Endogeneity of store attributes in heterogeneous store-level sales response models

Retailing firms as a rule decide on store attributes (e.g., store size) considering an assessment of future sales of these stores. Typically, managers allocate better or more equipment to stores for which they expect higher sales. Models which ignore the fact that this behavior leads to endogeneity overestimate effects of these attributes. Managers, who base decisions on such models, loose profits by installing more (or more costly) equipment. The number of papers studying store-level sales response models accounting for endogeneity appears to be very limited. We consider potential endogeneity of store attributes in the sales response function by an instrumental variable approach. We also allow for heterogeneity across stores by assuming that store-level coefficients are generated by a finite mixture distribution. Models are estimated by a Markov chain Monte Carlo simulation technique which combines two Gibbs sampling algorithms. In the empirical study both heterogeneity and endogeneity turn out to influence estimates. For a cross section of more than 1,000 gas stations credible intervals of differences of coefficients are computed between models ignoring and models considering endogeneity. These intervals indicate that models which ignore endogeneity overestimate the effects of two store attributes on sales. We also discuss managerial implications of these endogeneity biases.     

Salesforce design with experience-based learning

This paper proposes and analyzes an integrated model of salesforce learning, product portfolio pricing and salesforce design. We consider a firm selling two products, with a pool of sales representatives that is split into separate salesforces, one for each product. The salesforce assigned to each product is faced with an independent stream of sales leads. The salesforce may also handle leads that overflow from other product salesforces. In addition, salespeople “learn by doing” over their tenure on the job. In particular, the more time they spend selling a particular product, the more productive the sales effort. The objective of the firm is to maximize profits by optimizing the size of all salesforces as well as the prices of all products. Using data collected from the salesforce of a large manufacturer, we provide evidence for the link between experience and sales, and we demonstrate how parameters of the model may be estimated from real data. Numerical experiments using parameters derived from the data analysis indicate that the optimal salesforce size increases with both sales productivity and the learning rate, and decreases with salesforce costs (e.g., wage per representative), product production costs and consumer price sensitivity. We also find that worker learning can significantly dampen the effect of rising costs (or decreasing margins) on staffing levels. Finally, we examine the impact of learning on both the optimal salesforce structure (specialists versus generalists) as well as the optimal routing of sales leads to sales representatives.     

Dynamic pricing for fashion goods with partial backlogging

In today’s very competitive business environment, one way that companies endeavour to cut their costs is by reducing inventory. In addition to the use of inventory management, retailers of fashion goods usually employ dynamic pricing to influence market demand, such as non-periodic clearance sales or markdowns to increase sales volume and deplete stocks of goods. This paper deals with the specific demand style of fashion goods under the condition in which partial backlogging is allowed and the number of replenishments is constrained in order to fit in the real world situation of limited supply. The optimal replenishment quantities and the corresponding intervals are obtained with consideration of customers’ reserve prices and their influence on demand. In addition, discrete dynamic pricing is considered to frequently change the product prices to meet the customer requirements in different periods and to avoid high inventory holding costs from unsold products. A numerical example is used to validate the feasibility and effectiveness of the proposed approach, and sensitivity analyses are performed to investigate the important factors that influence the replenishment cycle and profit.     

Wholesale price discrimination with interdependent retailers

This paper examines the relationship between one manufacturer and two retailers who sell a product on their downstream markets. If a retailer invests in activities that enhance demand and, for example, improve the perceived image of the product, he or she might attract more customers, as well as increase the sales volumes of other retailers. In such a situation, free rider problems arise between the retailers, which finally lead to reduced sales efforts. We show that for linear wholesale prices, the manufacturer’s pricing strategy depends on the retailers’ investment costs and derive conditions for the optimality of wholesale price discrimination. We find that for low and high costs the manufacturer charges the retailers identical wholesale prices and thus does not have to bear any agency costs due to free riding. In all other cases, the manufacturer mitigates this problem by engaging in wholesale price discrimination. Our results indicate why it might make sense for a manufacturer to charge different wholesale prices even when the retailers have equal cost structures, market conditions, and investment options.     

