收益管理中基于结构特征的概率预测与资源分配问题研究
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摘要
收益管理是运筹学在管理中成功应用的一个重要领域，也是当今科学研究的难点和热点之一。所谓收益管理，是指企业基于对消费行为的理解与不确定环境的预测，通过选择能力、价格和时机等决策要素，有效分配资源，从而管理需求以实现收益最大化。随着经济全球化趋势的快速发展，市场需求层次的不断升级，消费需求结构的日益多样化，产品的供应链不断延长，产品的生命周期越来越短。在这种环境下，如何利用有限的资源实现收益最大化就成为企业需要解决的迫切问题。收益管理是企业应对剧烈市场竞争的有效模式，是企业分配资源、管理需求的便利途径。收益管理已在许多领域得到研究与推广应用，如航空运输、零售管理、酒店经营、汽车租赁、能源管理等行业。
在这种日益加剧的竞争环境下，企业主要面临两个问题：一、如何认识瞬息万变的不确定环境；二、如何利用有限的资源满足多样化的市场需求。大多数收益管理决策问题都是随机优化模型，模型的输入涉及相关决策要素的概率分布，需要预测不确定环境要素的整体分布。概率预测的结果是决策模型求解的基础，概率预测的质量直接影响决策的优劣，因此改善概率预测精度对收益管理有着重要的价值，研究概率预测问题成为收益管理中的一个基本问题。收益管理决策问题本质上是资源分配问题，一般是通过数量或价格决策控制有限资源的分配。资源分配决策直接影响企业收益，改善资源分配决策对实现收益最大化尤其重要，因此研究资源分配问题成为收益管理中的一个核心问题。
收益管理中概率预测面临的主要困难是，有待预测的要素一般表现出一些特征，如间断特征、非平稳特征、不完全特征、非对称特征等。这些表现特征使得多数传统的预测方法一般难以应用或预测精度不高。这些表现特征一般与收益管理问题的实际背景有关，分析这些表现特征的形成机理，有助于研究捕获这些表现特征的方法，有助于充分利用问题特征改善概率预测的精度。收益管理中资源分配问题大多数是大规模非线性优化问题，利用一般性的最优化技术一般难以有效求解。收益管理中资源分配问题一般具有一些问题特征，如目标凸／凹性、可分离性等。分析这些问题特征，研究问题结构特征与最优解性质之间的关系，可以改善资源分配问题的求解方法。基于此，本文在分析问题的结构特征的基础上，寻求能够充分利用问题结构特征的解决思路与方法，研究了收益管理中若干需求与价格的概率预测问题与多种资源分配问题，取得了一定的研究结果。
本文的主要工作与贡献包括以下几个方面：
(1)若干需求与价格的概率预测问题研究。需求与价格是收益管理中的两类主要不确定要素。随着信息技术在收益管理中的广泛应用，发掘并利用数据的规律与问题的特征，以改善需求与价格的概率预测精度是收益管理的一个迫切要求。本文分别针对三个具有典型表现特征的收益管理问题——间断需求收益管理、具有删失信息的需求管理和非对称价格收益管理问题，通过提炼分析形成这些表现特征的内在机理，研究了需求与价格的概率预测问题。间断需求的形成主要受自身规律与外部要素的影响，如间断销售受到正常销售与大型促销活动的综合影响，间断备件需求受到备件寿命与设备维护操作的共同影响。航空业与零售业缺货造成的删失需求分布具有平滑性特点。股票与债券价格变动受到投资者风险偏好的影响存在非对性特点。
本文在发掘数据表现特征与分析表现特征形成机理的基础上，研究了可以充分利用问题特征，捕获数据表现特征的预测思路，提出了多种基于问题特征的概率预测方法。针对需求间断与非零需求是否平稳的特点，分析外部信息对间断需求的影响，研究了考虑自身规律与外部信息影响的间断需求概率预测问题，提出了两种将时间序列与因果分析进行集成的概率预测方法。针对删失需求数据不完全的特点，分析经典非参数方法在关键点处的估计偏差，利用需求分布具有平滑性特点，研究了具有删失信息的需求预测问题，提出了三种删失需求的概率预测方法。针对价格数据的非对称特点，分析非对称特点的形成原因，研究了非对称价格概率预测问题，提出了三种利用非对称分布的概率预测方法。在概率预测方法研究的基础上，进一步研究了一般性的概率预测评价问题。
上述部分研究已在国际上得到认可，相关结果发表在以下国际期刊：European Journal of Operational Research (2008, 185(2): 716-725), Journal of the Operational Research Society (2007, 58(1): 52-61), Applied Mathematics and Computation (2006, 181(2): 1035-1048), Expert Systems with Applications (2007,33(2)：434-440)。相关研究获得2006年安徽省高等学校优秀科技成果(自然科学类)一等奖。部分研究成果已开发成应用软件系统，在企业中获得应用推广，取得较好的经济效益。
(2)若干资源分配问题及其求解研究。研究资源分配问题的结构特征与解的性质，利用模型的结构特征，改善资源分配问题的求解，对收益管理在更多领域的推广应用有着重要的价值。收益管理中的资源分配问题主要包括基于数量与基于价格两类。基于数量的资源分配问题本质上都是大规模约束凸规划问题，这些问题从不同的角度可分为连续变量／整数变量问题，线性／非线性约束问题，目标函数可分离／不可分离问题等。基于价格的收益管理主要通过价格调整实现资源的合理分配，因此动态定价问题就成为收益管理的一个重要问题。
本文在分析资源分配问题结构特征与解的性质的基础上，研究了可以充分利用这些结构特征的模型求解思路和方法，提出了多种基于结构特征的资源分配问题的求解方法。针对凸可分线性约束与凸可分非线性两类连续多产品资源分配问题，通过分析问题的一般结构特征，得出了问题最优解的一般性质，提出了基于问题结构特征的最优解求解方法。针对NP完全的大规模整数多产品资源分配问题，通过分析模型的结构特征和解的性质，研究了利用问题的结构特征改善问题求解的思路，提出了基于结构特征的变量缩减方法和多种基于结构特征的启发式方法与近似求解方法。针对收益管理中市场份额与顾客价格敏感性同时未知，销售期内无法实现补充订货的零售问题特点，研究了带有主动需求学习的动态定价问题，比较了多种定价策略的异同。
上述部分研究已在国际上得到认可，相关结果发表(或接受发表)在以下国际期刊：European Journal of Operational Research, International Journal of Production Economics, Computers & Operations Research (33(3): 660-673),Applied Mathematical Modelling。所提出的基于结构特征的求解方法可快速有效地求得资源分配问题的最优解或近似解。
除了上述研究结果与贡献外，本文还指出了该领域一些值得进一步研究的前沿问题。
Revenue management (RM) is one of the most sucessful application areas ofoperations research, and it is also a hot spot of research on management science andoperations research. What is RM? RM is the process of understanding, anticipatingand reacting to consumer behavior and uncertain environment in order to maximizerevenues by allocating resources to different demands. As the rapid development ofeconomy globalization, and diversification of consumer behavior, supply chain forproducts is prolonged, and life cycle of products is shortened. In this environment, itis a critical problem faced bythe firms to study how to maximize the revenue withlimited resources. Revenue management is an effective pattern for addressing fiercemarket competition, and is a convenient way to allocate resources for managingdifferent demands. Theory and practice of revenue management has gained attentionrecently in many application areas, such as airlines, retailing, hotels, rental car, andenergy management.
In this growing competitive environment, the firms face two importantchallenges: one is how to recognize rapidly changing uncertain environment; antoheris how to utilize limited resources to meet diversified market demands. The majorityof revenue management decision-making problem is stochastic optimization model,and the input of the model relates to the probability distribution of decision elements.This needs to forecast the overall distribution of the uncertain environment elements.The result of probability forecast is the the basis of solving the decision-makingmodel, and the quality of probability forecast has direct influence on the decisions,thus it is important to improve probability forecast, and reseach on probabilityforecast issues becomes a fundamental issue in revenue management. Thedecision-making problems in revenue management are essentially resourceallocation problems, in which the limited resources are usually allocated throughquantity or price decisions. Resource allocation decisions directly affect corporate'srevenues, and the improvement on resource allocation decisions is particularlyimportant for maximizing the revenues, therefore the study on resource allocation problems is a core issue in revenue management.
The major difficulty of probability forecast in revenue management is, thatelements to be predicted show some specific features, such as intermittent,nonstationary, incomplete and asymmetry. These features make that most traditionalforecasting methods are generally difficult to be used or their forecast accuracy islow. These features generally relate to the the problem background of revenuemanagement. It is helpful to analyze the formation mechanism of these features forcapturing these features and improving the accuracy of probability forecasts. Most ofresource allocation problems in revenue management are large-scale nonlinearoptimization problems, which is not easily solved by applying the generaloptimization techniques. The resource allocation problems in revenue managementoften have some special features, such as concavity or convexity, separability of theobjective function, and so on. It can be used to develop solution methods for theresource allocation problems through analyzing these features and establishing therelationship between the optimal solution and these structural features. This thesisattempts to seek solution ideas and methods by taking full advantage of the problemstructural features for addressing several probability forecast problems and resourceallocation problem in RM, and some results are obtained.
Main contributions of this thesis are summarized as follows:
(1) Studies on several probability forecast problems. Demand and price are twomajor uncertain elements in revenue management. As the wider use of informationtechnology in revenue management, it is an urgent requirement to improve theaccuracy of probability forecast by exploring and using data features. For threerevenue management problem with typical features (intertimment demand, censoreddemand, and asymmetry price), we study probability forecast problems by extractingand modeling the inherent mechanism of these features. Intermittent demand can beattributed to its self-discipline and the impact of external factors, for example,intermittent sales data may come into being due to normal sales and large-scalepromotional activities; the intermittent spare parts demand is affected by the life ofspare parts and equipment maintenance operations. In airlines or retail industry,censored demand caused by shortages has smoothing demand distributions. The price change of stocks and bonds has some asymmetries due to the impact of riskpreferences of investors.
This thesis studies intrinsic features of different RM problems, and investigatestheir formation mechanism. Based on these analyses, the ideas and methods, whichcan be used to capture these features, are investigated, and several feature-basedprobablity forecasting methods are proposed. By analyzing the impact of externalfactors on intermittent demand, we propose two probability forecasting methods tointegrate auto-correlated process and the relationship between explanatory variablesand the nonzero demand, for predicting intertimment demand with stationary andnonstationary nonzero demand. By analyzing the estimation bias of product limitestimator on special points, and using the smoothing demand feature, we developthree distribution completion methods to forecast demand distribution from censoredobservations. By analyzing and capturing the asymmetry features in economic timeseries, we propose three density forecasting methods under two-piece normaldistribution. Based on the studies of probability forecasting methods, we also studyhow to evalute probability forecast, and a general definition for reliability ofprobability forecasts and three reliability-oriented measures are proposed.
Some of the above studies have been internationally recognized, and the relevantresults have been pubished on the following international journals: EuropeanJournal of Operational Research (2008, 185(2): 716-725), Journal of theOperational Research Society (2007, 58(1): 52-61), Applied Mathematics andComputation (2006, 181(2): 1035-1048), Expert Systems with Applications (2007,33(2): 434-440). Some researches have developed into application software systems,which achieved significant economic benefits in several enterprises.
(2) Studies on several resource allocation problems. It has an important value tostudy the resource allocation problems in RM by analyzing and utilizing theirstructural features. Resource allocation problems in RM can be divided into twocategries: quantity-based RM and price-based RM. Most of quantity-based resourceallocation problems in revenue management are large-scale convex optimizationproblem. These problems can be divided from different perspectives into: continuousor integer variables, linear or nonlinear constraints, separable or nonseparable objective. Price-based RM studies how to adjust price for allocating resources, sodynamic pricing probem is another important problem in RM.
