Price-setting newsvendor with strategic consumers

We consider a newsvendor who sells a single product over a single season with the objective of determining both the selling price and stock quantity to maximize the expected profit. The customers are strategic and we consider two demand cases: additive and multiplicative. For each case, we derive the newsvendor׳s optimal decisions and demonstrate that neglecting the price-sensitivity of demand leads the newsvendor to make sub-optimal decisions. Moreover, we show that under certain conditions, strategic consumer behavior may positively affect the newsvendor׳s optimal expected profit in the additive demand case.     

On Comparing Alternative Advertising Policies of Pulsation*

In this paper, five alternative advertising policies that belong to the advertising pulsation class are compared analytically for linear and concave response functions using a modified version of the Vidale-Wolfe model. The results of the research show that (1) For both linear and concave response functions, advertising pulsing/maintenance policy dominates advertising pulsing policy but is dominated by the Uniform Advertising Policy. For convex response functions, the order of dominance is reversed. (2) For linear response functions, uniform advertising policy dominates the impulse advertising policy but is dominated by the chattering advertising policy. (3) For concave response functions, uniform advertising policy dominates both the impulse advertising policy and the chattering advertising policy. (4) For convex response functions, chattering advertising policy dominates both the advertising pulsing policy and the impulse advertising policy. The Vidale-Wolfe model is estimated using the well-known Lydia Pinkham data. Optimality analysis shows that the company was overadvertising about half of the time studied. Overadvertising seems to have produced appreciable gain in sales and created significant barriers to competitive entry at a little cost in terms of foregone profits.     

Profit implications of estimation methods for the allocation of marketing resources

We deal with the question whether estimating heterogeneous multiplicative sales response models without carry over effects by either ordinary least squares or Gibbs sampling makes a difference if resources (like advertising budgets, sales budgets, sales force sizes, sales calls) have to be allocated to sales units (like sales districts, customer groups, individual costumers or prospects) in a profit maximizing way and only short time series are available. To this end we generate artificial series on sales and allocations by stochastic simulation. These series are used to estimate multiplicative models whose coefficients are either specific to individual sales units or follow a hierarchical Bayesian framework. Ordinary least squares and Gibbs sampling serve as appropriate estimation methods. Performance of the two estimation methods is measured by recovery of optimal profits which are computed on the basis of the known true parameter values. We start to determine optimal allocations based on the plug-in method which uses average coefficients to determine expected profits. Gibbs sampling always leads to profits nearer to the true optima. This advantage of Gibbs sampling is especially pronounced for combinations with high average elasticity, high variation of elasticity and high number of sales units. On the other hand, differences between Gibbs sampling and OLS become smaller the more observations are available. Optimization with expected profits taking parameter uncertainty (i.e., the distribution of parameters) into account leads to higher profits than the plug-in method, but relative increases turn out to be rather small.     

The price-setting newsvendor with service and loss constraints

Current performance measurement systems consider not only financial measures, like costs and profits, but also non-financial indicators with respect to customer service, quality and flexibility. Using the newsvendor model, we analyse the respective influence of these possibly conflicting performance measures on important operations and marketing decisions, for instance the order quantity and the selling price of a product. As in the classical newsvendor model for price-independent as well as price-dependent demand distribution, the objective of the firm is to maximise expected profit. In this paper, we also consider a service constraint—a lower bound for the level of product availability—and a loss constraint—an upper bound for the probability of a loss occurring. For both models, we provide conditions for the existence of solutions. We then analyse the influence of demand variability using a set of conditions specifying the quantiles of the predetermined performance measures: a higher variability of demand implies a smaller admissible region of the decision variables. In the price-independent case, the optimal solution has a control-limit structure: the optimal order quantity is thus given either by the classical newsvendor solution or by the control-limits corresponding to the constraints. In the price-setting model with multiplicative demand, this structure is used to check whether small admissible prices are determined by the service constraint or by the loss constraint. Using these structural results, a procedure is developed to more easily enable the computation of the optimal values of the order quantity, selling price and expected profit.     

