Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.     

Dynamic optimal control policy in advertising price and quality

This study presents an algorithm for deriving the long-term polices of quality level, price and advertisement for a product. The diffusion models and cost functions are combined to formulate profit functions capable of determining future profit trends. The algorithm first implements the optimal control theory to derive the optimal conditions of the profit function. Then the genetic algorithm is employed to search for the approximate solutions of quality level, price and advertising expenditure at each period on the planning horizon (life cycle). Examples of different scenarios of the model parameters are presented to describe the results obtained herein. Sensitivity analysis for the major parameters is performed to specify their effects on profits. Results in this study allow us, firstly, to obtain explicit solutions simultaneously with respect to quality, price and advertising policies, secondly, to propose an appropriate algorithm for solving the different scenarios of the dynamic profit function, which consists of the diffusion function and cost function, and thirdly, to enhance the long-term profit performance via the polices proposed herein, that is the approximation of the best solution.     

制造商竞争与合作下双渠道供应链联合减排的微分博弈分析

以两个制造商与一个零售商组成的双渠道供应链为研究对象,分析制造商竞争与合作模型下供应链的最优均衡策略,并探讨系统关键参数对供应链各成员利润的影响.研究发现,只有当减排效率差异水平满足一定条件时,两制造商才会同时选择合作,且合作模型下制造商的利润总和增大,而减排努力、广告分担率、广告努力和零售商的利润减小.随着传统渠道市场占有率、减排竞争和广告竞争的增大,竞争模型下零售商的利润增大,而合作模型下的利润与广告竞争无关;制造商的利润变化取决于减排效率、网络渠道和传统渠道的边际利润.     

Modeling the dynamic optimal advertising in stochastic condition

An effort to model the dynamic optimal advertising was made with the uncertainty of sales responses in consideration. The problem of dynamic advertising was depicted as a Markov decision process with two state variables. When a firm launches an advertising campaign, it may predict the probability that the campaign will obtain the sales reponse. This probability was chosen as one state variable. Cumulative sales volume was chosen as another state variable which varies randomly with advertising. The only decision variable was advertising expenditure. With these variables, a multi-stage Markov decision process model was formulated. On the basis of some propositions the model was analyzed. Some analytical results about the optimal strategy have been derived, and their practical implications have been explained.     

需求信息不对称下的双渠道供应链合作广告投资决策分析

研究制造商主导的Stackelberg 博弈下双渠道供应链的合作广告策略, 分析信息不对称及双渠道对供应链合作广告投资决策的影响. 研究表明, 零售商在具有需求信息优势时会谎报需求信息, 并且在一定条件下其谎报决策会降低制造商的利润, 但能提高供应链的利润, 这种情况下制造商无法通过激励合同促使零售商共享信息. 另外, 在最优合作广告策略下, 当直销渠道与分销渠道所占市场份额的分配比例小于一定值时, 制造商采取双渠道会使供应链参与者均受益.

     

A cooperative advertising collaboration policy in supply chain management under uncertain conditions

Many industries are facing big challenges to design supply chains in a way to maximize the profit and meet the heightened expectations of the customer. This new era entirely relies on the dynamic advantages of competition and the role played by the collaboration policy. A global economy and increasing demand have put a huge pressure on supply chain partners to build a collaboration policy based on price, order quantity, and advertising. Companies are adopting the idea of ”shaking hands” to obtain more profit instead of taking risks through competition. Cooperative (co-op) advertising is a significant policy of centralized supply chain management (SCM) to boost the revenues generated by the supplier, manufacturer, and retailers. The uncertain costs associated with the supply chain management also create obstacles in economic analysis and feasibility. These uncertainties are associated with the basic costs of all supply chain partners, which are represented using a signed distance formula. This paper develops the concept of co-op advertising among the supplier, manufacturer, and retailers with a variable demand driven by selling price and advertising costs, where all basic costs are considered as fuzzy. The profit is optimized by considering variable cycle time, shipments, pricing and advertising costs for the decision support system of the supply chain management. The optimal results of the co-op advertisement ensured an increase in the revenue of whole supply chain.     

基于碳排放限额和低碳销售努力的博弈模型分析及控制

以双渠道供应链为研究对象,在考虑碳排放限额和低碳销售努力的基础上,分别构建单周期静态博弈模型和多周期动态博弈模型,研究最优决策和系统稳定性问题.在静态模型中,给出集中决策和分散决策下的最优策略解析式;在动态模型中,探究博弈系统的局部渐近稳定性条件,讨论时滞等参数对系统稳定性的影响,并对失稳系统进行有效控制.研究表明:提高碳排放限额能够增加供应链系统利润;随着低碳销售努力的增加,供应链系统利润和制造商利润均呈下降趋势;不合理的延迟策略将导致系统失去稳定.     