This thesis studies several resource allocation problems with different structuralfeatures, and propose several feature-based solution methods for these problems, byanalyzing the relationship between the solution and the structural features. Forcontinuous convex seperable multi-product resource allocation problems with linearand nonlinear constraints, we propose several methods for solving their optimalsolution by utilizing their structural features. For large-scale NP-complete integralresource allocation problems, we propose a variable reduction technique to reducethe size of problem without sacrificing optimality. Based on the structural features,we also propose several efficient heuristics and approximate solution methods. Forthe case that the market size and customers' response to price are both unknown, andthere is no chance of inventory replenishment during the sales season, we study anactive demand learning pricing strategy for dynamic pricing problem, and compare itwith other pricing strategies.
Part of these studies has been internationally recognized, and the relevant resultshave been pubished (or accepted for publication) on the following internationaljournals: European Journal of Operational Research, International Journal ofProduction Economics, Computers & Operations Research (33(3): 660-673),Applied Mathematical Modelling. The proposed methods can solve the optimal orappoximate solutions to the resource allocation problems quickly.
Finally, in addtion to the above achivements in RM, the thesis discusses somechallenging topics which deserve further research in future.
在这种日益加剧的竞争环境下，企业主要面临两个问题：一、如何认识瞬息万变的不确定环境；二、如何利用有限的资源满足多样化的市场需求。大多数收益管理决策问题都是随机优化模型，模型的输入涉及相关决策要素的概率分布，需要预测不确定环境要素的整体分布。概率预测的结果是决策模型求解的基础，概率预测的质量直接影响决策的优劣，因此改善概率预测精度对收益管理有着重要的价值，研究概率预测问题成为收益管理中的一个基本问题。收益管理决策问题本质上是资源分配问题，一般是通过数量或价格决策控制有限资源的分配。资源分配决策直接影响企业收益，改善资源分配决策对实现收益最大化尤其重要，因此研究资源分配问题成为收益管理中的一个核心问题。
收益管理中概率预测面临的主要困难是，有待预测的要素一般表现出一些特征，如间断特征、非平稳特征、不完全特征、非对称特征等。这些表现特征使得多数传统的预测方法一般难以应用或预测精度不高。这些表现特征一般与收益管理问题的实际背景有关，分析这些表现特征的形成机理，有助于研究捕获这些表现特征的方法，有助于充分利用问题特征改善概率预测的精度。收益管理中资源分配问题大多数是大规模非线性优化问题，利用一般性的最优化技术一般难以有效求解。收益管理中资源分配问题一般具有一些问题特征，如目标凸／凹性、可分离性等。分析这些问题特征，研究问题结构特征与最优解性质之间的关系，可以改善资源分配问题的求解方法。基于此，本文在分析问题的结构特征的基础上，寻求能够充分利用问题结构特征的解决思路与方法，研究了收益管理中若干需求与价格的概率预测问题与多种资源分配问题，取得了一定的研究结果。
本文的主要工作与贡献包括以下几个方面：
(1)若干需求与价格的概率预测问题研究。需求与价格是收益管理中的两类主要不确定要素。随着信息技术在收益管理中的广泛应用，发掘并利用数据的规律与问题的特征，以改善需求与价格的概率预测精度是收益管理的一个迫切要求。本文分别针对三个具有典型表现特征的收益管理问题——间断需求收益管理、具有删失信息的需求管理和非对称价格收益管理问题，通过提炼分析形成这些表现特征的内在机理，研究了需求与价格的概率预测问题。间断需求的形成主要受自身规律与外部要素的影响，如间断销售受到正常销售与大型促销活动的综合影响，间断备件需求受到备件寿命与设备维护操作的共同影响。航空业与零售业缺货造成的删失需求分布具有平滑性特点。股票与债券价格变动受到投资者风险偏好的影响存在非对性特点。
本文在发掘数据表现特征与分析表现特征形成机理的基础上，研究了可以充分利用问题特征，捕获数据表现特征的预测思路，提出了多种基于问题特征的概率预测方法。针对需求间断与非零需求是否平稳的特点，分析外部信息对间断需求的影响，研究了考虑自身规律与外部信息影响的间断需求概率预测问题，提出了两种将时间序列与因果分析进行集成的概率预测方法。针对删失需求数据不完全的特点，分析经典非参数方法在关键点处的估计偏差，利用需求分布具有平滑性特点，研究了具有删失信息的需求预测问题，提出了三种删失需求的概率预测方法。针对价格数据的非对称特点，分析非对称特点的形成原因，研究了非对称价格概率预测问题，提出了三种利用非对称分布的概率预测方法。在概率预测方法研究的基础上，进一步研究了一般性的概率预测评价问题。
上述部分研究已在国际上得到认可，相关结果发表在以下国际期刊：European Journal of Operational Research (2008, 185(2): 716-725), Journal of the Operational Research Society (2007, 58(1): 52-61), Applied Mathematics and Computation (2006, 181(2): 1035-1048), Expert Systems with Applications (2007,33(2)：434-440)。相关研究获得2006年安徽省高等学校优秀科技成果(自然科学类)一等奖。部分研究成果已开发成应用软件系统，在企业中获得应用推广，取得较好的经济效益。
(2)若干资源分配问题及其求解研究。研究资源分配问题的结构特征与解的性质，利用模型的结构特征，改善资源分配问题的求解，对收益管理在更多领域的推广应用有着重要的价值。收益管理中的资源分配问题主要包括基于数量与基于价格两类。基于数量的资源分配问题本质上都是大规模约束凸规划问题，这些问题从不同的角度可分为连续变量／整数变量问题，线性／非线性约束问题，目标函数可分离／不可分离问题等。基于价格的收益管理主要通过价格调整实现资源的合理分配，因此动态定价问题就成为收益管理的一个重要问题。
本文在分析资源分配问题结构特征与解的性质的基础上，研究了可以充分利用这些结构特征的模型求解思路和方法，提出了多种基于结构特征的资源分配问题的求解方法。针对凸可分线性约束与凸可分非线性两类连续多产品资源分配问题，通过分析问题的一般结构特征，得出了问题最优解的一般性质，提出了基于问题结构特征的最优解求解方法。针对NP完全的大规模整数多产品资源分配问题，通过分析模型的结构特征和解的性质，研究了利用问题的结构特征改善问题求解的思路，提出了基于结构特征的变量缩减方法和多种基于结构特征的启发式方法与近似求解方法。针对收益管理中市场份额与顾客价格敏感性同时未知，销售期内无法实现补充订货的零售问题特点，研究了带有主动需求学习的动态定价问题，比较了多种定价策略的异同。
上述部分研究已在国际上得到认可，相关结果发表(或接受发表)在以下国际期刊：European Journal of Operational Research, International Journal of Production Economics, Computers & Operations Research (33(3): 660-673),Applied Mathematical Modelling。所提出的基于结构特征的求解方法可快速有效地求得资源分配问题的最优解或近似解。
除了上述研究结果与贡献外，本文还指出了该领域一些值得进一步研究的前沿问题。
Revenue management (RM) is one of the most sucessful application areas ofoperations research, and it is also a hot spot of research on management science andoperations research. What is RM? RM is the process of understanding, anticipatingand reacting to consumer behavior and uncertain environment in order to maximizerevenues by allocating resources to different demands. As the rapid development ofeconomy globalization, and diversification of consumer behavior, supply chain forproducts is prolonged, and life cycle of products is shortened. In this environment, itis a critical problem faced bythe firms to study how to maximize the revenue withlimited resources. Revenue management is an effective pattern for addressing fiercemarket competition, and is a convenient way to allocate resources for managingdifferent demands. Theory and practice of revenue management has gained attentionrecently in many application areas, such as airlines, retailing, hotels, rental car, andenergy management.
In this growing competitive environment, the firms face two importantchallenges: one is how to recognize rapidly changing uncertain environment; antoheris how to utilize limited resources to meet diversified market demands. The majorityof revenue management decision-making problem is stochastic optimization model,and the input of the model relates to the probability distribution of decision elements.This needs to forecast the overall distribution of the uncertain environment elements.The result of probability forecast is the the basis of solving the decision-makingmodel, and the quality of probability forecast has direct influence on the decisions,thus it is important to improve probability forecast, and reseach on probabilityforecast issues becomes a fundamental issue in revenue management. Thedecision-making problems in revenue management are essentially resourceallocation problems, in which the limited resources are usually allocated throughquantity or price decisions. Resource allocation decisions directly affect corporate'srevenues, and the improvement on resource allocation decisions is particularlyimportant for maximizing the revenues, therefore the study on resource allocation problems is a core issue in revenue management.
The major difficulty of probability forecast in revenue management is, thatelements to be predicted show some specific features, such as intermittent,nonstationary, incomplete and asymmetry. These features make that most traditionalforecasting methods are generally difficult to be used or their forecast accuracy islow. These features generally relate to the the problem background of revenuemanagement. It is helpful to analyze the formation mechanism of these features forcapturing these features and improving the accuracy of probability forecasts. Most ofresource allocation problems in revenue management are large-scale nonlinearoptimization problems, which is not easily solved by applying the generaloptimization techniques. The resource allocation problems in revenue managementoften have some special features, such as concavity or convexity, separability of theobjective function, and so on. It can be used to develop solution methods for theresource allocation problems through analyzing these features and establishing therelationship between the optimal solution and these structural features. This thesisattempts to seek solution ideas and methods by taking full advantage of the problemstructural features for addressing several probability forecast problems and resourceallocation problem in RM, and some results are obtained.
Main contributions of this thesis are summarized as follows:
(1) Studies on several probability forecast problems. Demand and price are twomajor uncertain elements in revenue management. As the wider use of informationtechnology in revenue management, it is an urgent requirement to improve theaccuracy of probability forecast by exploring and using data features. For threerevenue management problem with typical features (intertimment demand, censoreddemand, and asymmetry price), we study probability forecast problems by extractingand modeling the inherent mechanism of these features. Intermittent demand can beattributed to its self-discipline and the impact of external factors, for example,intermittent sales data may come into being due to normal sales and large-scalepromotional activities; the intermittent spare parts demand is affected by the life ofspare parts and equipment maintenance operations. In airlines or retail industry,censored demand caused by shortages has smoothing demand distributions. The price change of stocks and bonds has some asymmetries due to the impact of riskpreferences of investors.
This thesis studies intrinsic features of different RM problems, and investigatestheir formation mechanism. Based on these analyses, the ideas and methods, whichcan be used to capture these features, are investigated, and several feature-basedprobablity forecasting methods are proposed. By analyzing the impact of externalfactors on intermittent demand, we propose two probability forecasting methods tointegrate auto-correlated process and the relationship between explanatory variablesand the nonzero demand, for predicting intertimment demand with stationary andnonstationary nonzero demand. By analyzing the estimation bias of product limitestimator on special points, and using the smoothing demand feature, we developthree distribution completion methods to forecast demand distribution from censoredobservations. By analyzing and capturing the asymmetry features in economic timeseries, we propose three density forecasting methods under two-piece normaldistribution. Based on the studies of probability forecasting methods, we also studyhow to evalute probability forecast, and a general definition for reliability ofprobability forecasts and three reliability-oriented measures are proposed.
Some of the above studies have been internationally recognized, and the relevantresults have been pubished on the following international journals: EuropeanJournal of Operational Research (2008, 185(2): 716-725), Journal of theOperational Research Society (2007, 58(1): 52-61), Applied Mathematics andComputation (2006, 181(2): 1035-1048), Expert Systems with Applications (2007,33(2): 434-440). Some researches have developed into application software systems,which achieved significant economic benefits in several enterprises.
(2) Studies on several resource allocation problems. It has an important value tostudy the resource allocation problems in RM by analyzing and utilizing theirstructural features. Resource allocation problems in RM can be divided into twocategries: quantity-based RM and price-based RM. Most of quantity-based resourceallocation problems in revenue management are large-scale convex optimizationproblem. These problems can be divided from different perspectives into: continuousor integer variables, linear or nonlinear constraints, separable or nonseparable objective. Price-based RM studies how to adjust price for allocating resources, sodynamic pricing probem is another important problem in RM.
