segmentation, the customers are assumed to cannibalize from a high price market segment to a lower price segment. Models to determine the optimal strategies for pricing and order quantity for the perfect as well as for the imperfect market segmentations are proposed with both the deterministic and stochastic customers’ demand. The study has shown that the perfect market segmentation always yields higher revenues compared to no segmentation for a firm facing both the deterministic and stochastic demand situations. In addition to this, the study has also shown that when cannibalization exists, a firm is still able to yield higher revenues compared to the case of no market segmentation facing both the deterministic and stochastic demands, however, greater the extent of cannibalization could result substantial losses in the profitability

Constructive solution methodologies to the capacitated newsvendor problem and surrogate extension

The newsvendor problem is a single-period stochastic model used to determine the order quantity of perishable product that maximizes/minimizes the profit/cost of the vendor under uncertain demand. The goal is to fmd an initial order quantity that can offset the impact of backlog or shortage caused by mismatch between the procurement amount and uncertain demand. If there are multiple products and substitution between them is feasible, overstocking and understocking can be further reduced and hence, the vendor\u27s overall profit is improved compared to the standard problem. When there are one or more resource constraints, such as budget, volume or weight, it becomes a constrained newsvendor problem. In the past few decades, many researchers have proposed solution methods to solve the newsvendor problem. The literature is first reviewed where the performance of each of existing model is examined and its contribution is reported. To add to these works, it is complemented through developing constructive solution methods and extending the existing published works by introducing the product substitution models which so far has not received sufficient attention despite its importance to supply chain management decisions. To illustrate this dissertation provides an easy-to-use approach that utilizes the known network flow problem or knapsack problem. Then, a polynomial in fashion algorithm is developed to solve it. Extensive numerical experiments are conducted to compare the performance of the proposed method and some existing ones. Results show that the proposed approach though approximates, yet, it simplifies the solution steps without sacrificing accuracy. Further, this dissertation addresses the important arena of product substitute models. These models deal with two perishable products, a primary product and a surrogate one. The primary product yields higher profit than the surrogate. If the demand of the primary exceeds the available quantity and there is excess amount of the surrogate, this excess quantity can be utilized to fulfill the shortage. The objective is to find the optimal lot sizes of both products, that minimize the total cost (alternatively, maximize the profit). Simulation is utilized to validate the developed model. Since the analytical solutions are difficult to obtain, Mathematical software is employed to find the optimal results. Numerical experiments are also conducted to analyze the behavior of the optimal results versus the governing parameters. The results show the contribution of surrogate approach to the overall performance of the policy. From a practical perspective, this dissertation introduces the applications of the proposed models and methods in different industries such as inventory management, grocery retailing, fashion sector and hotel reservation

An analysis of portfolio selection with multiplicative background risk

This paper investigates the impact of multiplicative background risk on an investor's portfolio choice in a mean-variance framework. We also study the efficient boundary frontiers with and without risk-free security

The Newsvendor Problem with Pricing

In the newsvendor problem with pricing, the seller of homogeneous items attempts to maximize expected profit by setting price(s) and inventory level(s) before realizing exact demand for the items. The first step in solving the problem is to model this demand, which in the literature, is most commonly done using additive or multiplicative uncertainty, often without justification for either choice. From here, the problem is solved in a variety of ways. In this document, a model for demand is derived from two basic quantities: size of customer base and distribution of reservation prices of the population, where a reservation price is the most a customer is willing to pay for an item. This demand model is then incorporated into expected profit functions for various scenarios of the problem, and the optimal results found using these functions are compared with those optimal results found using other methods found in the literature

Research of Behavioral Newsvendor Problem Based on Pessimistic and Optimistic Biases

