Optimal pricing and inventory policy with order cancelations under the cash-on-delivery payment scheme

Considering a periodic review system where the online seller allows the customers to pay when the products are delivered to them（referred as cash-on-delivery payment scheme in this paper）,the authors investigate the seller＇s joint pricing and inventory control policy with a finite planning horizon.In particular,the authors incorporate the customers＇ possible order cancellation behavior with the cash-on-delivery scheme.It can be proven that the base-stock list price policy is optimal under mild conditions.The authors also analyze the impact of the customers＇ forward looking behavior on the optimal policy.     

考虑库存能力约束的批量问题与定价的联合决策

针对多周期离散时间情形,研究了库存能力约束下如何有效地协调定价决策与批量决策,使得企业利润最大化。建立了非线性混合整数规划模型。分析了最优解的特征,详细讨论了子问题的求解方法。提出了基于动态规划的精确算法,可以在多项式时间内求解出联合决策问题的最优定价与最优生产计划。实验结果分析了库存能力与最优利润、最优生产计划之间的关系。     

Optimal Dual-Channel Dynamic Pricing of Perishable Items under Different Attenuation Coefficients of Demands

This paper discusses optimal dual-channel dynamic pricing of a retailer who sells perishable products in a finite horizon.The type of product which is equipped with different attenuation coefficients of demands on different sales channels is considered.Novel demand functions for the two channels are proposed according to attenuation coefficients of demands,and then a decision model is constructed,which can be handled stage-by-stage.It is shown that the sales price and the sales quantity of the channel which possesses more market shares are both higher than the ones of the other channel at each sales stage.More importantly,by analyzing the reasonability of the obtained solution,a necessary and sufficient condition is proposed to guarantee that both of the two channels will not stop selling through the entire period.We also propose an approach by the elimination method to deal with cases in which some channel stops selling.Further,we demonstrate that the channel which possesses more market shares is the optimal option when only one channel runs.Finally,numerical examples are presented to investigate the change of sales prices of the two channels under different market potential demands.     

A multi-period pricing and inventory control model

<正> The authors analyze a finite horizon,single product,period review model in which pricingand inventory decisions are made simultaneously.Demands in different periods are random variablesthat are independent of each other and their distributions depend on the product price.Pricing andordering decisions are made at the beginning of each period and all shortage are backlogged.Orderingcost is a convex function of the amount ordered.The objective is to find an inventory and pricing policymaximizing expected discounted profit over the finite horizon.The authors characterize the structure ofthe optimal combined pricing and inventory strategy for this model.Moreover,the authors demonstratehow the profit-to-go function,order up to level,reorder point and optimal price change with respectto state and time.     

Coordinating Pricing,Ordering and Advertising for Perishable Products Over an Infinite Horizon

Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions interact with each other and what is the effect of advertising on pricing and ordering decisions? To understand this interaction, we consider a newsvendor-type firm that sells a perishable product in a stable market and dynamically determines the joint ordering, pricing and advertising strategies. The problem is modeled as an infinite horizon newsvendor problem with an advertising carryover effect and price-sensitive demand. We characterize the optimal pricing, advertising and inventory strategies and their comparative statics, and consider how this policy differs from the traditional approach without the advertising effect. We show that the optimal effective advertising level is monotonically increasing with the effective advertising level in the previous period, and hence the optimal strategies (advertising, pricing, inventory level) globally converge to the steady states in the long run. We numerically show that the optimal policy can reap significant profit, which underscores the importance of the advertising-driven ordering and pricing strategies.     

最优均匀广告与订货策略的联合决策模型

传统的经济订货量模型通常不考虑广告对商品需求的影响，而事实上广告却是商家促销的重要手段之一．文章则将广告宣传引入到时变需求的经济订货量模型，通过分析均匀广告策略对需求的影响、运用最小二乘法确定均匀广告策略下商品需求率，为销售商建立了在有限计划期内寻求最优均匀广告投入和相应订货策略的联合决策模型，最后给出了应用实例，并分析了模型费用参数变化对最优解的影响．     

Optimal pricing,production, and sales policies for new product under supply constraint

This paper considers a firm that sells a durable product with a given market potential. The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.     