This thesis studies several resource allocation problems with different structuralfeatures, and propose several feature-based solution methods for these problems, byanalyzing the relationship between the solution and the structural features. Forcontinuous convex seperable multi-product resource allocation problems with linearand nonlinear constraints, we propose several methods for solving their optimalsolution by utilizing their structural features. For large-scale NP-complete integralresource allocation problems, we propose a variable reduction technique to reducethe size of problem without sacrificing optimality. Based on the structural features,we also propose several efficient heuristics and approximate solution methods. Forthe case that the market size and customers' response to price are both unknown, andthere is no chance of inventory replenishment during the sales season, we study anactive demand learning pricing strategy for dynamic pricing problem, and compare itwith other pricing strategies.
Part of these studies has been internationally recognized, and the relevant resultshave been pubished (or accepted for publication) on the following internationaljournals: European Journal of Operational Research, International Journal ofProduction Economics, Computers & Operations Research (33(3): 660-673),Applied Mathematical Modelling. The proposed methods can solve the optimal orappoximate solutions to the resource allocation problems quickly.
Finally, in addtion to the above achivements in RM, the thesis discusses somechallenging topics which deserve further research in future.
引文
[1] Talluri KT, van Ryzin GJ. The theory and practice of revenue management. Kluwer Academic Publishers, Boston; 2004.
[2] Belobaba PP. Air travel demand and airline seat inventory management, Ph.D. thesis, Flight Transportation Laboratory, Massachusetts Institute of Technology, Cambridge, MA; 1987.
[3] Smith BC, Leimkuhler JF, Darrow RM. Yield Management at American Airlines. Interfaces 1992; 22; 8-31.
[4] Cross RG. An introduction to revenue management. In The Handbook of Airline Economics, Jenkins D, (ed.), The Aviation Weekly Group of the McGraw-Hill Companies, New York, NY; 1995; 443-468,.
[5] Dunleavy HN. Airline passenger overbooking. In The Handbook of Airline Economics, Jenkins (ed.) D, The Aviation Weekly Group of the McGraw-Hill Companies, New York, NY; 1995; 469-482.
[6] Vinod B. Origin-and-destination yield management. In The Handbook of Airline Economics, Jenkins (ed.) D, The Aviation Weekly Group of the McGraw-Hill Companies, New York, NY; 1995; 459-468.
[7] McGill JI, van Ryzin GJ. Revenue management: Research overview and prospects. Transportation Science 1999; 33; 233-256.
[8] Bitran GR, Caldentey R. An overview of pricing models for revenue management. Manufacturing & Service Operations Management 2003; 5; 203-229.
[9] Elmaghraby W, Keskinocak P. Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 2003; 49(10); 1287-1309.
[10] Box GEP, Jenkins G M. Time Series Analysis: Forecasting and Control. Holden-Day, Oakland, CA; 1976.
[11] DeGroot MH. Probability and Statistics, Addison Wesley, Reading, MA, 2nd edition, 1985.
[12] Sun S. The fine-tuned learning enhancement to the standard backpropagation algorithm. In Reservations and Yield Management Study Group Annual Meeting Proceedings, Zurich, Switzerland, 1996. AGIFORS.
[13] Ting SC, Tzeng GH. Fuzzy multi-objective programming approach to allocating containership slots for liner shipping revenue management. In MCDM Winter Conference, Semmering, Austria, 2002.
[14] Basgall M. Hotel help: Fuzzy thinking helps clear up tradeoffs on hotel reservations, June 1998. Duke University News, News release.
[15] Mulhern FJ, Caprara RJ. A nearest neighbor model for forecasting market response. International Journal of Forecasting 1994; 10; 191-207.
[16] J. M. Bates and C. W. J. Granger. The combination of forecasts. Operational Research Quarterly 1969; 20; 451-468.
[17] McGill JI. Censored regression analysis of multiclass demand data subject to joint capacity constraints. Annals of Operations Research 1995; 60; 209-240.
[18] Allenby GM, Arora N, Ginter JL. On the heterogeneity of demand. Journal of Marketing Research 1998; 35; 384-89.
[19] Kaplan EL, Meier P. Nonparametric estimates from incomplete observations. American Statistical Association Journal 1958; 53; 457-481.
[20] Zeni RH. Improved forecast accuracy in airline revenue management by unconstraining demand estimates from censored data. PhD thesis, Graduate School, Rutgers, State University of New Jersey, 2001.
[21] Willemain TR, Smart CN, Schwarz HF. A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting 2004; 20; 375-387.
[22] Littlewood K. Forecasting and control of passenger bookings, in AGIFORS Symposium Proc. 12, Nathanya, Israel; 1972.
[23] Belobaba PP. Revenue and competitive impacts of O-D control: Summary of PODS results. In First Annual INFORMS Revenue Management Section Meeting, New York, NY; 2001.
[24] Williamson EL. Airline Network Seat Inventory Control: Methodologies and Revenue Impacts. PhD thesis, Flight Transportation Laboratory, MIT, Cambridge, MA; 1992.
[25] Karaesman I, van Ryzin GJ. Overbooking with substituable inventory classes. Operations Research 2004; 52(1); 83-104.
[26] Bitran GR, Gilbert SM. Managing Hotel Reservations with Uncertain Arrivals. Operations Research 1996; 44; 35-49.
[27] Lee TC, Hersh M. A model for dynamic airline seat inventory control with multiple seat bookings. Transportation Sciece 1993; 27; 252-265.
[28] Talluri KT, van Ryzin G. Revenue management under a general discrete choice model of consumer behavior. Management Science 2004; 50; 15-33.
[29] Bitran GR, Caldentey R. An overview of pricing models for revenue management. Manufacturing & Service Operations Management 2003; 5; 203-229.
[30] Elmaghraby W, Keskinocak P. Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 2003; 49(10); 1287-1309.
[31] Polt S. Forecasting is difficult-especially if it refers to the future. In Reservations and Yield Management Study Group Annual Meeting Proceedings, Melbourne, Australia, 1998.
[1] Huiskonen J. Maintenance spare parts logistics: Special characteristics and strategic choices, International Journal of Production Economics 2004; 71; 125- 133.
[2] Croston JD. Forecasting and stock control for intermittent demands. Operational Research Quarterly 1972; 23(3); 289-303.
[3] Rao AV. A comment on: forecasting and stock control for intermittent demands. Operational Research Quarterly 1973; 24(4); 639-640.
[4] Willemain TR, Smart CN and Schwarz HF. A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting 2004; 20; 375-387.
[5] Willemain TR, Smart CN, Shockor JH and DeSautels PA. Forecasting intermittent demand in manufacturing: a comparative evaluation of Croston's method. International Journal of Forecasting 1994; 10(4); 529-538.
[6] Willemain TR, Ratti EWL, Smart CN. Forecasting intermittent demand using a cox process model. INFORMS Meetings, Boston, USA, 1994; 1-14.
[7] Johnston FR and Boylan JE. Forecasting for items with intermittent demand, Journal of the Operational Research Society 1996; 47; 113-121.
[8] Ghobbar AA and Friend CH. Evaluation of forecasting methods for intermittent parts demand in the field of aviation: a predictive model. Computers & Operations Research 2003;30;2097-2114.
[9] Silver EA. Operations research in inventory management: A review and critique. Operations Research 1981; 29; 628-645.
[10] Kennedy WJ, Patterson JW, Fredendall LD. An overview of recent literature on spare parts inventories. International Journal of Production Economics 2002; 76; 201-215.
[11] Wang M, Rao SS. Estimating reorder points and other management science applications by bootstrap procedure. European Journal of Operational Research 1992; 56; 332-342.
[12]Lau HS, Wang MC. Estimating the lead-time demand distribution when the daily demand is non-normal and autocorrelated. European Journal of Operational Research 1987; 29; 60-69.
[13] Tyworth JE, O'Neill L. Robustness of the normal approximation of lead-time demand in a distribution setting. Naval Research Logistics 1997; 44; 165-186.
[14]Petrovic D, Petrovic R. SPARTA II: Further development in an expert system for advising on stocks of spare parts. International Journal of Production Economics 1992; 24; 291-300.
[15]Dunsmuir WTM, Snyder RD. Control of inventories with intermittent demand. European Journal of Operational Research 1989; 40; 16-21.
[16] Ward JB. Determining reorder points when demand is lumpy. Management Science 1978; 24; 623-632.
[17] Bier IJ. Boeing commercial airplane group spares department: simulation of spare parts operations. ORSA/TIMS Joint National Meeting, Detroit, MI, 1984.
[18] Sani B, Kingsman BG. Selecting the best periodic inventory control and demand forecasting methods for low demand items. Journal of the Operational Research Society 1997; 48; 700-713.
[19] Efron B. Bootstrap methods: another look at the jackknife. Annals of Statistics 1979; 7; 1-26.
[20] Gamero MJ, Garcia JM and Reyes AM. Bootstrapping statistical functionals, Statistics & Probability Letters 1998; 39(3); 229-236.
[21] Bookbinder JH and Lordahl AE. Estimation of inventory re-order levels using the bootstrap statistical procedure. HE Transactions 1989; 21; 302-312.
[22] Snyder R. Forecasting sales of slow and fast moving inventories. European Journal of Operational Research 2002; 140; 684-699.
[23] Vapnik VN. The Nature of Statistical Learning Theory. New York: Springer; 2000.
[24] Vapnik VN, Golowich SE, Smola AJ. Support vector method for function approximation, regression estimation, and signal processing. Advances in Neural Information Processing Systems 1996; 9; 281-287.
[25] Muller KR, Smola AJ, Ratsch G, Scholkopf B, Kohlmorgen J. Using support vector machines for time series prediction. In: Scholkopf B, Burges CJC, Smola AJ (Eds.). Advances in Kernel Methods—Support Vector Learning, MIT Press, Cambridge, MA, 1999;243-254.
[26] Tay FEH, Cao LJ. Application of support vector machines in financial time series forecasting, Omega 2001; 29(4); 309-317.
[27] Cao LJ, Tay FEH. Support vector machine with adaptive parameters in financial time series forecasting. IEEE Transactions on Neural Networks 2003; 14(6); 1506-1518.
[28] Kim K. Financial time series forecasting using support vector machines. Neurocomputing 2003; 55; 307-319.
[29] Bao Y, Wang W, Zhang J. Forecasting intermittent demand by SVMs regression. IEEE International Conference on Systems, Man and Cybernetics 2004; 1; 461-466.
[30] Pai PF, Lin CS. A hybrid ARIMA and support vector machines model in stock price forecasting. Omega 2005; 33; 497-505.
[31] Jovanis PP and Chang H. Modeling the relationship of accidents to miles traveled. Transportation Research Record 1068, TRB, National Research Council, Washington, DC, 1986; 42-51.
[32] Milton J, Mannering F. Relationship among highway geometric, traffic-related elements, and motor-vehicle accident requencies. In the 76th Annual Meeting of the Transportation Research Board, Washington, DC; 1997.
[33] Gooijer JGD, Vidiella-i-Anguera A. Forecasting threshold cointegrated systems. International Journal of Forecasting 2004; 20; 237-253.
[34] Herzel H, Grope I. Measuring correlations in symbol sequences. Physica A 1995; 216; 518-542.
[35] Mosteller F, Tukey JW. Data analysis and regression: A second course in statistics. Reading, MA: Addison-Wesley; 1977.
[36] 张斌，华中生。一种改进的求解含等式约束凸二次规划问题的Lemke算法。中国科学技术大学学报 2004；34(6)；668-677。
[37] Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 1958; 53; 457-481.
[38] Khouja M. The single-period (news-vendor) problem: literature review and suggestions for future research. Omega 1999; 27(5); 537-553.
[39] Hadley G, Whitin, TM. Analysis of inventory systems. Prentice-Hall, Englewood Cliffs; 1963.
[40] Lau HS, Lau, AHL. Estimating the demand distributions of single-period items having frequent stockouts. European Journal of Operational Research 1996; 92; 254-265.
[41] Gillespie B, Gillespie J, Iglewicz B. A comparison of the bias in four versions of the product-limit estimator. Biometrika 1992; 79; 149-155.
[42] Conrad SA. Sales data and the estimation of demand. Operational Research Quarterly 1976; 27(1); 123-127.
[43] Wecker W. Predicting demand from sales data in the presence of stockouts. Management Science 1978; 24; 1043-1054.