有效管理库存一直以来都是运筹学和管理学研究主要议题，也是整个供应链有效运行的重要环节。面对快速变化的随机需求，每个制造企业如何决定自己的最优产量？每个零售企业如何决定自己的最优库存量？一些重要的服务业如何设计最优的运作空间？这些都是世界上各大企业所面对的共同难题。而作为对这类问题研究的理论基石，经典的报贩模型由于其结构简单，并能够刻画大量现实中商业和生产运作模式，从而具有广泛的应用前景，因此长期以来都是学者和管理者强烈关注的焦点。 近30年来，在随机环境下，基于期望效用理论的传统经济和金融理论由于无法解释现实世界中一些异象，因而受到越来越多学者的质疑，一些学者通过把人类的行为因素纳入到决...How to manage inventory effectively has been being the focus of research in operation and management science and the important step in effective operation of the whole supply chain. In face of fast changing stochastic demand, how does each manufacturer decides its optimal production?how does every retailer makes its inventory decision? how do those service enterprises design their optimal operati...学位：理学博士院系专业：数学科学学院数学与应用数学系_应用数学学号：1902009015361

Probabilistic Forecasting in Decision-Making: New Methods and Applications

This thesis develops new methods to generate probabilistic forecasts and applies these methods to solve operations problems in practice. The first chapter introduces a new product life cycle model, the tilted-Gompertz model, which can predict the distribution of period sales and cumulative sales over a product's life cycle. The tilted-Gompertz model is developed by exponential tilting the Gompertz model, which has been widely applied in modelling human mortality. Due to the tilting parameter, this new model is flexible and capable of describing a wider range of shapes compared to existing life cycle models. In two empirical studies, one on the adoption of new products and the other on search interest in social networking websites, I find that the tilted-Gompertz model performs well on quantile forecasting and point forecasting, when compared to other leading life-cycle models. In the second chapter, I develop a new exponential smoothing model that can capture life-cycle trends. This new exponential smoothing model can also be viewed as a tilted-Gompertz model with time-varying parameters. The model can adapt to local changes in the time series due to the smoothing parameters in the exponential smoothing formulation. When estimating the parameters, prior information is included in the regularization terms of the model. In the empirical studies, the new exponential smoothing model outperforms several leading benchmark models in predicting quantiles on a rolling basis. In the final chapter, I develop a predictive system that predicts distributions of passengers' connection times and transfer passenger flows at an airport using machine learning methods. The predictive system is based on regression trees and copula-based simulations. London Heathrow airport currently uses this proposed system and has reported significant accuracy improvements over their legacy systems

Benefits of postponement for fashion products with forecast updates

Thesis (M. Eng. in Logistics)--Massachusetts Institute of Technology, Engineering Systems Division, 2005.Includes bibliographical references (leaves 67-69).This thesis examines the benefit of postponement of fashion products by considering the overage cost of the intermediate product and the correlation between the demand for each end products produced from it. The benefit of postponement is measured by the percentage increase in maximum expected profit after demand is realized. the production process is modelled as a two stage newsvendor problem and the forecast update path follows an additive martingale. An optimal solution and a myopic solution are proposed to solve this problem. Numerical results indicate that the benefit of postponement decreases with the overage cost of the intermediate product and the correlation between demand for each end products. It becomes less sensitive to the overage cost of the intermediate product when end products are more negatively correlated. It is also less sensitive to the demand correlation between end products when the overage cost of the intermediate product is low. In addition, the benefit of postponement is sensitive to the additional unit costs introduced by postponement. A case study to NFL Jerseys purchase planning indicates that an increase of unit cost by 10% can reduce the benefit of postponement by over 50%.by Huiling Gong.M.Eng.in Logistic

Carbon restricted newsvendor problem under CVAR objective and resource constraints

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 183-188.Newsboy problem has been studied in the literature extensively. The classical newsvendor, representing the risk neutral decision maker, determines the optimal order/production quantity by maximizing the expected profit or minimizing the expected total cost of a single period with stochastic demand. This approach is not suitable if one also aims to reduce the chances of facing unexpected losses due to demand uncertainty. In this thesis, two problems are investigated with a single product newsvendor under CVaR maximization objective. The first problem addresses the newsvendor model with two different carbon emission reduction policies, namely, mandatory emission allowance and carbon emission trading mechanism. In the second problem, as an extension of the first one, a newsvendor with multiple resource constraints is considered for the cases where the resources have quotas with trade options. Analytical expressions for optimal order/production quantities are determined together with the optimal trading policy and numerical examples are provided.Korkmaz, ÖzümM.S