不同技术授权模式下的沙漠治理

在沙漠化治理规模和企业商誉均动态变化的基础上，通过构建两竞争企业治理沙漠化的微分博弈模型，研究了不同治理技术授权模式下双方的产品定价、沙漠化治理投入水平和治理规模以及收益变化。研究发现，两企业经营的沙漠特色产品最优定价和技术授权方的沙漠化治理投入水平均不受技术授权模式影响。在无技术授权情况下，两企业的收益均处于最低水平。在特许权费用技术授权模式下，被授权方的沙漠化治理投入水平和治理规模以及两企业的收益均有提高，且被授权方的收益增长幅度大于授权方的收益增长幅度。在固定费用技术授权模式下，被授权方的沙漠化治理投入水平和治理规模以及两企业的收益均最高，且此时两企业的沙漠化治理规模相同。     

消费者参考质量和参考价格影响下质量改进与过程创新动态控制研究

为探讨垄断企业产品质量改进与过程创新的最优控制问题，考虑参考质量和参考价格对消费者需求的影响，建立了双参考效应下的动态控制模型，分析系统稳态均衡及投资策略并进行数值模拟。研究结果表明：企业利润最大化条件下，存在可行的参数取值使系统为鞍点均衡，企业稳态投资受到产品质量、边际生产成本、参考质量及参考价格的影响。随着参考质量的增大，企业对质量改进的瞬时投资率不断增长而对过程创新的瞬时投资率不断下降，两种瞬时投资率随参考价格的增长而下降，且符号相同时投资组合具有互补性。企业通过对质量与创新投资策略的选择提升消费者需求及企业竞争力。     

多设备系统的生产批量、质量控制与预知维护联合优化

针对由多台设备通过串、并混联构成的多阶段生产系统,对其生产批量、质量控制以及预知维护进行了联合建模与优化.系统中的各台设备随时间逐渐发生劣化,可靠性及产品加工质量随之降低.在每个生产批量结束时,对各设备进行状态检测并评估其在下个生产期内的可靠性.预知维护同时以设备的可靠性、结构重要度以及产能比为决策依据,以合理分配维护资源.在每个阶段设置质检台以实时检测各设备加工产品的质量,并根据质量反馈信息,对次品率超过控制阈值的设备进行预防性更换以改善性能提高产品质量.以批量生产周期、质量控制阈值以及预知维护参数为三维联合决策变量,建立了有限时域内的平均费用率模型.基于蒙特卡罗仿真和响应曲面法设计了优化算法,实现了对模型的快速近似求解.最后通过一个实例演示了本模型,并对结果作了相关统计学分析.     

考虑资源约束和变质期的订货批量与定价的联合决策

传统的订货计划一般假定需求事先已知.研究了需求是价格的函数、订货能力有限情形时,订货商对变质性产品协调地进行定价决策和订货决策,使得利润最大化.建立了二次规划数学模型. 提出了基于动态规划的算法,可以在多项式时间内求解原问题的最优定价策略和最优订货计划.实验结果表明,与分散决策相比,联合决策可以给订货商带来更多的利润.通过订货能力的灵敏度分析,表明订货能力变化对利润和价格产生显著影响,有助于订货商选择恰当的订货能力水平.通过变质期的灵敏度分析,揭示了变质期对订货策略影响显著.     

呼叫中心中排队系统服务率的动态控制方法

对多服务台、缓存容量受限、用户等待太久后厌烦而中途离开的呼叫中心排队系统,运用马尔科夫决策过程理论,建立折扣准则最小期望代价函数模型,动态控制服务率.结果表明,合适的服务台数和到达率的情况时,最优策略会具有单调性,提高决策的效率, 并且结合有限阶段和无限阶段进行分析,兼顾了系统稳态工作时服务台利用率.     

Optimal Output Feedback Control and Stabilization for NCSs with Packet Dropout and Delay: TCP Case

This paper considers the output feedback control and stabilization problems for network control systems (NCSs) with packet dropout and input delay, and the TCP (transmission control protocol) case is mainly investigated. Specifically, whether the control signal is lost can be acknowledged by the receiver in the NCSs. The main contributions are: 1) For the finite horizon case, the “optimal” output feedback control is derived by using the dynamic programming approach, and it is noted that the separation principle holds for the considered situation; 2) For the infinite horizon case, for the first time, the necessary and sufficient stabilization conditions are derived for NCSs with packet dropout and delay.     

排污约束下企业的投资与定价

考察了在政府对企业污染排放进行限制的条件下,当企业资本存在随机波动时企业如何进行动态投资和价值评估.运用随机动态最优控制方法,得到了企业价值的自由边界常微分方程以及相应的最优投资策略和治污策略.数值计算表明, 在企业资本规模较小时, 企业无排污支出,且排污约束对企业的投资和定价影响较弱, 而当企业资本规模较大时,企业必须支付一定的治污费用以降低自身的污染排放量; 同时,排污约束不仅显著降低了企业的总价值以及资本的平均和边际价值,还减小了企业的投资动机.     