Managing Retail Budget Allocation between Store Labor and Marketing Activities

The performance of a retail store depends on its ability to attract customer traffic, match labor with incoming traffic, and convert the incoming traffic into sales. Retailers make significant investments in marketing activities (such as advertising) to bring customers into their stores and in‐store labor to convert that traffic into sales. Thus, a common trade‐off that retail store managers face concerns the allocation of a store's limited budget between advertising and labor to enhance store‐level sales. To explore that trade‐off, we develop a centralized model to allocate limited store budget between store labor and advertising with the objective of maximizing store sales. We find that a store's inherent potential to drive traffic plays an important role, among other factors, in the relative allocation between advertising and store labor. We also find that as advertising instruments become more effective in bringing traffic to stores, managers should not always capitalize this effectiveness by increasing their existing allocations to advertising. In addition, we discuss a decentralized setting where budget allocation decisions cannot be enforced by a store manager and present a simple mechanism that can achieve the centralized solution. In an extension, we address the budget allocation problem in the presence of marketing efforts to shift store traffic from peak to off peak hours and show that our initial findings are robust. Further, we illustrate how the solution from the budget allocation model can be used to facilitate store level sales force planning/scheduling decisions. Based on the results of our model, we present several insights that can help managers in budget allocation and sales force planning.     

基于Vidale-Wolfe模型的多市场广告预算分配决策模型

广告决策问题很长时间以来都是营销经理和学者们关注的热点。随着社会经济发展,越来越多的企业面对多个市场。如何在多个市场、广告总预算固定的状况下,合理分配各个市场广告预算以收到最优广告效果,是一个企业关心的较为重要的问题。经过比较,选择Vidale-Wolfe模型作为广告反应模型,在此基础上建立了多市场广告预算分配决策模型。考虑到一些营销策略对某些市场有特殊销售速率要求,该模型分为无特殊销售速率维持要求的多市场广告预算分配决策模型和有特殊销售速率维持要求的多市场广告预算分配决策模型两类,后者探讨了销售速率变化与达到指定销售速率两种要求下的广告预算最优分配问题,构建了优化模型,提出了模型参数取值与模型求解方法,最后给出了一个算例。     

基于预期的报童问题研究

Koszegi与Rabin认为参照点往往由决策者的理性预期确定，本文选取报童的预期作为参照点，利用参照依赖偏好理论对报童问题进行了研究。研究发现，基于预期的报童的最优订货量不仅与货物销售的概率分布、价格等有关还与报童的损失厌恶程度有关。如果报童是损失厌恶的，报童的订货量要小于经典报童问题的订货量；反之，报童的订货量则大于经典报童问题的订货量，该结论与大部分实证结果是一致的。最后，用算例来验证了文中有关结论的正确性。     

The single-period inventory problem: Extension to random yield from the perspective of the supply chain

A special form of the single-period inventory problem (newsvendor problem) with a known demand and stochastic supply (yield) is studied. A general analytic solution for two types of yield risks, additive and multiplicative, is described. Numerical examples demonstrate the solutions for special cases of uniform distribution yield risks. An analysis of a two-tier supply chain of customer and producer reveals that the customer may find it optimal to order more than is needed, since a larger order increases the producer's optimal production quantity.     

Cooperative Advertising and Pricing in a Dynamic Stochastic Supply Chain: Feedback Stackelberg Strategies

Cooperative (co‐op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co‐op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi's stochastic sales‐advertising model. We obtain the condition when offering co‐op advertising is optimal for the manufacturer. We provide in feedback form the optimal advertising and pricing policies for the manufacturer and the retailer. We contrast the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.     

A Maximum Entropy Joint Demand Estimation and Capacity Control Policy

We propose a tractable, data‐driven demand estimation procedure based on the use of maximum entropy (ME) distributions, and apply it to a stochastic capacity control problem motivated from airline revenue management. Specifically, we study the two fare class “Littlewood” problem in a setting where the firm has access to only potentially censored sales observations; this is also known as the repeated newsvendor problem. We propose a heuristic that iteratively fits an ME distribution to all observed sales data, and in each iteration selects a protection level based on the estimated distribution. When the underlying demand distribution is discrete, we show that the sequence of protection levels converges to the optimal one almost surely, and that the ME demand forecast converges to the true demand distribution for all values below the optimal protection level. That is, the proposed heuristic avoids the “spiral down” effect, making it attractive for problems of joint forecasting and revenue optimization problems in the presence of censored observations.     

