随机环境下若干易逝品定价模型研究
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摘要
随着经济全球化、产品多样化和科学技术的进步,顾客对产品和服务的价格及价格变动更为敏感,其多样化的购买行为和购买动机给企业的销售预测和决策带来了极大的难度。相比其他类型的产品(或服务),易逝品的销售周期更短,顾客的需求更加多样化,市场的竞争更为激烈,给企业带来了更为严峻的挑战。如何在激烈的市场竞争中制定合理的价格,获得竞争优势,保证企业可持续发展,已成为理论界和实践界迫切需要解决的课题。
目前,解决易逝品定价最得力的方法是基于收益管理的动态定价,它是在不增加成本的情况下,通过科学的市场需求预测和合理定价使企业现有资源配置最优化。起源于航空业的收益管理不仅在客运、货运等运输领域得到了广泛应用,也已经扩展到了包括酒店、租车、零售、广播电视、互联网服务等众多服务行业,甚至在制造业(如高科技产业)也得到了相应的应用。虽然收益管理的理念能够应用于不同行业,但是每个行业的市场发展程度状况,市场运作、管理和组织存在较大的差异,因此在引进并运用收益管理来改造和完善企业运作水平和收入能力时,需要考虑行业特点,合理界定运用收益管理的方式和规模。
作为收益管理应用扩展的重要行业—集装箱运输业、零售业、互联网服务业,收益管理的应用具有鲜明的行业特征,且取得一定的成效,引起了学术界与商界的巨大重视。但就我国而言,在这些行业中,关于收益管理的理论研究和实践工作进展缓慢。特别在我国进入WTO后,行业面对愈来愈激烈的国际竞争,有必要结合行业的自身特点,以收益管理的思想和技术提高行业的服务和运作水平,进而提高行业的整体竞争力。因此,本文选择集装箱运输业、零售业、互联网服务业中具有代表性的易逝品作为研究对象。主要内容分成三个部分进行论述。
(1)集装箱运输业中易逝品定价问题。建立了以期望收益最大化为目标,需求服从泊松分布、保留价格服从指数分布和威布尔分布的集装箱舱位定价模型,得到最优定价方程,并用解析的方法得到了最优价格完整、全面的性质,最后应用算例对性质进行验证和解释。
(2)零售业中易逝品定价问题。分别研究了库存离散和库存连续下易腐商品的定价模型。对于库存连续的情形,建立了符合易腐商品特性的多阶段定价模型。该模型是以期望收益最大化为目标,库存连续、时间离散的模型。借助基于价格的报童模型,应用递归的方法对该模型进行求解。最后通过算例探讨了易腐商品的损耗对商品价值、库存及价格的影响,并对之进行管理上的解释。对于库存离散的情形,基于易腐商品的特性,建立有限时域中以期望收益最大化为目标的易腐商品的动态定价模型。这个模型是基于多级离散价格和离散库存的连续时间的收益管理模型。然后由最大凹向包络理论产生的最优价格的可行集,结合利用动态规划方法得到的价格调整的最优时间序列,形成最优价格的控制策略。
(3)互联网服务业中易逝品定价问题。分别研究了基于网上拍卖的传统易逝品定价问题和关键字广告位定价问题。在基于网上拍卖的传统易逝品定价问题中,针对商品数量有限下逢低买入拍卖模型,设计一种带极值扰动算子的QPSO(Quantum-behaved ParticleSwarm Optimization)算法进行优化和数值计算,分析了成本与价格是两级阶段以上情形时逢低买入拍卖的适用条件。在此基础上,把拍卖时间引入到模型中作为一个决策变量,分析逢低买入拍卖网站陷入困境的原因。在关键字广告位定价问题中,建立了包含保留价格的关键字广告位拍卖模型,分析了保留价格对投标者的投标策略和搜索引擎提供商的期望收益的影响,并通过数值仿真的方法对影响投标者的投标策略和搜索引擎提供商的期望收益的因素进行讨论,给出了保留价格的设置方法。
Due to economic globalization, product proliferation and technological progress, customer demand becomes highly uncertain across many industry sectors, which brings the huge difficulties to the enterprises. Compare to the other kind products or services, the perishable products have some special characters, such as the shorter product life cycle, the more discriminating customers demand, the more fierce market competition, which make the enterprises face the more stern challenge. It has become an urgent topic in both theoretical field and practical field how to make out feasible prices for the competition dominance and the enterprises' continuously developing.
The dynamic pricing based on revenue management has been the efficient tool in solving the problem of price of perishable products. It optimizes the enterprises' existing resources by scientific prediction of market requirements and reasonable prices without increasing costs. Firstly it is widely used in such service industry as aviation and gets good results. Then it is gradually applied in other service industries, e.g. hotel, car rental, broadcasting, Internet service, even in manufacturing industry. Though the theory of revenue management can be applied in the vary industries, there is the obvious difference in the market mechanism, and the manner must be reasonably specified and defined based on industrial features.