[44] Braden DB, Freimer M. Informational dynamics of censored observations. Management Science 199t; 37(11); 1390-1404.
[45] Agrawal NS, Smith A. Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Research Logistics 1996; 43; 839-861.
[46] Bell PC. Adaptive sales forecasting with many stockouts. Journal of the Operational Research Society 1981; 32; 865-873.
[47] Bell PC. A new procedure for the distribution of periodicals. Journal of the Operational Research Society 1978; 29; 427-434.
[48] Bell PC. Forecasting demand variation when there are stockouts. Journal of the Operational Research Society 2000; 51(3); 358-363.
[49] Ding X. Estimation and optimization in discrete inventory models. Ph.D. thesis, Faculty of Commerce, The University of British Columbia, Vancouver, Canada; 2002.
[50] Coolen FPA, Yan K.J. Nonparametric predictive inference with right-censored data. Journal of Statistical Planning and Inference 2004; 126; 25-54.
[51] Efron B. The two sample problem with censored data. Proceedings of the 5th Berkeley Symposium 1967; 4; 831-852.
[52] Gill RD. Censoring and stochastic integrals. Mathematical Centre Tract No. 124, Mathematisch Centrum, Amsterdam; 1980.
[53] Chen Z, Phadia E. An optimal completion of the product limit estimator. Statistics & Probability Letters 2006; 76; 913-919.
[54] Brown BW, Jr. Hollander M, Korwar RM. Nonparametric tests of independence for censored data, with applications to heart transplant studies. In: Proschan F, Serfling, RJ (Eds.), Reliability and Biometry: Statistical Analysis of Lifelength, Philadelphia: Society for Industrial and Applied Mathematics 1974; 291-302.
[55] Moeschberger ML, Klein JP. A comparison of several methods of estimating the survival function when there is extreme right censoring. Biometrics 1985; 41; 253-259.
[56] Meier P. Estimation of a distribution function from incomplete observations. In: Gani J (Eds.), Perspectives in Probability and Statistics, Sheffield, England: Applied Probability Turst 1975; 67-87.
[57] Geurts JHJ. Some small-samplel nonproportional hazards results for the Kaplan-Meier esitmator. Statistica Neerlandica 1985; 39; 1-13.
[58] Geurts JHJ. On the small-sample performance of Efron's and of Gill's version of the product limit estimator under nonproportional hazards. Biometrics 1987; 43; 683-692.
[59] Sarno L, Valente G. Comparing the accuracy of density forecasts from competing models. Journal of Forecasting 2004; 23; 541-555.
[60] Bellini F, Figa-Talamanca G. Runs tests for assessing volatility forecastability in financial time series. European Journal of Operational Research 2005; 163; 102-114.
[61] Reeves JJ. Bootstrap prediction intervals for ARCH models. International Journal of Forecasting 2005; 21; 237-248.
[62]Tay AS, Wallis KF. Density forecasting: a survey. Journal of Forecasting 2000; 19; 235-254.
[63] Wallis KF. Asymmetric density forecasts of inflation and the bank of England's fan chart. National Institute Economic Review 1999; 167; 106-112.
[64] Wallis KF; An assessment of bank of England and national institute inflation forecast uncertainties. National Institute Economic Review 2004; 189; 64-71.
[65] Li WK, Lam K. Modelling asymmetry in stock returns by a threshold ARCH model. The Statistician 1995; 44; 333-341.
[66] Sarantis N. Nonlinearities, cyclical behavior and predictability in stock markets: International evidence. International Journal of Forecasting 2001; 17; 459-482.
[67] Brannas K, De Gooijer JG. Asymmetries in conditional mean and variance: modelling stock returns by asMA-asQGARCH. Journal of Forecasting 2004; 23; 155-171.
[68] Bekaert G, Wu G. Asymmetric volatility and risk in equity markets, Review of Financial Studies 2000; 13; 1-42.
[69] Wu G. The determinants of asymmetric volatility. Review of Financial Studies 2001; 14(3); 837-859.
[70] Engle RF, Ng VK. Measuring and testing the impact of news on volatility. Journal of Finance 1993; 48; 1749-1778.
[71] Rabemananjara R, Zakoian JM. Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics 1993; 8; 271-301.
[72] So MKP, Li WK, Lam K. A threshold stochastic volatility model. Journal of Forecasting 2002; 21; 473-500.
[73] Box GEP, Jenkins GM, Reinsel GC. Time series analysis, Forecasting and Control, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall; 1994.
[74] Carrasco M, Chen X. Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 2002; 18; 17-39.
[75] Engle RF. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 1982; 50; 987-1008.
[76] Bollerslev T. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 1986; 31; 307-327.
[77] Taylor JW. Evaluating volatility and interval forecasts. Journal of Forecasting 1999; 18; 111-128.
[78] Maddala GS, Li H. Bootstrap based tests in financial models. In Maddala, G.S. and Rao, CR. (eds). Handbook of Statistics, vol. 14, Elsevier, Amsterdam, 1996; 463-488.
[79] Kunsch HR. The jackknife and the bootstrap for general stationary observations. Annals of Statistics 1989; 17; 1217-1241.
[80] Ruiz E, Pascual L. Bootstrapping financial time series. Journal of Economic Surveys 2002; 16(3); 271-300.
[81] Politis DN, Romano JP. The stationary bootstrap, Journal of the American Statistical Association 1994; 89; 1303-1313.
[82] Hansen PR, Lunde A. A forecast comparison of volatility models: does anything beat a GARCH (1,1)? Journal of Applied Econometrics 2005; 20; 873-889.
[83] Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions, 2nd ed., vol.1. New York: Wiley; 1994.
[84] John S. The three-parameter two-piece normal family of distributions and its fitting. Communications in Statistics-Theory and Methods 1982; 11; 879-885.
[85] Huang YC, Lin BJ. Value-at-risk analysis for Taiwan stock index futures: Fat tails and conditional asymmetries in return innovations. Review of Quantitative Finance and Accounting 2004; 22; 79-95.
[86] Newey WK, West KD. A Simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 1987; 55(3); 703-708.
[87] Diebold FX, Gunther TA, Tay AS. Evaluating density forecasts: with application to financial risk management. International Economic Review 1998; 39; 863-883.
[88] Berkowitz J. Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics 2001; 19; 465-474.
[89] Boero G, Marrocu E. The performance of SETAR models: a regime conditional evaluation of point, interval and density forecasts. International Journal of Forecasting 2004; 20(2); 305-320.
[90] Clements MP, Taylor N. Evaluating interval forecasts of high-frequency financial data, Journal of Applied Econometrics 2003; 18(4); 445-456.
[91] Pascual L, Romo J, Ruiz E. Bootstrap prediction intervals for power-transformed time series. International Journal of Forecasting 2005; 21; 219-236.
[92] Alho JM, Vanne R. On predictive distributions of public net liabilities. International Journal of Forecasting, doi: 10.1016/j.ijforecast.2005.11.005; 2006.
[93] Clements MP, Smith J. Evaluating multivariate forecast densities: A comparison of two approaches. International Journal of Forecasting 2002; 18; 397- 407.
[94] De Gooijer JG, Hyndman RJ. 25 years of time series forecasting. International Journal of Forecasting, doi: 10.1016/j.ijforecast.2005.07.001; 2006.
[95] Jewson S, Ziehmann C. Five guidelines for the evaluation of site-specific medium range probabilistic temperature forecasts. http://arxiv.org/PS_cache/physics/pdf/0310/ 0310021.pdf; 2003.
[96] Diebold FX, Lopez JA. Forecast evaluation and combination. In Handbook of Statistics 14, Maddala GS, Rao CA (eds). Elsevier: Amsterdam 1996; 241-268.
[97] Wilks DS. Statistical Methods in the Atmospheric Sciences-An Introduction. Academic Press: London; 1995.
[98] Potgieter AB, Everingham YL, Hammer GL. On measuring quality of a probabilistic commodity forecast for a system that incorporates seasonal climate forecasts. International Journal of Climatology 2003; 23; 1195-1210.
[99] Clements MP, Smith J. Evaluating the forecast densities of linear and non-linear models: applications to output growth and unemployment. Journal of Forecasting 2000; 19; 255-276.
[100] Wallis KF. Chi-squared tests of interval and density forecasts, and the Bank of England fan charts. International Journal of Forecasting 2003; 19; 165-175.
[101] Christoph K, Burkhart F. Instrumental and test-retest reliability of saccadic measures. Biological Psychology 2005; 68(3); 201-213.
[102] Ebeling CE. An Introduction to Reliability and Maintainability Engineering, McGraw-Hill International Editions 1997; pp 487.
[103] Jolliffe IT, Stephenson DB. Forecast Verification. A Practitioner's Guide in Atmospheric Science. Wiley and Sons Ltd; 2003.
[104] Potts JM, Folland CK, Jolliffe IT, Sexton D. Revised "LEPS" scores for assessing climate model simulations and long-range forecasts. Journal of Climate 1996; 9; 34-53.
[105] Mason SJ, Graham NE. Conditional probabilities, relative operating characteristics, and relative operating levels. Weather and Forecasting 1999; 14; 713-725.
[106] Lee WC. Selecting diagnostic tests for ruling out or ruling in disease: the use of the Kullback-Leibler distance. International Journal of Epidemiology 1999; 28; 521-525.
[107] Kruskall WH, Wallis WA. Use of ranks on one-criterion variance analysis. Journal of the American Statistical Association 1952; 48; 907-911.
[1] Hadley G, Whitin T. Analysis of Inventory Systems. Prentice-Hall, Englewood Cliffs, NJ; 1963.
[2] Khouja M. The single-period (news-vendor) problem: Literature review and suggestions for future research. Omega International Journal of Management Science 1999; 27; 537-553.
[3] Erlebacher SJ. Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint. Production and Operations Management 2000; 9(3); 303-318.
[4] Vairaktarakis GL. Robust multi-item Newsboy models with a budget constraint. International Journal of Production Economics 2000; 66; 213-226.
[5] Abdel-Malek L, Montanari R, Morales LC. Exact, approximate, and generic terative models for the multi-product newsboy with budget constraint. International Journal of Production Economics 2004; 91; 189-198.
[6] Abdel-Malek L, Montanari R. An analysis of the multi-product newsboy problem with a budget constraint. International Journal of Production Economics 2005; 97; 296-307.
[7] Ben-Daya M, Raouf A. On the constrained multi-product single period inventory problem. International Journal of Operations & Production Management 1993; 13; 104-112.
[8] Gallego G, Moon I. The distribution free newsboy problem: Review and extensions. Journal of Operational Research Society 1993; 44; 825-834.
[9] Moon I, Silver E. The multi-item newsvendor problem with a budget constraint and fixed ordering costs. Journal of Operational Research Society 2000; 51; 602-608.
[10] Lau HS, Lau AHL. The multi-product multi constraint Newsboy problem: Applications formulation and solution. Journal of Operations Management 1995; 13; 153-162.
[11] Lau HS, Lau AHL. The newsstand problem: A capacitated multiple-product single-period inventory problem. European Journal of Operational Research 1996; 94; 29-42.
[12] Hua Z, Zhang B, Liang L. An approximate dynamic programming approach to convex quadratic knapsack problems. Computers & Operations Research 2006; 33(3); 660-673.
[13] Bretthauer KM, Shetty B. The nonlinear knapsack problem-algorithms and applications. European Journal of Operational Research 2002; 138; 459-472.
[14] Zhang B, Hua ZS, 2007. A binary solution method for the multi-product newsboy problem with budget constraint. Accepted by International Journal of Production Economics.
[15]Luss H, Gupta SK. Allocation of effort resources among competing activities. Operations Research 1975; 23; 360-366.
[16] Zipkin PH. Simple ranking methods for allocation of one resource. Management Science 1980; 26; 34-43.
[17] Bitran GR, Hax AC. Disaggregation and resource allocation using convex knapsack problems with bounded variables. Management Science 1981; 27; 431-441.
[18] Hochbaum DS. Lower and upper bounds for the allocation problem and other nonlinear optimization problems. Mathematics of Operations Research 1994; 19; 390-409.