Relational analysis model of weather conditions and sales patterns based on nonnegative tensor factorization

It is necessary to analyze the relationships between the retail sales of various items and weather conditions. However, the relationship between the sales of each item and the weather condition may vary among stores. Additionally, it is necessary to model the statistical relationships between a wide variety of goods and weather conditions by using past sales data. In such a case, it becomes unrealistic to construct a forecast model for every individual item owing to the breadth of items and the number of retail shops. This study proposes a model to analyze the relationships between the sales of various items and weather conditions. This method can be used to decompose the data into three matrices based on the nonnegative tensor factorization (NTF) method. The results of the analysis clarified that the proposed model can identify important items whose demand is strongly influenced by weather conditions, thereby increasing the effectiveness of inventory management. Additionally, the store clusters estimated by the proposed model can facilitate the construction of regression models that demonstrate the relationship between the sales of each item and weather conditions.     

Joint pricing and advertising strategy with reference price effect

Consumers are susceptible to reference price effects when they make purchase decisions for a certain product. Meanwhile, the sales price and advertisement are the determinable factors that have impact on consumers’ reference price which are also fundamental marketing strategies. Therefore, how to determine an appropriate sales price and advertising effort level to maximise firms’ profits is an essential task. A joint pricing and advertising problem for a monopolistic firm with consideration of reference price effect is investigated, where consumer demand rate is price-sensitivity and depends on the gap between the sales price and the reference price in consumers’ mind. An optimisation model is established to maximise the firm’s total profit by making a joint pricing and advertising strategy. The static and dynamic joint strategies are obtained by applying Pontryagin’s maximum principle. Results show that the dynamic strategies dominate the static ones. Furthermore, the dynamic pricing and dynamic advertising strategies are strategic complements. Additionally, the length of the sales period plays a key role in determining the superiority of the two dynamic strategies. Specifically, a relatively short sales period highlights the value of the dynamic advertising while a long sales period strengthens the function of the dynamic pricing.     

Value chain management for commodities: a case study from the chemical industry

We present a planning model for chemical commodities related to an industry case. Commodities are standard chemicals characterized by sales and supply volatility in volume and value. Increasing and volatile prices of crude oil-dependent raw materials require coordination of sales and supply decisions by volume and value throughout the value chain to ensure profitability. Contract and spot demand differentiation with volatile and uncertain spot prices, spot sales quantity flexibility, spot sales price–quantity functions and variable raw material consumption rates in production are problem specifics to be considered. Existing chemical industry planning models are limited to production and distribution decisions to minimize costs or makespan. Demand-oriented models focus on uncertainty in demand quantities not in prices. We develop an integrated model to optimize profit by coordinating sales quantity, price and supply decisions throughout the value chain. A two-phase optimization approach supports robust planning ensuring minimum profitability even in case of worst-case spot sales price scenarios. Model evaluations with industry case data demonstrate the impact of elasticities, variable raw material consumption rates and price uncertainties on planned profit and volumes.     

新鲜度差异下两种可替代生鲜品的多阶段定价策略研究

研究单个零售商销售2种可替代生鲜产品时的价格决策,建立3种定价策略下的决策模型,得到2种产品的最优固定价格、最优折扣价格和最优捆绑价格售价;通过数值仿真分析影响零售商价格决策的因素及其影响大小。研究结果表明,3种策略下产品价格都与产品新鲜度临界值同方向变化;最优固定价格随销售期临近度的增大而变高;对比3种策略下零售商的利润发现,有时捆绑价格是占优策略,有时折扣价格是占优策略,参数的大小是关键因素。     

竞争环境下的港口企业两种定价策略比较研究

通过建立港口的空间Hotelling模型,分析了同一区域内双垄断港口企业采用不同定价策略时的均衡价格、需求量和利润,并且对比了不同定价策略下港口的利润.理论研究结果表明:在服务水平相同时,两个竞争的港口企业采用统一定价策略会获得更多的利润;在服务水平不相同时,两个竞争的港口企业采取何种定价策略与它们的地理位置、内陆运费率、服务水平有关.     

Optimal markdown policy of perishable food under the consumer price fairness perception

Markdown policies are widely used by retailers to sell perishable food. Consumers purchase food at different prices during different sales periods. Some consumers may compare their experience with others who purchase the same items. Price unfairness or inequity is perceived when different prices are quoted without reasonable explanations. This study develops an optimal markdown model for perishable food pricing to optimise the food retailer revenue and enable a maximum aggregated consumer utility considering individuals’ price fairness perception. The model serves as the first step in evaluating trade-offs between food retailer revenue and consumer utility. In addition, it enables consumer utility to be depicted through perceived price fairness by including the effects of food perishability and scarcity. Another innovative feature is the equalisation of the consumer average aggregated utility during different sales periods as a condition of intertemporal price fairness perception. The proposed model is compared with two benchmark models to justify the effectiveness and advantages in the example. Finally, a sensitive analysis based on the food deterioration rate, consumer food desire rate and consumer average reservation price is conducted to justify the manner in which these factors influence the optimal pricing policy, and managerial insights are suggested for food retailers.     