The theory and application of revenue management on container shipping industry, retail trade and Internet services industry is emphasized. For some reason there is little application of revenue management on these industries. With opening to WTO, our country faces more and more competitions, and it is necessary to improve the service level of these industries based on revenue management. So three stochastic pricing problems are studied due to various industrial features, and the main content is listed as follows:
(1) Pricing Model for Perishable products in container shipping industry. To gain maximum expected revenue, pricing model of container liner shipping is proposed. The optimized pricing equation is drawn under the condition that demand is a Poisson process and reservation price is exponential distribution or weibull distribution, and the whole optimized policies are drawn by the analytical measure. Finally, the characters of optimal price are drawn and numerical example is provided.
(2) Pricing Model for Perishable products in retail trade. The discrete-inventory model and the continuous-inventory model are both discussed respectively. And the character of the time to deterioration is represented. For continuous-inventory condition, dynamic pricing model of deteriorating items is proposed to gain maximum expected revenue, which is a continuous-inventory and discrete-time revenue management model. Then optimal solution is drawn by dynamic programming recursions based on a price-setting newsvendor problem. Finally, it is found how items deterioration is influential to price, expected revenue and inventory by numerical examples. For discrete-inventory condition, dynamic pricing model of deteriorating items is proposed, which is a continuous-time revenue management model based on a set of discrete price levels. Then we show a subset of these prices which form a concave envelope is potentially optimal, and draw the optimal solution by dynamic programming recursions. Finally, it is found how items deterioration is influential to the optimal solutionby numerical examples.
(3) Pricing Model for Perishable products in Internet services industry. The pricing problems for traditional perishable products and AdWords are discussed. For traditional perishable products condition, the optimal pricing problem with the group-buying auction is mainly studied. Since the function of seller's expected revenue is difficult for the normal function optimization methods to solve, the QPSO with the extremum disturbed arithmetic operators is introduced to settle it. Then the auction time is introduced into the model as decision variable, and the failure reason of the group-buying auction is discussed. For AdWords condition, the AdWords auction model with reserve price is proposed, and we analyze the strategy of bidders and the optimal auction mechanism of search engine providers. Then, it is analyzed how reserve price is influential to the bidding strategies and search engine providers' expected revenue. On the basis of the above, Ad Words are classified, and the various Ad Words' principles of setting reserve price are drawn by numerical simulation. Finally, the method of setting reserve price is proposed.
目前,解决易逝品定价最得力的方法是基于收益管理的动态定价,它是在不增加成本的情况下,通过科学的市场需求预测和合理定价使企业现有资源配置最优化。起源于航空业的收益管理不仅在客运、货运等运输领域得到了广泛应用,也已经扩展到了包括酒店、租车、零售、广播电视、互联网服务等众多服务行业,甚至在制造业(如高科技产业)也得到了相应的应用。虽然收益管理的理念能够应用于不同行业,但是每个行业的市场发展程度状况,市场运作、管理和组织存在较大的差异,因此在引进并运用收益管理来改造和完善企业运作水平和收入能力时,需要考虑行业特点,合理界定运用收益管理的方式和规模。
作为收益管理应用扩展的重要行业—集装箱运输业、零售业、互联网服务业,收益管理的应用具有鲜明的行业特征,且取得一定的成效,引起了学术界与商界的巨大重视。但就我国而言,在这些行业中,关于收益管理的理论研究和实践工作进展缓慢。特别在我国进入WTO后,行业面对愈来愈激烈的国际竞争,有必要结合行业的自身特点,以收益管理的思想和技术提高行业的服务和运作水平,进而提高行业的整体竞争力。因此,本文选择集装箱运输业、零售业、互联网服务业中具有代表性的易逝品作为研究对象。主要内容分成三个部分进行论述。
(1)集装箱运输业中易逝品定价问题。建立了以期望收益最大化为目标,需求服从泊松分布、保留价格服从指数分布和威布尔分布的集装箱舱位定价模型,得到最优定价方程,并用解析的方法得到了最优价格完整、全面的性质,最后应用算例对性质进行验证和解释。
(2)零售业中易逝品定价问题。分别研究了库存离散和库存连续下易腐商品的定价模型。对于库存连续的情形,建立了符合易腐商品特性的多阶段定价模型。该模型是以期望收益最大化为目标,库存连续、时间离散的模型。借助基于价格的报童模型,应用递归的方法对该模型进行求解。最后通过算例探讨了易腐商品的损耗对商品价值、库存及价格的影响,并对之进行管理上的解释。对于库存离散的情形,基于易腐商品的特性,建立有限时域中以期望收益最大化为目标的易腐商品的动态定价模型。这个模型是基于多级离散价格和离散库存的连续时间的收益管理模型。然后由最大凹向包络理论产生的最优价格的可行集,结合利用动态规划方法得到的价格调整的最优时间序列,形成最优价格的控制策略。
(3)互联网服务业中易逝品定价问题。分别研究了基于网上拍卖的传统易逝品定价问题和关键字广告位定价问题。在基于网上拍卖的传统易逝品定价问题中,针对商品数量有限下逢低买入拍卖模型,设计一种带极值扰动算子的QPSO(Quantum-behaved ParticleSwarm Optimization)算法进行优化和数值计算,分析了成本与价格是两级阶段以上情形时逢低买入拍卖的适用条件。在此基础上,把拍卖时间引入到模型中作为一个决策变量,分析逢低买入拍卖网站陷入困境的原因。在关键字广告位定价问题中,建立了包含保留价格的关键字广告位拍卖模型,分析了保留价格对投标者的投标策略和搜索引擎提供商的期望收益的影响,并通过数值仿真的方法对影响投标者的投标策略和搜索引擎提供商的期望收益的因素进行讨论,给出了保留价格的设置方法。