基于提前支付的非瞬时变质产品批量订货定价策略

当供应商处于供应链节点的买方市场时,通常要求零售商提前支付一定比例购置成本作为订金.针对该问题研究零售商促销努力下存在随机需求的非瞬时变质产品批量订货定价策略,考虑零售商提前支付策略,允许部分缺货.在一定条件下可得零售商最优补货周期和局部最优定价策略,随之提出相应的求解算法.数值计算结果表明:若提前支付购置成本占比或利率增大,则零售商利润将显著减少;提前支付期限和期数均对最优利润产生消极影响;零售商采取积极促销策略可有效提升自身利润.     

Advertising channel selection in a segmented market

We consider a market with a finite number of segments and assume that several advertising channels are available, with different diffusion spectra and efficiencies. The problem of the choice of an advertising channel to direct the pre-launch campaign for a new product is analyzed in two steps. First, an optimal control problem is solved explicitly in order to determine the optimal advertising policy for each channel. Then a maximum profit channel is chosen. In a simulation example we consider the choice of a newspaper among six available and analyze the relations among the firm target market and the advertising channels environment which induce the optimal decision.     

考虑线上线下零售商竞争的制造商双渠道定价策略

根据现有的不同电商销售平台模式,将制造商双渠道销售模式划分为自营模式、平台模式和混合模式.分析在制造商主导的双渠道供应链中,3种不同渠道模式下价格竞争系数和佣金比例系数对其他经济变量的影响,以及制造商的最优定价决策与渠道选择问题.通过模型和数值分析发现,在平台模式和混合模式中,当制造商保证佣金比例系数在一定范围内,制造商利润随佣金比例系数的增加而减少,传统零售商、网络零售商和供应链总利润随佣金比例系数的增加而增加.在3种渠道模式中,混合模式对传统零售商和制造商利润增加更有利,平台模式对网络零售商和供应链总利润增加更有利.     

需求随机依赖库存环境下的订货仿真优化模型

需求的随机性和依赖库存性是库存问题的特点之一,在需求以泊松分布的形式随机依赖库存的条件下讨论了（Q,T）型库存控制问题。为了评估库存控制策略的平均盈利水平,建立了该库存问题的离散事件系统仿真模型,设计了一种基于仿真的种群重叠、遗传操作非重叠的进化算法,用以优化库存控制策略,类似设计了基于仿真的模拟退火和粒子群优化算法进行比较。通过实例分析了不同参数的变化对模型最优解的影响,灵敏度分析表明需求依赖库存效应越明显时,利润水平越高,最优订货策略越倾向于高库存、短周期和现货销售。仿真实例说明了基于仿真的优化算法的可行性、有效性。     

Analysis of Admission and Inventory Control Policies for Production Networks

Problems of inventory control and customer admission control are considered for a manufacturing system that produces one product to meet random demand. Four admission policies are investigated: lost sales, complete backordering, randomized admission, and partial backordering. These policies are combined with an integral inventory control policy, which releases raw items only when an incoming order is accepted and keeps the inventory position (total inventory minus outstanding orders) constant. The objective is to determine the inventory level and the maximum number of backorders, as well as the admission probability that maximize the mean profit rate of the system. The system is modeled as a closed queueing network and its performance is computed analytically. The optimal parameters for each policy are found using exhaustive search and convex analysis. Numerical results show that managing inventory levels and sales jointly through partial backordering achieves higher profit than other control policies.     

Co-op advertising and pricing models in manufacturer–retailer supply chains

Cooperative (co-op) advertising plays a significant role in marketing programs in conventional supply chains and makes up the majority of promotional budgets in many product lines for both manufacturers and retailers. Nevertheless, most studies to date on co-op advertising have only assumed that the market demand is only influenced by the advertising level but not in any way by the retail price. That is why our work is concerned with co-op advertising and pricing strategies in distribution channels consisting of a manufacturer and a retailer. Four different models are discussed which are based on three non-cooperative games (i.e., Nash, Stackelberg retailer and Stackelberg manufacturer) and one cooperative game. We identify optimal co-op advertising and pricing strategies for both firms mostly analytically but we have to resort to numerical simulations in one case. Comparisons are then made about various outcomes, especially the profits, for all cases. This leads to consider more specifically the cooperation case in which profits are the highest for both the retailer and the manufacturer, and how they should share the extra joint profit achieved by moving to cooperation. We solve this bargain problem using the Nash bargaining model.     

Dynamic optimisation of price,warranty length and production rate

This study investigates a marketing and production problem that uses price, warranty length and production rate as simultaneous dynamic decision variables. Furthermore, this study was conducted under a policy of free replacement of defective items; and under conditions where demand was dynamic and dependent on price, warranty and cumulative sales. A continuous profit maximisation model was formulated, which first considers the expected warranty cost per item. Then, it considers the steps for dynamic optimisation, which eventually derive the optimal price, warranty length and production rate. Discretisation was then applied to the profit maximisation model and a digital computer was used to identify the optimal control paths, obtaining a finite solution that is a set of real numbers for practical application. A model-driven Decision Support System is finally established, which provides a graphical user interface for overcoming the complexity of the analytical process. Subsequently, the proposed system was tested and the analytical solution was verified using several demand functions for additive lifetime distributions, thereby demonstrating the system's effectiveness.     