Solving the grocery backroom sizing problem

Backrooms are an important echelon of the retail supply chain. However, research focus has been mostly targeted to optimise both distribution centres and stores' sales area. In this paper, we propose two mathematical programming formulations to solve the grocery backroom sizing problem. This problem consists of determining the dimension of each storage department in the backroom area to optimise its overall efficiency. The first formulation is a bottom-up approach that aims to reduce the backroom life-cycle costs by determining the optimum floor space and storage height for each department. The second is a top-down approach based on Data Envelopment Analysis (DEA), which determines the efficient level of storage floor space for each backroom department, based on a comparison with the benchmarks observed among existing stores. Each approach has distinct characteristics that turn the models suitable for different retail contexts. We also describe the application of the proposed approaches to a case study of a European retailer. The application of this methodology in the design process demonstrated substantial potential for space savings (6% for the bottom-up model and 16% for the top-down model). This space reduction should either allow higher revenues in the sales area and/or lower backroom-related costs.     

Pricing decisions of complementary products in a two-level fuzzy supply chain

Pricing decisions of two complementary products in a two-level fuzzy supply chain with two manufacturers and one common retailer are studied in this paper. By considering the two manufacturers and one common retailer’s leader–follower relationship, the two manufacturers’ pricing strategy and the fuzzy uncertainties associated with the manufacturing costs and customer demands of the complementary products, seven pricing games are considered. The corresponding closed-form optimal pricing decisions are obtained in the seven pricing games. Through using numerical studies and sensitivity analysis of parameters’ fuzzy degree, we compare the analytical results of different games and investigate the firms’ optimal decisions facing changing pricing environments. At last, we analyse the effect of the fuzzy degree of key parameters on optimal prices, maximal expected demands and maximal expected profits of different games. Some interesting and valuable managerial insights are established.     

基于双寡头竞争的航空客运模糊销售定价决策

针对近年来航空公司机票销售领域流行的模糊分销模式,利用Hotelling模型建立了季末单一模糊销售以及直销与模糊销售共存的双寡头竞争模型,求解供大于求和供小于求下两种销售模式各利益主体的均衡价格及收益,旨在发现哪种销售模式更有利于提高航空公司的收益。研究表明,当市场竞争激烈时,模糊分销模式存在,且季末共同销售策略下航空公司的期望总收益高于单一模糊销售,同时模糊中介商有动力实施该模式,凸显了双渠道同期销售对市场需求的引导作用。该研究结果可为航空公司竞争环境下的均衡定价决策和销售模式选择提供理论参考。     

电商引入自有品牌策略对制造商销售模式选择的影响

研究了电商引入自有品牌产品和制造商入驻模式选择之间的博弈竞争关系,构建了双方的Stackelberg博弈模型,利用逆向归纳法解析得到双方不同策略下的利润,在此基础上比较双方利润,得到不同条件下的均衡策略。研究发现,制造商销售模式的选择受到电商引入自有品牌策略的影响。当佣金比例过低或过高时,引入自有品牌策略不会影响销售模式的选择,此时佣金费用决定了销售模式的选择;当佣金比例适中时,引入自有品牌则制造商会选择代销模式,不引入则会选择分销模式。平台佣金比例和消费者对自有品牌的认可程度会影响电商引入自有品牌的策略,较高的消费者认可程度反而促使电商不引入自有品牌。     

Active demand management for substitute products through price optimisation

This paper presents a systematic mathematical programming approach for active demand management in process industries. The proposed methodology aims to determine optimal pricing policies as well as output levels for substitute products, while taking into consideration manufacturing costs, resource availability, customer demand elasticity, outsourcing and market competition. First, profit maximisation analytical formulae are derived for determining Nash equilibrium in prices for a duopolistic market environment where each company produces only one product. An iterative algorithm is then proposed so as to determine the decision-making process by solving a series of non-linear mathematical programming (NLP) models before determining the Nash equilibrium in prices for the competing companies. The proposed algorithm is extended in order to accommodate the case of multi-product companies, each one selling a set of substitute products at different prices. The applicability of the proposed methodology is demonstrated by a number of illustrative examples.     