[19] Bretthauer KM, Shetty B, Syam S, White S. A model for resource constrained production and inventory management. Decision Sciences 1994; 25; 561-580.
[20] Bretthauer KM, Shetty B, Syam S. A branch and bound algorithm for integer quadratic knapsack problems. ORSA Journal on Computing 1995; 7; 109-116.
[21 ] Bretthauer KM, Ross A, Shetty B. Nonlinear integer programming for optimal allocation in stratified sampling. European Journal of Operational Research 1999; 116; 667-680.
[22] Jucker JV, de Faro C. A simple algorithm for Stone's version of the portfolio selection problem. Journal of Financial and Quantitative Analysis 1975; 10; 859-870.
[23] Ali A, Helgason R, Kennington J, Lall H. Computational comparison among three multicommodity network flow algorithms. Operations Research 1980; 28; 995-1000.
[24] Ohuchi A, Kaji I. Lagrangian dual coordinatewise maximization algorithm for network transportation problems with quadratic costs. Networks 1984; 14; 515-530.
[25] More JJ, Toraldo G. Algorithms for bounded constrained quadratic programming problems. Numerische Mathematik 1989; 55; 377-400
[26] Robinson AG, Jiang N, Lerme CS. On the continuous quadratic knapsack problem. Mathematical Programming 1992; 55; 99-108.
[27] Bretthauer KM, Shetty B, Syam S. A projection method for the integer quadratic knapsack problem. Journal of the Operational Research Society 1996; 47; 457-462.
[28] Bretthauer KM, Shetty B. The nonlinear resource allocation problem. Operations Research 1995; 43; 670-683.
[29] Kodialam MS, Luss H. 1998. Algorithms for separable nonlinear resource allocation problems. Operations Research 1998; 46; 272-284.
[30] Bretthauer KM, Shetty B. A pegging algorithm for the nonlinear resource allocation problem. Computers and Operations Research 2002; 29(5); 505-527.
[31]Stefanov SM. Convex separable minimization subject to bounded variables. Computational Optimization and Applications 2001; 18; 27-48.
[32] Cui Y. Dynamic programming algorithms for the optimal cutting of equal rectangles. Applied Mathematical Modelling 2005; 29; 1040-1053.
[33] Hua ZS, Banerjee P. Aggregate line capacity design for PWB assembly systems, International Journal of Production Research 2000; 38(11); 2417-2441.
[34] Sun J, Gu Y. A nonlinear integer programming model for a postal design problem, International Journal of Operational Quantity Management 2000; 6; 157-168.
[35] Abdel-Malek L, Areeratchakul N. A quadratic programming approach to the multi-product newsvendor problem with side constraints. European Journal of Operational Research, doi:10.1016/j.ejor.2005.11.002, 2006.
[36] Billionnet A, Soutif E. An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem, European Journal of Operational Research 2004; 157; 565-575.
[37] Caprara A, Pisinger D, Toth P. Exact solution of the quadratic knapsack problem. INFORMS Journal on Computing 1999; 11; 125-137.
[38] Kellerer H, Pferschy U, Pisinger D. Knapsack Problems, Berlin: Springer, 2004.
[39] Dembo RS, Hammer PL. A reduction algorithm for knapsack problems, Methods of Operatioins Research 1980; 36; 49-60.
[40] Osorio MA, Glover F, Hammer PL. Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions, Annals of Operations Resserach 2002; 117; 71-93.
[41] Lemke CE. Bimatrix equilibrium points and mathematical programming, Management Science 1965; 11:681-689.
[42] Hammer PL, Hansen P, Simeone B. Roof duality, complementation and persistency in quadratic 0-1 optimization. Mathematical Programming 1984; 28; 121-155.
[43] Laughhunn DJ. Quadratic binary programming with application to capital-budgeting problems. Operations Research 1970; 18; 454-461.
[44] Gallo G, Hammer PL, Simeone B. Quadratic knapsack problems. Mathematical programming 1980; 12; 132-149.
[45] Johnson EL, Mehrotra A, Nemhauser GL. Min-cut clustering. Mathematical Programming 1993; 62; 133-151.
[46] Martello S, Toth P. Knapsack problems: algorithms and computer implementations. Wiley, Chichester, UK, 1990.
[47] McCallum CJ. An algorithm for certain quadratic integer programs, Technical Report, Bell laboratories, Holmdel, NJ, Undated.
[48] Mathur K, Salkin HM. A branch and search algorithm for a class of nonlinear knapsack problems. Operations Research Letters 1983; 2; 155-160.
[49] Djerdjour M, Mathur K, Salkin HM. A surrogate relaxation based algorithm for a general quadratic multi-dimensional knapsack problem. Operations Research Letters. 1988; 7; 253-258.
[50] Ferreira CE, Martin A, De Souza C, Weismantel R, Wolsey L. Formulations and valid inequalities for the node capacitated graph partitioning problem. Mathematical Programming 1996; 74; 247-261.
[51]HeImberg C, Rendl F, Weismantel R. A semidefinite programming approach to the quadratic knapsack problem. Journal of Combinatorial Optimization 2000; 4; 197-215.
[52] Bellman RE. Dynamic programming. Princeton University Press, Princeton, NJ, 1975.
[53]Morin TL. Dynamic programming and its applications. M. L. Puterman, ed. Computational Advances in Dynamic Programming. Academic Press, NY, 1978; 53-90.
[54] Cooper L, Cooper MW. Introduction to dynamic programming. Pergamon Press, Elmsford,NY, 1981.
[55] Bertsimas D, Demir R. An approximate dynamic programming approach to multidimensional knapsack problems. Management Science 2002; 48; 550-565.
[56] Billionnet A. Maximizing a tree-structured pseudo-Boolean function with a cardinality constraint. Manuscript.
[57] Rader Jr DJ, Woeginger GJ. The quadratic 0-1 knapsack problem with series-parallel support. Operations Research Letters 2002; 30; 159-166.
[58] Billionnet A. Approximation algorithms for fractional knapsack problems. Operations Research Letters 2002; 30; 336-342.
[59] Forrester RJ. Addressing formulation size, strength, and mathematical structure in modeling discrete decision problems. The graduate school of Clemson university, Ph.D. thesis, 2002; 81-98.
[60] Hochbaum DS. The nonlinear knapsack problem. Operational Research Letters 1995; 17; 103-110.
[61] Bertsimas D, Shioda R. Restaurant revenue management. Operations Research 2003; 51(3); 472-486.
[62] Brouwer AE, Cohen AM, Neumaier A. Distance regular graphs. New York: Springer-Verlag, 1989.
[1] McGill JI, van Ryzin GJ. Revenue management: Research overview and prospects. Transportation Science 1999; 33; 233-256.
[2] Bitran GR, Caldentey R. An overview of pricing models for revenue management. Manufacturing & Service Operations Management 2003; 5; 203-229.
[3] Elmaghraby W, Keskinocak P. Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 2003; 49(10); 1287-1309.
[4] Aviv Y, Pazgal A. Pricing of short life-cycle products through active learning. Working paper, The John M. Olin School of Business, Washington University, St. Louis, MO; 2002.
[5] Talluri KT, van Ryzin GJ. The theory and practice of revenue management. Kluwer Academic Publishers, Boston; 2004
[6] Chan L, Shen ZJM, Simchi-Levi D, Swann J. Coordination of pricing and inventory decisions: A survey and classification. Working paper, Georgia Institute of Technology, Atlanta, GA; 2003.
[7] Trefler D. The ignorant monopolist: Optimal learning with endogenous information. International Economic Review 1993; 34; 565-581.
[8] Xu X, Hopp WJ. Dynamic pricing and inventory control: The value of demand learning. Working paper, Department of Industrial Engineering, Northwestern University; 2005.
[9] Araman V, Caldentey R. Dynamic pricing for non-perishable products with demand learning. Working paper, Stern School of Business, New York University, New York, NY; 2005.
[10] Aviv Y, Pazgal A. A partially observed Markov decision process for dynamic pricing. Management Science 2005; 51(9); 1400-1416.
[11] Federgruen A, Heching A. Combined pricing and inventory control under uncertainty. Operations Research 1999; 47; 454-475.
[12] Petruzzi NC, Dada M. Pricing and the newsvendor problem: A review with extensions. Operations Research 1999; 47(2); 183-194.
[13] Weatherford LR, Bodily SE. A taxonomy and research overview of perishable asset revenue management: Yield management, overbooking, and pricing. Operations Research 1992; 40(5); 831-844.
[14] Yano CA, Gilbert SM. Coordinated pricing and production/procurement decisions: A review. Chakravarty A, Eliashberg J. eds. Managing business interfaces: marketing, engineering and manufacturing perspectives. Kluwer Academic Publishers, Boston, MA; 2002.
[15]Monahan GE, Petruzzi NC, Zhao W. The dynamic pricing problem from a newsvendor's perspective. Manufacturing & Service Operations Management 2004; 6(1); 73-91.
[16] Deng S, Yano CA. Joint production and pricing decisions with setup costs and capacity constraints. Management Science 2006; 52(5); 741-756.
[17] Sen A, Zhang AX. Style goods pricing with demand learning. Working paper, Bilkent University, Bilkent, Ankara, Turkey; 2002.
[18]Azoury KS. Bayes solutions to dynamic inventory models under unknown demand distribution, Management Science 1985; 31(9); 1150-1160.
[19] Bitran GR, Haas EA, Matsuo H. Production planning of style goods with high setup costs and forecast revisions. Operations Research 1986; 34; 226-236.
[20] Lovejoy WS. Myopic policies for some inventory models with uncertain demand distributions. Management Science 1990; 36; 724-738.
[21] Braden DJ, Freimer M. Informational dynamics of censored observations. Management Science 1991; 37; 1390-1404.
[22] Matsuo H. A stochastic sequencing problem for style goods with forecast revisions and hierarchical structure. Management Science 1990; 36;332—347.
[23] Nahmias S. Demand estimation in lost sales inventory systems. Naval Research Logistics 1994; 41; 739-757.
[24] Agrawal N, Smith SA. Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Research Logistics 1996; 43; 839-861.
[25] Fisher M, Raman A. Reducing the cost of demand uncertainty through accurate response to early sales. Operations Research 1996; 44(1); 87-99.
[26] Eppen GD, Iyer V. Improved fashion buying with Bayesian updates. Operations Research 1997; 45(6); 805-819.
[27] Abernathy FH, Dunlop JT, Hammond JH, Weil D. A Stitch in time. Lean retailing and the transformation of manufacturing—Lessons from the apparel and textile industries. Oxford University Press, New York, NY; 1999.
[28] Lariviere MA, Porteus EL. Stalking information: Bayesian inventory management with unobserved lost sales. Management Science 1999; 45(3); 346-363.
[29] Alpern S, Snower DJ. A search model of pricing and production. Engineering Costs and Production Economics 1988; 15; 279-285.
[30] Petruzzi NC, Dada M. Information and inventory recourse for a two-market, price-setting retailer. Manufacturing and Service Operations Management 2001; 3(3); 242-263.
[31] Bertsimas D, Perakis G. Dynamic pricing: A learning approach. Working Paper, Sloan School of Management, MIT, Cambridge. Massachusetts; 2005.
[32] Balvers RJ, Cosimano TF. Actively learning about demand and the dynamics of price adjustments. The Economic Journal 1990; 100; 882-898.
[33] Mirman L, Samuelson L, Urbano A. Monopoly experimentation. International Economic Review 1993; 34; 549-563.
[34] Subrahmanyan S, Shoemaker R. Developing optimal pricing and inventory policies for retailers who face uncertain demand. Journal of Retailing 1996; 72(1); 7-30.
[35] Bisi A, Dada M. Dynamic learning, pricing, and ordering by a censored newsvendor. Working paper, Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana; 2005.
[36] Zhang JL, Chen J. Bayesian solution to pricing and inventory control under unknown demand distribution. Operations Research Letters 2006; 34; 517-524.
[37] Petruzzi NC, Dada M. Dynamic pricing and inventory control with learning. Naval Research Logistics 2002; 49; 303-325.