On optimum advertising pulsing decisions in a non-stationary market

Using empirical findings available in the literature, sales behavior in response to advertising pulsing policy has been modeled mathematically in a non-stationary market. The paper discusses in detail optimum advertising pulsing policy.This policy has been compared with an alternative policy commonly used in practice. The results of the research indicate the possibility of achieving substantial savings in the advertising budget and/or increase in sales revenues of a firm when implementing advertising pulsing policy.     

Optimal advertising decisions for promoting retail and online channels in a dynamic framework

Advertising plays an important role in sales promotion in supply chains. In this paper, advertising decisions for retail and online channels respectively, by retailer and manufacturer will be analyzed. The competition between retailer and manufacturer will be modeled by differential game theory, and feedback Nash equilibrium of the game will be obtained. Some insights are provided by using comparative statics. The obtained results show that compatibility factor of a product with online marketing, difference between manufacturer's online price and wholesale price, effectiveness of advertising, marginal profits, and cost of advertising all have significant effects on the advertising decisions in the equilibrium.     

Service cooperation and marketing strategies of infomediary and online retailer with eWOM effect

In contemporary electronic commerce, an infomediary displays electronic word-of-mouth (eWOM) information of customers and links shoppers to retail websites, thus acting as an intermediary between buyers and sellers. This paper studies an online supply chain system in which the infomediary presents demand-referral services to online retailers based on eWOM of customer information. It is assumed that online demand is affected by retailer price, referral service effort, and eWOM. The demand function is extended and developed based on Bass’s model. A Stackelberg game model of service cooperation is presented, and then the optimal decisions on retailers’ prices and infomediary service efforts in the decentralized supply chain are analyzed. Moreover, the profits and cumulative sales in supply chain equilibrium are analyzed under several parameters. A computational experiment is implemented to verify the validity and effectiveness of the model. The results show that price sensitivity has a significant negative effect on cumulative retailer sales and the profits of retailers and infomediary, but the effect of service sensitivity and sales periods on profits is absolutely positive. Specifically, eWOM has two different impacts on the profit of the retailer and infomediary respectively. Finally, conclusions and management implications for supply chain parties are presented, along with some possible directions for further research.     

Dynamic selling of quality-graded products under demand uncertainties

This paper examines dynamic selling (DS) problems under demand uncertainties. Quality-graded products with fully downward substitutable demands are considered. Downward demand substitution indicates that demands for lower quality grade products can be fulfilled by either designated or higher quality grade products. In this dynamic selling problem, decision makers need to choose an optimal selling policy in each decision epoch. The objective is to identify an optimal policy for the dynamic selling of quality-graded inventory.DS problems are formulated as a discrete-time Markov decision process (MDP) model. In the MDP model, demand type and inventory levels are state variables. The objective is to maximize expected profits. In such a multi-dimensional dynamic decision problem, computational complexity is a chief concern. This study proves the structure of optimal policies that significantly reduce computational complexity. Performance of optimal dynamic selling policies is evaluated in detailed numerical studies.     

实时动态规划的最优行动判据及算法改进

主要以提高求解马尔可夫决策问题的实时动态规划(real-time dynamic programming,简称RTDP)算法的效率为目的.对几类典型的实时动态规划算法所使用的收敛判据进行了对比分析,并利用值函数上界、下界给出了称为最优行动判据的收敛判据,以及一个更适合实时算法的分支选择策略.最优行动判据可以更早地标定当前状态满足精度要求的最优行动供立即执行,而新的分支选择策略可以加快这一判据的满足.据此设计了一种有界增量实时动态规划(bounded incremental RTDP,简称BI-RTDP)算法.在两种典型仿真实时环境的实验中,BI-RTDP均显示出优于现有相关算法的实时性能.     

Determining profit-optimizing return policies – a two-step approach on data from taobao.com

Selecting an optimal return policy requires taking into account two effects: the potential positive effect on sales and the potential negative effect of higher costs. We propose a two-step model, in which we first utilize a robust regression to explain purchase behavior, and then apply a zero-inflated negative binominal regression to model the return behavior. We apply this model to data from the most important online platform in China and obtain three main findings. First, the adoption of return policies results in increased sales, while reputation works as a moderator in this process. Second, good reputation and traditional customer friendly return policies (like the Seven-Day Return policy) can significantly increase the number of returns, while more guarantee credibility (enhanced by Guarantee Money) is related to fewer returns. Taken together, both the Seven-Day Return policy (profit increase of +0.29 %) and Guarantee Money (profit increase of +0.016 % per Yuan guarantee) ultimately increase firms’ profit.