Due to economic globalization, product proliferation and technological progress, customer demand becomes highly uncertain across many industry sectors, which brings the huge difficulties to the enterprises. Compare to the other kind products or services, the perishable products have some special characters, such as the shorter product life cycle, the more discriminating customers demand, the more fierce market competition, which make the enterprises face the more stern challenge. It has become an urgent topic in both theoretical field and practical field how to make out feasible prices for the competition dominance and the enterprises' continuously developing.
The dynamic pricing based on revenue management has been the efficient tool in solving the problem of price of perishable products. It optimizes the enterprises' existing resources by scientific prediction of market requirements and reasonable prices without increasing costs. Firstly it is widely used in such service industry as aviation and gets good results. Then it is gradually applied in other service industries, e.g. hotel, car rental, broadcasting, Internet service, even in manufacturing industry. Though the theory of revenue management can be applied in the vary industries, there is the obvious difference in the market mechanism, and the manner must be reasonably specified and defined based on industrial features.
The theory and application of revenue management on container shipping industry, retail trade and Internet services industry is emphasized. For some reason there is little application of revenue management on these industries. With opening to WTO, our country faces more and more competitions, and it is necessary to improve the service level of these industries based on revenue management. So three stochastic pricing problems are studied due to various industrial features, and the main content is listed as follows:
(1) Pricing Model for Perishable products in container shipping industry. To gain maximum expected revenue, pricing model of container liner shipping is proposed. The optimized pricing equation is drawn under the condition that demand is a Poisson process and reservation price is exponential distribution or weibull distribution, and the whole optimized policies are drawn by the analytical measure. Finally, the characters of optimal price are drawn and numerical example is provided.
(2) Pricing Model for Perishable products in retail trade. The discrete-inventory model and the continuous-inventory model are both discussed respectively. And the character of the time to deterioration is represented. For continuous-inventory condition, dynamic pricing model of deteriorating items is proposed to gain maximum expected revenue, which is a continuous-inventory and discrete-time revenue management model. Then optimal solution is drawn by dynamic programming recursions based on a price-setting newsvendor problem. Finally, it is found how items deterioration is influential to price, expected revenue and inventory by numerical examples. For discrete-inventory condition, dynamic pricing model of deteriorating items is proposed, which is a continuous-time revenue management model based on a set of discrete price levels. Then we show a subset of these prices which form a concave envelope is potentially optimal, and draw the optimal solution by dynamic programming recursions. Finally, it is found how items deterioration is influential to the optimal solutionby numerical examples.
(3) Pricing Model for Perishable products in Internet services industry. The pricing problems for traditional perishable products and AdWords are discussed. For traditional perishable products condition, the optimal pricing problem with the group-buying auction is mainly studied. Since the function of seller's expected revenue is difficult for the normal function optimization methods to solve, the QPSO with the extremum disturbed arithmetic operators is introduced to settle it. Then the auction time is introduced into the model as decision variable, and the failure reason of the group-buying auction is discussed. For AdWords condition, the AdWords auction model with reserve price is proposed, and we analyze the strategy of bidders and the optimal auction mechanism of search engine providers. Then, it is analyzed how reserve price is influential to the bidding strategies and search engine providers' expected revenue. On the basis of the above, Ad Words are classified, and the various Ad Words' principles of setting reserve price are drawn by numerical simulation. Finally, the method of setting reserve price is proposed.
引文
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