[38] Lin K. Dynamic pricing with real-time demand learning. European Journal of Operational Research 2006; 174; 522-538.
[39] Cope E. Bayesian strategies for dynamic pricing in e-commerce. Naval Research Logistics 2007; 54; 265-281.
[40] Johnson ME. Learning from toys: Lessons in managing supply chain risk from the toy industry. California Management Review 2001; 43(3); 106-124.
[41] Hammond JH, Raman A. Sport Obermeyer, Ltd. Case study 9-695-022. Harvard Business School, Boston, MA; 1996.
[2] Belobaba PP. Air travel demand and airline seat inventory management, Ph.D. thesis, Flight Transportation Laboratory, Massachusetts Institute of Technology, Cambridge, MA; 1987.
[3] Smith BC, Leimkuhler JF, Darrow RM. Yield Management at American Airlines. Interfaces 1992; 22; 8-31.
[4] Cross RG. An introduction to revenue management. In The Handbook of Airline Economics, Jenkins D, (ed.), The Aviation Weekly Group of the McGraw-Hill Companies, New York, NY; 1995; 443-468,.
[5] Dunleavy HN. Airline passenger overbooking. In The Handbook of Airline Economics, Jenkins (ed.) D, The Aviation Weekly Group of the McGraw-Hill Companies, New York, NY; 1995; 469-482.
[6] Vinod B. Origin-and-destination yield management. In The Handbook of Airline Economics, Jenkins (ed.) D, The Aviation Weekly Group of the McGraw-Hill Companies, New York, NY; 1995; 459-468.
[7] McGill JI, van Ryzin GJ. Revenue management: Research overview and prospects. Transportation Science 1999; 33; 233-256.
[8] Bitran GR, Caldentey R. An overview of pricing models for revenue management. Manufacturing & Service Operations Management 2003; 5; 203-229.
[9] Elmaghraby W, Keskinocak P. Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 2003; 49(10); 1287-1309.
[10] Box GEP, Jenkins G M. Time Series Analysis: Forecasting and Control. Holden-Day, Oakland, CA; 1976.
[11] DeGroot MH. Probability and Statistics, Addison Wesley, Reading, MA, 2nd edition, 1985.
[12] Sun S. The fine-tuned learning enhancement to the standard backpropagation algorithm. In Reservations and Yield Management Study Group Annual Meeting Proceedings, Zurich, Switzerland, 1996. AGIFORS.
[13] Ting SC, Tzeng GH. Fuzzy multi-objective programming approach to allocating containership slots for liner shipping revenue management. In MCDM Winter Conference, Semmering, Austria, 2002.
[14] Basgall M. Hotel help: Fuzzy thinking helps clear up tradeoffs on hotel reservations, June 1998. Duke University News, News release.
[15] Mulhern FJ, Caprara RJ. A nearest neighbor model for forecasting market response. International Journal of Forecasting 1994; 10; 191-207.
[16] J. M. Bates and C. W. J. Granger. The combination of forecasts. Operational Research Quarterly 1969; 20; 451-468.
[17] McGill JI. Censored regression analysis of multiclass demand data subject to joint capacity constraints. Annals of Operations Research 1995; 60; 209-240.
[18] Allenby GM, Arora N, Ginter JL. On the heterogeneity of demand. Journal of Marketing Research 1998; 35; 384-89.
[19] Kaplan EL, Meier P. Nonparametric estimates from incomplete observations. American Statistical Association Journal 1958; 53; 457-481.
[20] Zeni RH. Improved forecast accuracy in airline revenue management by unconstraining demand estimates from censored data. PhD thesis, Graduate School, Rutgers, State University of New Jersey, 2001.
[21] Willemain TR, Smart CN, Schwarz HF. A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting 2004; 20; 375-387.
[22] Littlewood K. Forecasting and control of passenger bookings, in AGIFORS Symposium Proc. 12, Nathanya, Israel; 1972.
[23] Belobaba PP. Revenue and competitive impacts of O-D control: Summary of PODS results. In First Annual INFORMS Revenue Management Section Meeting, New York, NY; 2001.
[24] Williamson EL. Airline Network Seat Inventory Control: Methodologies and Revenue Impacts. PhD thesis, Flight Transportation Laboratory, MIT, Cambridge, MA; 1992.
[25] Karaesman I, van Ryzin GJ. Overbooking with substituable inventory classes. Operations Research 2004; 52(1); 83-104.
[26] Bitran GR, Gilbert SM. Managing Hotel Reservations with Uncertain Arrivals. Operations Research 1996; 44; 35-49.
[27] Lee TC, Hersh M. A model for dynamic airline seat inventory control with multiple seat bookings. Transportation Sciece 1993; 27; 252-265.
[28] Talluri KT, van Ryzin G. Revenue management under a general discrete choice model of consumer behavior. Management Science 2004; 50; 15-33.
[29] Bitran GR, Caldentey R. An overview of pricing models for revenue management. Manufacturing & Service Operations Management 2003; 5; 203-229.
[30] Elmaghraby W, Keskinocak P. Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 2003; 49(10); 1287-1309.
[31] Polt S. Forecasting is difficult-especially if it refers to the future. In Reservations and Yield Management Study Group Annual Meeting Proceedings, Melbourne, Australia, 1998.
[1] Huiskonen J. Maintenance spare parts logistics: Special characteristics and strategic choices, International Journal of Production Economics 2004; 71; 125- 133.
[2] Croston JD. Forecasting and stock control for intermittent demands. Operational Research Quarterly 1972; 23(3); 289-303.
[3] Rao AV. A comment on: forecasting and stock control for intermittent demands. Operational Research Quarterly 1973; 24(4); 639-640.
[4] Willemain TR, Smart CN and Schwarz HF. A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting 2004; 20; 375-387.
[5] Willemain TR, Smart CN, Shockor JH and DeSautels PA. Forecasting intermittent demand in manufacturing: a comparative evaluation of Croston's method. International Journal of Forecasting 1994; 10(4); 529-538.
[6] Willemain TR, Ratti EWL, Smart CN. Forecasting intermittent demand using a cox process model. INFORMS Meetings, Boston, USA, 1994; 1-14.
[7] Johnston FR and Boylan JE. Forecasting for items with intermittent demand, Journal of the Operational Research Society 1996; 47; 113-121.
[8] Ghobbar AA and Friend CH. Evaluation of forecasting methods for intermittent parts demand in the field of aviation: a predictive model. Computers & Operations Research 2003;30;2097-2114.
[9] Silver EA. Operations research in inventory management: A review and critique. Operations Research 1981; 29; 628-645.
[10] Kennedy WJ, Patterson JW, Fredendall LD. An overview of recent literature on spare parts inventories. International Journal of Production Economics 2002; 76; 201-215.
[11] Wang M, Rao SS. Estimating reorder points and other management science applications by bootstrap procedure. European Journal of Operational Research 1992; 56; 332-342.
[12]Lau HS, Wang MC. Estimating the lead-time demand distribution when the daily demand is non-normal and autocorrelated. European Journal of Operational Research 1987; 29; 60-69.
[13] Tyworth JE, O'Neill L. Robustness of the normal approximation of lead-time demand in a distribution setting. Naval Research Logistics 1997; 44; 165-186.
[14]Petrovic D, Petrovic R. SPARTA II: Further development in an expert system for advising on stocks of spare parts. International Journal of Production Economics 1992; 24; 291-300.
[15]Dunsmuir WTM, Snyder RD. Control of inventories with intermittent demand. European Journal of Operational Research 1989; 40; 16-21.
[16] Ward JB. Determining reorder points when demand is lumpy. Management Science 1978; 24; 623-632.
[17] Bier IJ. Boeing commercial airplane group spares department: simulation of spare parts operations. ORSA/TIMS Joint National Meeting, Detroit, MI, 1984.
[18] Sani B, Kingsman BG. Selecting the best periodic inventory control and demand forecasting methods for low demand items. Journal of the Operational Research Society 1997; 48; 700-713.
[19] Efron B. Bootstrap methods: another look at the jackknife. Annals of Statistics 1979; 7; 1-26.
[20] Gamero MJ, Garcia JM and Reyes AM. Bootstrapping statistical functionals, Statistics & Probability Letters 1998; 39(3); 229-236.
[21] Bookbinder JH and Lordahl AE. Estimation of inventory re-order levels using the bootstrap statistical procedure. HE Transactions 1989; 21; 302-312.
[22] Snyder R. Forecasting sales of slow and fast moving inventories. European Journal of Operational Research 2002; 140; 684-699.
[23] Vapnik VN. The Nature of Statistical Learning Theory. New York: Springer; 2000.
[24] Vapnik VN, Golowich SE, Smola AJ. Support vector method for function approximation, regression estimation, and signal processing. Advances in Neural Information Processing Systems 1996; 9; 281-287.
[25] Muller KR, Smola AJ, Ratsch G, Scholkopf B, Kohlmorgen J. Using support vector machines for time series prediction. In: Scholkopf B, Burges CJC, Smola AJ (Eds.). Advances in Kernel Methods—Support Vector Learning, MIT Press, Cambridge, MA, 1999;243-254.
[26] Tay FEH, Cao LJ. Application of support vector machines in financial time series forecasting, Omega 2001; 29(4); 309-317.
[27] Cao LJ, Tay FEH. Support vector machine with adaptive parameters in financial time series forecasting. IEEE Transactions on Neural Networks 2003; 14(6); 1506-1518.
[28] Kim K. Financial time series forecasting using support vector machines. Neurocomputing 2003; 55; 307-319.
[29] Bao Y, Wang W, Zhang J. Forecasting intermittent demand by SVMs regression. IEEE International Conference on Systems, Man and Cybernetics 2004; 1; 461-466.
[30] Pai PF, Lin CS. A hybrid ARIMA and support vector machines model in stock price forecasting. Omega 2005; 33; 497-505.
[31] Jovanis PP and Chang H. Modeling the relationship of accidents to miles traveled. Transportation Research Record 1068, TRB, National Research Council, Washington, DC, 1986; 42-51.
[32] Milton J, Mannering F. Relationship among highway geometric, traffic-related elements, and motor-vehicle accident requencies. In the 76th Annual Meeting of the Transportation Research Board, Washington, DC; 1997.
[33] Gooijer JGD, Vidiella-i-Anguera A. Forecasting threshold cointegrated systems. International Journal of Forecasting 2004; 20; 237-253.
[34] Herzel H, Grope I. Measuring correlations in symbol sequences. Physica A 1995; 216; 518-542.
[35] Mosteller F, Tukey JW. Data analysis and regression: A second course in statistics. Reading, MA: Addison-Wesley; 1977.
[36] 张斌，华中生。一种改进的求解含等式约束凸二次规划问题的Lemke算法。中国科学技术大学学报 2004；34(6)；668-677。
[37] Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 1958; 53; 457-481.
[38] Khouja M. The single-period (news-vendor) problem: literature review and suggestions for future research. Omega 1999; 27(5); 537-553.
[39] Hadley G, Whitin, TM. Analysis of inventory systems. Prentice-Hall, Englewood Cliffs; 1963.
[40] Lau HS, Lau, AHL. Estimating the demand distributions of single-period items having frequent stockouts. European Journal of Operational Research 1996; 92; 254-265.
[41] Gillespie B, Gillespie J, Iglewicz B. A comparison of the bias in four versions of the product-limit estimator. Biometrika 1992; 79; 149-155.
[42] Conrad SA. Sales data and the estimation of demand. Operational Research Quarterly 1976; 27(1); 123-127.
[43] Wecker W. Predicting demand from sales data in the presence of stockouts. Management Science 1978; 24; 1043-1054.
[44] Braden DB, Freimer M. Informational dynamics of censored observations. Management Science 199t; 37(11); 1390-1404.
[45] Agrawal NS, Smith A. Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Research Logistics 1996; 43; 839-861.
[46] Bell PC. Adaptive sales forecasting with many stockouts. Journal of the Operational Research Society 1981; 32; 865-873.
[47] Bell PC. A new procedure for the distribution of periodicals. Journal of the Operational Research Society 1978; 29; 427-434.