公平关切下闭环供应链的决策与创新投入

新旧动能转换政策的出台对闭环供应链提出了新的要求与挑战,考虑政府奖励机制,构建公平中性的分散决策、零售商公平关切的分散决策及集中决策3种决策模式。给出3种模式的最优决策,并分析新动能创新投入成本、公平关切系数对闭环供应链定价、新动能创新投入、回收率及各方利润的影响。在此基础上,设计“收益共享联合固定费用-成本共担”契约实现分散决策的协调。研究显示：随着创新成本的增加,新旧动能转化效率降低,制造商和零售商的谈判空间变小,同时批发价和销售价格降低,这与传统“投入越高售价越高”的观点不同;零售商的公平关切行为不仅损害了主导企业制造商的利润,也损害了己方利润,同时降低了新动能创新投入水平、回收率和消费者效用,但增加了己方系统利润的占比;集中决策下新动能创新投入、回收率和各方利润最高,零售价格反而最低,可以通过“收益共享联合固定费用-成本共担”协调机制达到这种效果。并且,在该机制下,在回收活动中受益越多的企业,承担的回收成本越多。     

Moral hazard strategy and quality contract design in a two-echelon supply chain

Based on game theory and principal-agent theory, this paper focuses on how to control product quality and design quality contract in supply chain when moral hazard exists. We set up the supplier and buyer’s expected profits function model, in which the supplier makes production process investment-level decision and decides on the product quality prevention level, whereas the buyer makes quality evaluation decision and decides on the product quality inspection level. The supplier with a moral hazard of reducing investment level may lack investment in the production process; thus, the buyer will pay the information rent to incentivize the supplier to improve the investment level. The buyer creates the moral hazard of exaggerating the product quality defective rate, who may overinvest in the inspection process. We use the optimal condition to solve supplier’s first-best investment level, product quality prevention level, and buyer’s first-best quality inspection level, internal penalty, and apportionment ratio of external failure cost. We also conduct a simulation test that shows the following: When the supplier improves its investment level, its product quality prevention level will increase, and the buyer’s quality inspection level will decrease. With the improvement in the buyer’s product quality inspection level, its internal penalty will increase, and the supplier’s external failure cost will also increase while its expected profits will decrease. Hence, the buyer will design an incentive contract, the expected profits of which will increase, and the whole supply chain’s joint expected profits function may become an inverse U shape. Finally, we develop a simulation example and propose suggestions for quality control strategy and contract design in the supply chain under the conditions of asymmetric information.     

考虑批量折扣的单供货商多销售商动态规划模型

建立了有限计划期内单供货商多销售商动态规划模型。引入分配系统及最小分配的概念重新描述多销售商联合订购问题。在假定供货商提供全单位批量折扣的前提下,利用本文得到的判定最小分配的充要条件给出了寻求供货商最优生产策略及各个销售商最优订购策略的动态规划算法。最后给出了应用实例。     

Dynamic pricing under temperature control for perishable foods

Consumers pay more and more attention to the quality of perishable roods, which is mainly affected by storage temperature. This paper presents a dynamic pricing model for perishable foods under temperature control. To maximize the total profit, the optimal price and storage temperature are obtained using Pontryagin＇s maximum principle. A static pricing model is provided to compare with the dynamic one. It is shown by a numerical example that the dynamic policy can make more revenue than the static one. Moreover, the managerial implications are analyzed and the effectiveness of the proposed method is demonstrated.     

非立即变质品的订购、定价与保鲜投资决策

考虑了一个非立即变质品的订购、定价与保鲜技术投资联合决策问题,其中产品的需求依赖于销售价格,变质率随时间变化,系统不允许缺货.此外,产品的时变变质率和保鲜期可以通过保鲜技术的投资得到控制,并采用一般形式的资本投资回报率构建模型.目的是决定最优的补货、定价和保鲜技术投资策略(包括是否投资和投资多少)以最大化系统的平均利润.证明了对于给定的定价和保鲜技术投资策略,最优补货策略唯一存在.在此基础上给出了一个寻找模型最优解的多阶段迭代求解算法.最后通过数值算例展示了模型和算法的应用,进一步采用数值方法对模型的数学性质进行了探讨,并对参数的灵敏度进行了分析.结果显示:当订购成本和产品购买成本较小或库存持有成本和产品初始保鲜期较大时,最优保鲜技术投资将为零,即不投资保鲜技术对系统最优.     

一种改进的collocation方法及其在动态定价问题中的应用

涉及多个状态变量的动态定价问题往往难以求解。基于此,引入多维插值与张量积,提出一种改进的collocation方法用于求解多状态变量的动态优化问题,并从理论上分析了改进后的collocation方法的收敛性。将改进的collocation方法应用于求解多个状态变量的动态经济问题。给出了改进后的collocation方法的实际运用,应用于解决有限记忆的动态定价问题。利用状态变量的切比雪夫格点与其估计值构造出时序的状态转移,并依据状态转移模拟最优价格路径。通过数值分析表明,改进后的collocation方法比线性二次逼近法更快的收敛于稳态。