Dynamic pricing with stochastic reference effects based on a finite memory window

Inspired by the latest empirical studies, we propose a new updating model for reference prices by assuming that consumers’ memories are limited and their recall of previous prices obeys a first-order Markov stochastic process. We investigate a dynamic pricing model with stochastic reference effects and finite memory. Consistent with the exponential smoothing model, we indicate that reference effects lead to monotonic convergence of the optimal price path to an expected steady-state price. The steady-state range tends to widen as consumers become loss-averse. The results of our numerical experiments differ from findings of certain models under the assumption of stochastic recall memory of consumers. The optimal price path fluctuates consistently around the steady state instead of remaining constant. The effect of the first price on the memory window and long-term profits decreases as the length of memory window increases.     

不同公平关切下的供应链定价决策分析

为了比较研究零售商绝对公平关切和相对公平关切下供应链的定价策略与利润,建立一对一两级供应链Stackelberg博弈模型,采用逆推法进行求解。数理推导结果表明：两种公平关切模型下,零售商的公平关切均不会影响其定价策略,但会削弱制造商的批发价格,从而导致零售商获取更多的供应链利润;另外,受零售商公平关切程度的影响,两种公平关切下制造商的批发价格及双方利润表现出明显的分段差异性。     

低碳需求约束下制造商技术创新决策的比较分析

为了分析消费者低碳需求约束的影响,在单个制造商和单个零售商组成的供应链系统中,通过在需求函数中引入减排技术创新水平参数,采用stackelberg博弈方法,构建了占主导地位的制造商实施减排技术创新是否有利可图的决策模型。分析了制造商不实施、单独实施以及与零售商联合实施技术创新3种情形对供应链成员定价与利润的影响。研究表明,制造商的减排技术创新决策不仅会受到消费者低碳需求的约束,而且也会受到零售商销售成本的制约,当满足一定条件时,制造商单独实施创新可以使制造商与零售商的价格与利润都高于不实施创新情形,而制造商与零售商联合创新却不一定是最优选择,零售商销售成本在一定程度上会制约制造商与零售商联合创新的效果。     

Pricing competition on innovative product between innovator and entrant imitator facing strategic customers

When an innovative product is introduced into the market, innovators always face competition from entrant imitators. Strategic customers may also anticipate this and can design their purchase plans accordingly. In this study, we develop a dynamic game model to formulate the problem associated with competitive product pricing between an innovator and an imitator for obtaining a pricing equilibrium. The influence of various factors on pricing policies, market sales and profits are analysed. We argue that when anticipating forthcoming competitors, innovators should not price too highly in the monopoly stage. The optimal monopoly price decreases with the quality ratio and forms a U shape along with the dimension of customers’ strategic level; however, the right tail of the U is mitigated when the quality ratio increases. In the duopoly phase, the markdown for the innovator and the difference in product cost performance between the innovator and imitator are investigated. We then analyse the value of demand information. The numerical analysis indicates that the value decreases with customers’ strategic level and increases with the quality ratio. The revealing behaviour of the innovator influences the imitator marginally in pricing and considerably in profit. Finally, a medium level is always preferred when the imitator chooses the product quality level.     

An econometric analysis of product variety impact on competitive market conduct in consumer goods markets

Decisions on product variety are a central part of the (strategic) marketing planning process of many consumer goods manufacturers. However, we have only limited information about the effects of product variety on competitive market conduct and profitability. In this paper, we introduce a simple econometric methodology for studying market conduct in prices and variety between rival brands of consumer goods markets. Our study follows the recent trend in empirical industrial organization, it is fully structural and starts from the specification of demand and supply functions. We introduce a number of different game theoretic regimes and characterize the equilibrium of each of these games. The equilibrium of each game is considered to be unique. On the basis of non-nested model selection, we can identify the form of competitive market conduct that is most suitable for the underlying data. Our empirical study identifies Nash behavior in pricing and collusive behavior in variety among the two leading brands in the market. The estimated parameters offer theoretically founded insight into the competitive rules in the market and the impact of prices and variety on profits.