资金约束下损失规避零售商的订购和广告协同策略

在损失规避下,探讨了零售商的订购和广告协同决策问题。零售商的初始资金状态存在三种情形：资金充足、资金相对短缺（不需融资）、资金短缺（对外融资）,分别在三种情形下刻画了零售商的最优运营策略,结果表明：零售商用于商品采购和广告的资金产生的边际效用与边际负效用之比相等,且介于1与单位融资资金的使用成本之间;用于两项活动的最后一单位资金产生的边际效用相等。探讨了损失规避、初始资金、融资利率、商品价格及广告促销的敏感性对运营策略的影响：在资金充足或资金短缺下,商品订购量和广告强度随影响因素的变动方向通常相同;在资金相对短缺下,商品订购量和广告强度随影响因素的变动方向则相反。讨论中揭示了一些管理启示。     

Accurate Response with Refurbished Consumer Returns

Centering around anticipative and reactive capabilities of firms, accurate response is an important supply‐side strategy to deal with demand uncertainty. Clearly, the structure of the possible reaction will crucially influence the optimal anticipative decision making. In this article, we extend the existing literature in this area by including a new reactive capability, namely the utilization of refurbished consumer returns from early sales to react to demand later in the selling season. Because consumer returns depend on previous sales, there is also a direct link to the anticipative supply decision. We capture this effect in a newsvendor‐type model and provide both analytical and numerical insights into the optimal anticipative and reactive decisions as well as the value of refurbishing in terms of the retailer's expected profitability.     

A Newsvendor Who Chooses Informational Effort

We study a newsvendor who can acquire the services of a forecaster, or, more generally, an information gatherer (IG) to improve his information about demand. When the IG's effort increases, does the average ex ante order quantity rise or fall? Do average ex post sales rise or fall? Improvements in information technology and in the services offered by forecasters provide motivation for the study of these questions. Much depends on our model of the IG and his efforts. We study an IG who sends a signal to a classic single‐period newsvendor. The signal defines the newsvendor's posterior probability distribution on the possible demands and the newsvendor uses that posterior to calculate the optimal order. Each of the possible posteriors is a scale/location transform of the same base distribution. When the IG works harder, the average scale parameter drops. Higher IG effort is always useful to the newsvendor. We show that there is a critical value of order cost. For costs on one side of this value more IG effort leads to a higher average ex ante order and for costs on the other side to a lower average order. But for all costs, more IG effort leads to higher average ex post sales. We obtain analogous results for a “regret‐averse” newsvendor who suffers a penalty that is a nonlinear function of the discrepancy between quantity ordered and true demand.     

基于再制造的多周期闭环营销投入及定价策略

针对再制造产品市场化艰难和缺少旧件来源的问题,结合"互联网+"战略提出了促进旧件回收与再制造零部件销售的闭环营销体系;闭环的营销投入可以同时发挥回收努力效应（增加单周期合格旧件回收量）和多周期广告效应（提升消费者对品牌的长期绿色认知度）,建立了多周期的闭环营销投入水平决策和产品差异定价模型并得到了最优决策;结合我国汽车零部件市场的现状,针对无闭环营销、初级闭环营销、闭环营销策略升级三种模式展开算例分析和对比。研究表明：闭环营销可以显著提高供应链总收益,营销策略的升级应考虑到回收努力效应和多周期广告效应的匹配,针对长生命周期的产品,闭环营销策略应经常调整。本研究结论有助于进一步完善再制造闭环供应链及营销理论基础。     

Retailer's Response to Alternate Manufacturer's Incentives Under a Single‐Period,Price‐Dependent,Stochastic‐Demand Framework*

This article considers the joint development of the optimal pricing and ordering policies of a profit‐maximizing retailer, faced with (i) a manufacturer trade incentive in the form of a price discount for itself or a rebate directly to the end customer; (ii) a stochastic consumer demand dependent upon the magnitude of the selling price and of the trade incentive, that is contrasted with a riskless demand, which is the expected value of the stochastic demand; and (iii) a single‐period newsvendor‐type framework. Additional analysis includes the development of equal profit policies in either form of trade incentive, an assessment of the conditions under which a one‐dollar discount is more profitable than a one‐dollar rebate, and an evaluation of the impact upon the retailer‐expected profits of changes in either incentive or in the degree of demand uncertainty. A numerical example highlights the main features of the model. The analytical and numerical results clearly show that, as compared to the results for the riskless demand, dealing with uncertainty through a stochastic demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower (higher) pass throughs if additive (multiplicative) error, (iii) higher claw backs in both error structures wherever applicable, and (iv) higher rebates to achieve equivalent profits in both error structures.     