[48] Bell PC. Forecasting demand variation when there are stockouts. Journal of the Operational Research Society 2000; 51(3); 358-363.
[49] Ding X. Estimation and optimization in discrete inventory models. Ph.D. thesis, Faculty of Commerce, The University of British Columbia, Vancouver, Canada; 2002.
[50] Coolen FPA, Yan K.J. Nonparametric predictive inference with right-censored data. Journal of Statistical Planning and Inference 2004; 126; 25-54.
[51] Efron B. The two sample problem with censored data. Proceedings of the 5th Berkeley Symposium 1967; 4; 831-852.
[52] Gill RD. Censoring and stochastic integrals. Mathematical Centre Tract No. 124, Mathematisch Centrum, Amsterdam; 1980.
[53] Chen Z, Phadia E. An optimal completion of the product limit estimator. Statistics & Probability Letters 2006; 76; 913-919.
[54] Brown BW, Jr. Hollander M, Korwar RM. Nonparametric tests of independence for censored data, with applications to heart transplant studies. In: Proschan F, Serfling, RJ (Eds.), Reliability and Biometry: Statistical Analysis of Lifelength, Philadelphia: Society for Industrial and Applied Mathematics 1974; 291-302.
[55] Moeschberger ML, Klein JP. A comparison of several methods of estimating the survival function when there is extreme right censoring. Biometrics 1985; 41; 253-259.
[56] Meier P. Estimation of a distribution function from incomplete observations. In: Gani J (Eds.), Perspectives in Probability and Statistics, Sheffield, England: Applied Probability Turst 1975; 67-87.
[57] Geurts JHJ. Some small-samplel nonproportional hazards results for the Kaplan-Meier esitmator. Statistica Neerlandica 1985; 39; 1-13.
[58] Geurts JHJ. On the small-sample performance of Efron's and of Gill's version of the product limit estimator under nonproportional hazards. Biometrics 1987; 43; 683-692.
[59] Sarno L, Valente G. Comparing the accuracy of density forecasts from competing models. Journal of Forecasting 2004; 23; 541-555.
[60] Bellini F, Figa-Talamanca G. Runs tests for assessing volatility forecastability in financial time series. European Journal of Operational Research 2005; 163; 102-114.
[61] Reeves JJ. Bootstrap prediction intervals for ARCH models. International Journal of Forecasting 2005; 21; 237-248.
[62]Tay AS, Wallis KF. Density forecasting: a survey. Journal of Forecasting 2000; 19; 235-254.
[63] Wallis KF. Asymmetric density forecasts of inflation and the bank of England's fan chart. National Institute Economic Review 1999; 167; 106-112.
[64] Wallis KF; An assessment of bank of England and national institute inflation forecast uncertainties. National Institute Economic Review 2004; 189; 64-71.
[65] Li WK, Lam K. Modelling asymmetry in stock returns by a threshold ARCH model. The Statistician 1995; 44; 333-341.
[66] Sarantis N. Nonlinearities, cyclical behavior and predictability in stock markets: International evidence. International Journal of Forecasting 2001; 17; 459-482.
[67] Brannas K, De Gooijer JG. Asymmetries in conditional mean and variance: modelling stock returns by asMA-asQGARCH. Journal of Forecasting 2004; 23; 155-171.
[68] Bekaert G, Wu G. Asymmetric volatility and risk in equity markets, Review of Financial Studies 2000; 13; 1-42.
[69] Wu G. The determinants of asymmetric volatility. Review of Financial Studies 2001; 14(3); 837-859.
[70] Engle RF, Ng VK. Measuring and testing the impact of news on volatility. Journal of Finance 1993; 48; 1749-1778.
[71] Rabemananjara R, Zakoian JM. Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics 1993; 8; 271-301.
[72] So MKP, Li WK, Lam K. A threshold stochastic volatility model. Journal of Forecasting 2002; 21; 473-500.
[73] Box GEP, Jenkins GM, Reinsel GC. Time series analysis, Forecasting and Control, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall; 1994.
[74] Carrasco M, Chen X. Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 2002; 18; 17-39.
[75] Engle RF. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 1982; 50; 987-1008.
[76] Bollerslev T. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 1986; 31; 307-327.
[77] Taylor JW. Evaluating volatility and interval forecasts. Journal of Forecasting 1999; 18; 111-128.
[78] Maddala GS, Li H. Bootstrap based tests in financial models. In Maddala, G.S. and Rao, CR. (eds). Handbook of Statistics, vol. 14, Elsevier, Amsterdam, 1996; 463-488.
[79] Kunsch HR. The jackknife and the bootstrap for general stationary observations. Annals of Statistics 1989; 17; 1217-1241.
[80] Ruiz E, Pascual L. Bootstrapping financial time series. Journal of Economic Surveys 2002; 16(3); 271-300.
[81] Politis DN, Romano JP. The stationary bootstrap, Journal of the American Statistical Association 1994; 89; 1303-1313.
[82] Hansen PR, Lunde A. A forecast comparison of volatility models: does anything beat a GARCH (1,1)? Journal of Applied Econometrics 2005; 20; 873-889.
[83] Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions, 2nd ed., vol.1. New York: Wiley; 1994.
[84] John S. The three-parameter two-piece normal family of distributions and its fitting. Communications in Statistics-Theory and Methods 1982; 11; 879-885.
[85] Huang YC, Lin BJ. Value-at-risk analysis for Taiwan stock index futures: Fat tails and conditional asymmetries in return innovations. Review of Quantitative Finance and Accounting 2004; 22; 79-95.
[86] Newey WK, West KD. A Simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 1987; 55(3); 703-708.
[87] Diebold FX, Gunther TA, Tay AS. Evaluating density forecasts: with application to financial risk management. International Economic Review 1998; 39; 863-883.
[88] Berkowitz J. Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics 2001; 19; 465-474.
[89] Boero G, Marrocu E. The performance of SETAR models: a regime conditional evaluation of point, interval and density forecasts. International Journal of Forecasting 2004; 20(2); 305-320.
[90] Clements MP, Taylor N. Evaluating interval forecasts of high-frequency financial data, Journal of Applied Econometrics 2003; 18(4); 445-456.
[91] Pascual L, Romo J, Ruiz E. Bootstrap prediction intervals for power-transformed time series. International Journal of Forecasting 2005; 21; 219-236.
[92] Alho JM, Vanne R. On predictive distributions of public net liabilities. International Journal of Forecasting, doi: 10.1016/j.ijforecast.2005.11.005; 2006.
[93] Clements MP, Smith J. Evaluating multivariate forecast densities: A comparison of two approaches. International Journal of Forecasting 2002; 18; 397- 407.
[94] De Gooijer JG, Hyndman RJ. 25 years of time series forecasting. International Journal of Forecasting, doi: 10.1016/j.ijforecast.2005.07.001; 2006.
[95] Jewson S, Ziehmann C. Five guidelines for the evaluation of site-specific medium range probabilistic temperature forecasts. http://arxiv.org/PS_cache/physics/pdf/0310/ 0310021.pdf; 2003.
[96] Diebold FX, Lopez JA. Forecast evaluation and combination. In Handbook of Statistics 14, Maddala GS, Rao CA (eds). Elsevier: Amsterdam 1996; 241-268.
[97] Wilks DS. Statistical Methods in the Atmospheric Sciences-An Introduction. Academic Press: London; 1995.
[98] Potgieter AB, Everingham YL, Hammer GL. On measuring quality of a probabilistic commodity forecast for a system that incorporates seasonal climate forecasts. International Journal of Climatology 2003; 23; 1195-1210.
[99] Clements MP, Smith J. Evaluating the forecast densities of linear and non-linear models: applications to output growth and unemployment. Journal of Forecasting 2000; 19; 255-276.
[100] Wallis KF. Chi-squared tests of interval and density forecasts, and the Bank of England fan charts. International Journal of Forecasting 2003; 19; 165-175.
[101] Christoph K, Burkhart F. Instrumental and test-retest reliability of saccadic measures. Biological Psychology 2005; 68(3); 201-213.
[102] Ebeling CE. An Introduction to Reliability and Maintainability Engineering, McGraw-Hill International Editions 1997; pp 487.
[103] Jolliffe IT, Stephenson DB. Forecast Verification. A Practitioner's Guide in Atmospheric Science. Wiley and Sons Ltd; 2003.
[104] Potts JM, Folland CK, Jolliffe IT, Sexton D. Revised "LEPS" scores for assessing climate model simulations and long-range forecasts. Journal of Climate 1996; 9; 34-53.
[105] Mason SJ, Graham NE. Conditional probabilities, relative operating characteristics, and relative operating levels. Weather and Forecasting 1999; 14; 713-725.
[106] Lee WC. Selecting diagnostic tests for ruling out or ruling in disease: the use of the Kullback-Leibler distance. International Journal of Epidemiology 1999; 28; 521-525.
[107] Kruskall WH, Wallis WA. Use of ranks on one-criterion variance analysis. Journal of the American Statistical Association 1952; 48; 907-911.
[1] Hadley G, Whitin T. Analysis of Inventory Systems. Prentice-Hall, Englewood Cliffs, NJ; 1963.
[2] Khouja M. The single-period (news-vendor) problem: Literature review and suggestions for future research. Omega International Journal of Management Science 1999; 27; 537-553.
[3] Erlebacher SJ. Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint. Production and Operations Management 2000; 9(3); 303-318.
[4] Vairaktarakis GL. Robust multi-item Newsboy models with a budget constraint. International Journal of Production Economics 2000; 66; 213-226.
[5] Abdel-Malek L, Montanari R, Morales LC. Exact, approximate, and generic terative models for the multi-product newsboy with budget constraint. International Journal of Production Economics 2004; 91; 189-198.
[6] Abdel-Malek L, Montanari R. An analysis of the multi-product newsboy problem with a budget constraint. International Journal of Production Economics 2005; 97; 296-307.
[7] Ben-Daya M, Raouf A. On the constrained multi-product single period inventory problem. International Journal of Operations & Production Management 1993; 13; 104-112.
[8] Gallego G, Moon I. The distribution free newsboy problem: Review and extensions. Journal of Operational Research Society 1993; 44; 825-834.
[9] Moon I, Silver E. The multi-item newsvendor problem with a budget constraint and fixed ordering costs. Journal of Operational Research Society 2000; 51; 602-608.
[10] Lau HS, Lau AHL. The multi-product multi constraint Newsboy problem: Applications formulation and solution. Journal of Operations Management 1995; 13; 153-162.
[11] Lau HS, Lau AHL. The newsstand problem: A capacitated multiple-product single-period inventory problem. European Journal of Operational Research 1996; 94; 29-42.
[12] Hua Z, Zhang B, Liang L. An approximate dynamic programming approach to convex quadratic knapsack problems. Computers & Operations Research 2006; 33(3); 660-673.
[13] Bretthauer KM, Shetty B. The nonlinear knapsack problem-algorithms and applications. European Journal of Operational Research 2002; 138; 459-472.
[14] Zhang B, Hua ZS, 2007. A binary solution method for the multi-product newsboy problem with budget constraint. Accepted by International Journal of Production Economics.
[15]Luss H, Gupta SK. Allocation of effort resources among competing activities. Operations Research 1975; 23; 360-366.
[16] Zipkin PH. Simple ranking methods for allocation of one resource. Management Science 1980; 26; 34-43.
[17] Bitran GR, Hax AC. Disaggregation and resource allocation using convex knapsack problems with bounded variables. Management Science 1981; 27; 431-441.
[18] Hochbaum DS. Lower and upper bounds for the allocation problem and other nonlinear optimization problems. Mathematics of Operations Research 1994; 19; 390-409.
[19] Bretthauer KM, Shetty B, Syam S, White S. A model for resource constrained production and inventory management. Decision Sciences 1994; 25; 561-580.
[20] Bretthauer KM, Shetty B, Syam S. A branch and bound algorithm for integer quadratic knapsack problems. ORSA Journal on Computing 1995; 7; 109-116.
[21 ] Bretthauer KM, Ross A, Shetty B. Nonlinear integer programming for optimal allocation in stratified sampling. European Journal of Operational Research 1999; 116; 667-680.