A Two-Period Repeated Game Advertising Investment Model for Oligopolistic Markets with an Application to the Beer Industry*

This paper proposes a simple analytical model of advertising competition in oligopoly markets. The widely used log-log sales response function underlies the model specification. Advertising carryover effects are assumed to persist for one period following the period in which the expenditure occurs. Firms are assumed to be engaged in a repeated competitive game in which in every period advertising levels are set such that they maximize current and next period (i.e., two-period) profits. A Nash equilibrium solution is sought for the game. Compared with previous empirical studies of advertising competition in a game theoretic framework, the proposed model offers the following advantages: (1) oligopoly, not duopoly, markets are analyzed; (2) industry sales is allowed to vary over time as a function of advertising expenditures; (3) non-zero discount rates are used for the players. An empirical application is provided using data from the beer market on sales and advertising expenditures of Anheuser-Busch and Miller Brewing. Comparisons are provided with policies that ignore the dependence of next period profits on current advertising levels, reaction function strategies and spending levels obtained from a market share game. Extension of the model formulation to multiple marketing instruments is briefly discussed.     

Joint chance-constrained staffing optimization in multi-skill call centers

This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.

     

Price,Rebate, and Returns Supply Contracts for Coordinating Supply Chains with Price‐Dependent Demands

Channel rebates and returns policies are common mechanisms for manufacturers to entice retailers to increase their order quantities and sales ultimately. However, when the underlying demand depends on the retail price, it has been known that channel coordination cannot be achieved if only one of these mechanisms is deployed. In this article, we show that a policy that combines the use of wholesale price, channel rebate, and returns can coordinate a channel with both additive and multiplicative price‐dependent demands. In addition to determining the sufficient conditions for the contract parameters associated with the equilibrium policy, we show that multiple equilibrium policies for channel coordination exist. We further explore how the equilibrium policy can be adjusted to achieve Pareto improvement. Other issues such as the maximum amount of expected profit that the manufacturer can share under the coordinated channel, the structural properties of the contracts under both the additive and multiplicative price‐dependent demand functions are also discussed.     

考虑延时效应的供应链动态合作广告策略研究

广告的延时效应是供应链广告过程中的普遍现象,对供应链合作广告策略的制定具有重要影响.文章研究当产品品牌信誉受广告延时效应影响时供应链的合作广告策略问题,建立了含有时间延迟的品牌信誉动态模型和考虑品牌信誉的产品销售量模型.运用极大值原理,得到了制造商和零售商在分散式决策和集中式决策下的最优广告投入、品牌信誉和利润,以及分散式决策下制造商的最优合作广告参与率.研究发现:在集中式决策下制造商和零售商的最优广告投入和产品销售量均高于分散式决策下的相应值;延迟时间存在一个阈值,当延迟时间低于该阈值时,集中式决策下的供应链利润较高,反之则分散式决策下的供应链利润较高.研究结果为供应链合作广告策略的制定及供应链决策机制的选择提供了一定的参考.最后,通过数值算例分析了广告延迟时间对供应链最优广告策略及决策机制的影响.     

竞争中的参考价格效应及承诺

消费者的社会感知会影响其对产品和品牌的评价。当消费者进行购买选择时,经常会受到参考价格效应的影响。而广告和价格不仅是企业经常要考虑的重要决策,还会对参考价格产生重要影响。为此,一个值得研究的的问题是：在考虑参考价格效应的情况下,企业该怎样确定其动态广告和价格策略？
为了研究该问题,本文构建了一个广告和价格的动态模型,来研究一个双寡头市场环境下两个寡头企业的价格和广告决策,并以此分析参考价格效应的作用。具体而言,我们假定企业可以采用广告承诺和价格承诺中的一种,其中前者承诺其在一段时间内的广告投入量恒定不变,而后者确保价格不变。两种策略不仅会影响消费者的购买决策,也会影响竞争对手的选择。在上述假定下,我们探讨了两个寡头企业在都采用广告承诺、都采用价格承诺及一个企业采用广告承诺而另一个企业采用价格承诺等三种不同情形下的最优广告和价格决策,并以此分析了三种情形下参考价格效应对最优的广告投入及定价策略的影响。最后,通过数值分析,探讨了不同情形下企业的最优策略选择。