[22] Jucker JV, de Faro C. A simple algorithm for Stone's version of the portfolio selection problem. Journal of Financial and Quantitative Analysis 1975; 10; 859-870.
[23] Ali A, Helgason R, Kennington J, Lall H. Computational comparison among three multicommodity network flow algorithms. Operations Research 1980; 28; 995-1000.
[24] Ohuchi A, Kaji I. Lagrangian dual coordinatewise maximization algorithm for network transportation problems with quadratic costs. Networks 1984; 14; 515-530.
[25] More JJ, Toraldo G. Algorithms for bounded constrained quadratic programming problems. Numerische Mathematik 1989; 55; 377-400
[26] Robinson AG, Jiang N, Lerme CS. On the continuous quadratic knapsack problem. Mathematical Programming 1992; 55; 99-108.
[27] Bretthauer KM, Shetty B, Syam S. A projection method for the integer quadratic knapsack problem. Journal of the Operational Research Society 1996; 47; 457-462.
[28] Bretthauer KM, Shetty B. The nonlinear resource allocation problem. Operations Research 1995; 43; 670-683.
[29] Kodialam MS, Luss H. 1998. Algorithms for separable nonlinear resource allocation problems. Operations Research 1998; 46; 272-284.
[30] Bretthauer KM, Shetty B. A pegging algorithm for the nonlinear resource allocation problem. Computers and Operations Research 2002; 29(5); 505-527.
[31]Stefanov SM. Convex separable minimization subject to bounded variables. Computational Optimization and Applications 2001; 18; 27-48.
[32] Cui Y. Dynamic programming algorithms for the optimal cutting of equal rectangles. Applied Mathematical Modelling 2005; 29; 1040-1053.
[33] Hua ZS, Banerjee P. Aggregate line capacity design for PWB assembly systems, International Journal of Production Research 2000; 38(11); 2417-2441.
[34] Sun J, Gu Y. A nonlinear integer programming model for a postal design problem, International Journal of Operational Quantity Management 2000; 6; 157-168.
[35] Abdel-Malek L, Areeratchakul N. A quadratic programming approach to the multi-product newsvendor problem with side constraints. European Journal of Operational Research, doi:10.1016/j.ejor.2005.11.002, 2006.
[36] Billionnet A, Soutif E. An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem, European Journal of Operational Research 2004; 157; 565-575.
[37] Caprara A, Pisinger D, Toth P. Exact solution of the quadratic knapsack problem. INFORMS Journal on Computing 1999; 11; 125-137.
[38] Kellerer H, Pferschy U, Pisinger D. Knapsack Problems, Berlin: Springer, 2004.
[39] Dembo RS, Hammer PL. A reduction algorithm for knapsack problems, Methods of Operatioins Research 1980; 36; 49-60.
[40] Osorio MA, Glover F, Hammer PL. Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions, Annals of Operations Resserach 2002; 117; 71-93.
[41] Lemke CE. Bimatrix equilibrium points and mathematical programming, Management Science 1965; 11:681-689.
[42] Hammer PL, Hansen P, Simeone B. Roof duality, complementation and persistency in quadratic 0-1 optimization. Mathematical Programming 1984; 28; 121-155.
[43] Laughhunn DJ. Quadratic binary programming with application to capital-budgeting problems. Operations Research 1970; 18; 454-461.
[44] Gallo G, Hammer PL, Simeone B. Quadratic knapsack problems. Mathematical programming 1980; 12; 132-149.
[45] Johnson EL, Mehrotra A, Nemhauser GL. Min-cut clustering. Mathematical Programming 1993; 62; 133-151.
[46] Martello S, Toth P. Knapsack problems: algorithms and computer implementations. Wiley, Chichester, UK, 1990.
[47] McCallum CJ. An algorithm for certain quadratic integer programs, Technical Report, Bell laboratories, Holmdel, NJ, Undated.
[48] Mathur K, Salkin HM. A branch and search algorithm for a class of nonlinear knapsack problems. Operations Research Letters 1983; 2; 155-160.
[49] Djerdjour M, Mathur K, Salkin HM. A surrogate relaxation based algorithm for a general quadratic multi-dimensional knapsack problem. Operations Research Letters. 1988; 7; 253-258.
[50] Ferreira CE, Martin A, De Souza C, Weismantel R, Wolsey L. Formulations and valid inequalities for the node capacitated graph partitioning problem. Mathematical Programming 1996; 74; 247-261.
[51]HeImberg C, Rendl F, Weismantel R. A semidefinite programming approach to the quadratic knapsack problem. Journal of Combinatorial Optimization 2000; 4; 197-215.
[52] Bellman RE. Dynamic programming. Princeton University Press, Princeton, NJ, 1975.
[53]Morin TL. Dynamic programming and its applications. M. L. Puterman, ed. Computational Advances in Dynamic Programming. Academic Press, NY, 1978; 53-90.
[54] Cooper L, Cooper MW. Introduction to dynamic programming. Pergamon Press, Elmsford,NY, 1981.
[55] Bertsimas D, Demir R. An approximate dynamic programming approach to multidimensional knapsack problems. Management Science 2002; 48; 550-565.
[56] Billionnet A. Maximizing a tree-structured pseudo-Boolean function with a cardinality constraint. Manuscript.
[57] Rader Jr DJ, Woeginger GJ. The quadratic 0-1 knapsack problem with series-parallel support. Operations Research Letters 2002; 30; 159-166.
[58] Billionnet A. Approximation algorithms for fractional knapsack problems. Operations Research Letters 2002; 30; 336-342.
[59] Forrester RJ. Addressing formulation size, strength, and mathematical structure in modeling discrete decision problems. The graduate school of Clemson university, Ph.D. thesis, 2002; 81-98.
[60] Hochbaum DS. The nonlinear knapsack problem. Operational Research Letters 1995; 17; 103-110.
[61] Bertsimas D, Shioda R. Restaurant revenue management. Operations Research 2003; 51(3); 472-486.
[62] Brouwer AE, Cohen AM, Neumaier A. Distance regular graphs. New York: Springer-Verlag, 1989.
[1] McGill JI, van Ryzin GJ. Revenue management: Research overview and prospects. Transportation Science 1999; 33; 233-256.
[2] Bitran GR, Caldentey R. An overview of pricing models for revenue management. Manufacturing & Service Operations Management 2003; 5; 203-229.
[3] Elmaghraby W, Keskinocak P. Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 2003; 49(10); 1287-1309.
[4] Aviv Y, Pazgal A. Pricing of short life-cycle products through active learning. Working paper, The John M. Olin School of Business, Washington University, St. Louis, MO; 2002.
[5] Talluri KT, van Ryzin GJ. The theory and practice of revenue management. Kluwer Academic Publishers, Boston; 2004
[6] Chan L, Shen ZJM, Simchi-Levi D, Swann J. Coordination of pricing and inventory decisions: A survey and classification. Working paper, Georgia Institute of Technology, Atlanta, GA; 2003.
[7] Trefler D. The ignorant monopolist: Optimal learning with endogenous information. International Economic Review 1993; 34; 565-581.
[8] Xu X, Hopp WJ. Dynamic pricing and inventory control: The value of demand learning. Working paper, Department of Industrial Engineering, Northwestern University; 2005.
[9] Araman V, Caldentey R. Dynamic pricing for non-perishable products with demand learning. Working paper, Stern School of Business, New York University, New York, NY; 2005.
[10] Aviv Y, Pazgal A. A partially observed Markov decision process for dynamic pricing. Management Science 2005; 51(9); 1400-1416.
[11] Federgruen A, Heching A. Combined pricing and inventory control under uncertainty. Operations Research 1999; 47; 454-475.
[12] Petruzzi NC, Dada M. Pricing and the newsvendor problem: A review with extensions. Operations Research 1999; 47(2); 183-194.
[13] Weatherford LR, Bodily SE. A taxonomy and research overview of perishable asset revenue management: Yield management, overbooking, and pricing. Operations Research 1992; 40(5); 831-844.
[14] Yano CA, Gilbert SM. Coordinated pricing and production/procurement decisions: A review. Chakravarty A, Eliashberg J. eds. Managing business interfaces: marketing, engineering and manufacturing perspectives. Kluwer Academic Publishers, Boston, MA; 2002.
[15]Monahan GE, Petruzzi NC, Zhao W. The dynamic pricing problem from a newsvendor's perspective. Manufacturing & Service Operations Management 2004; 6(1); 73-91.
[16] Deng S, Yano CA. Joint production and pricing decisions with setup costs and capacity constraints. Management Science 2006; 52(5); 741-756.
[17] Sen A, Zhang AX. Style goods pricing with demand learning. Working paper, Bilkent University, Bilkent, Ankara, Turkey; 2002.
[18]Azoury KS. Bayes solutions to dynamic inventory models under unknown demand distribution, Management Science 1985; 31(9); 1150-1160.
[19] Bitran GR, Haas EA, Matsuo H. Production planning of style goods with high setup costs and forecast revisions. Operations Research 1986; 34; 226-236.
[20] Lovejoy WS. Myopic policies for some inventory models with uncertain demand distributions. Management Science 1990; 36; 724-738.
[21] Braden DJ, Freimer M. Informational dynamics of censored observations. Management Science 1991; 37; 1390-1404.
[22] Matsuo H. A stochastic sequencing problem for style goods with forecast revisions and hierarchical structure. Management Science 1990; 36;332—347.
[23] Nahmias S. Demand estimation in lost sales inventory systems. Naval Research Logistics 1994; 41; 739-757.
[24] Agrawal N, Smith SA. Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Research Logistics 1996; 43; 839-861.
[25] Fisher M, Raman A. Reducing the cost of demand uncertainty through accurate response to early sales. Operations Research 1996; 44(1); 87-99.
[26] Eppen GD, Iyer V. Improved fashion buying with Bayesian updates. Operations Research 1997; 45(6); 805-819.
[27] Abernathy FH, Dunlop JT, Hammond JH, Weil D. A Stitch in time. Lean retailing and the transformation of manufacturing—Lessons from the apparel and textile industries. Oxford University Press, New York, NY; 1999.
[28] Lariviere MA, Porteus EL. Stalking information: Bayesian inventory management with unobserved lost sales. Management Science 1999; 45(3); 346-363.
[29] Alpern S, Snower DJ. A search model of pricing and production. Engineering Costs and Production Economics 1988; 15; 279-285.
[30] Petruzzi NC, Dada M. Information and inventory recourse for a two-market, price-setting retailer. Manufacturing and Service Operations Management 2001; 3(3); 242-263.
[31] Bertsimas D, Perakis G. Dynamic pricing: A learning approach. Working Paper, Sloan School of Management, MIT, Cambridge. Massachusetts; 2005.
[32] Balvers RJ, Cosimano TF. Actively learning about demand and the dynamics of price adjustments. The Economic Journal 1990; 100; 882-898.
[33] Mirman L, Samuelson L, Urbano A. Monopoly experimentation. International Economic Review 1993; 34; 549-563.
[34] Subrahmanyan S, Shoemaker R. Developing optimal pricing and inventory policies for retailers who face uncertain demand. Journal of Retailing 1996; 72(1); 7-30.
[35] Bisi A, Dada M. Dynamic learning, pricing, and ordering by a censored newsvendor. Working paper, Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana; 2005.
[36] Zhang JL, Chen J. Bayesian solution to pricing and inventory control under unknown demand distribution. Operations Research Letters 2006; 34; 517-524.
[37] Petruzzi NC, Dada M. Dynamic pricing and inventory control with learning. Naval Research Logistics 2002; 49; 303-325.
[38] Lin K. Dynamic pricing with real-time demand learning. European Journal of Operational Research 2006; 174; 522-538.
[39] Cope E. Bayesian strategies for dynamic pricing in e-commerce. Naval Research Logistics 2007; 54; 265-281.
[40] Johnson ME. Learning from toys: Lessons in managing supply chain risk from the toy industry. California Management Review 2001; 43(3); 106-124.
[41] Hammond JH, Raman A. Sport Obermeyer, Ltd. Case study 9-695-022. Harvard Business School, Boston, MA; 1996.