多产品销售薪酬机制的最优提成率研究

多产品销售的提成率由于其直接影响销售人员的精力投入和分配，一直是销售人员薪酬合同设计的焦点。以往最优提成率研究没有区分环境因素和销售努力对销售量的影响。本文运用代理理论设计了一种基于销售人员对产品销售的贡献的多产品销售合同模型，论证了该合同具有激励销售人员努力销售和使其如实上报定额的特性，并对多产品销售相对独立的情况下销售提成率设置进行了分析，推出了各产品提成率与销售反应参数之间的关系特点，提出了一些指导性结论。     

回收再制造与定价决策模型及供应链协调分析

假定负责废旧产品回收再制造的生产商为主导者.针对单生产商和单零售商组成的逆向供应链,分析了Stackelberg博弈(分散式控制)下和合作(集中式控制)下的零售价和回收再制造率决策,发现集中式供应链的利润较高,给出了协调供应链的利润共享合同.针对单生产商和n个竞争零售商组成的供应链,分析了一主多从Stackelberg博弈和联合决策,结果表明供应链合作可降低产品的零售价格、提高回收再制造率和供应链总利润,进而给出了协调单生产商和n个零售商决策的利润共享合同.最后的算例表明了模型的合理性和协调合同的有效性.     

不对称信息下制造商契约设计

考虑由制造商和销售人员组成的供应链,其中市场需求依赖于制造商的货物质量,销售人员的努力以及市场的随机因素,建立由制造商起主导作用的数学模型.制造商通过制定产品质量,工资契约,销售价格来最大化自己的利润.销售人员针对不同质量的货物决定相应努力水平以最大化自己的利润.关于销售人员的努力水平在对称信息及不对称信息情形下,制造商运用激励相容原理设计最优契约,得到销售价格,产品质量及销售提成之间的关系.结果表明,信息对称情形下,销售人员的努力水平与产品的质量成正比.信息不对称情形下,类型为H(很努力)的销售人员的固定收入随类型为L(一般努力)的销售人员的销售提成增大而增加.     

考虑预付定金和退货的SMPEs产品定价与优化策略

借鉴中小制造型企业(SMPEs)在线渠道预售模式,考虑市场中存在预付订金和不预付订金的顾客,并将其退货情况引入到生产商利润表达式中,构建确定性和随机性市场需求下的SMPEs产品销售利润最大化模型,推导生产商产品最优定价的解析解;对比两种销售模式的利润,得到了生产商选择不同销售策略的条件。进一步考虑预付定金的产品数量、预交定金比例、退货数量是关于价格折扣敏感的情况,采用拉格朗日乘子法对生产商产品定价及优化问题进行研究,分析求得生产商销售策略(产品定价和价格折扣)的近似最优解。最后,通过数值算例对研究结论进行了验证并给出经济学解释。     

退货情形下基于替代率的两产品联合订货决策研究

研究了一类在产品订货模型中考虑客户退货和产品间替代的两产品联合最优订货决策问题.假定客户以一概率退回其所购产品,退货产品经修复后可重新在市场上进行销售,销售期末未售出的商品只能在二级市场上降价处理,且不同产品间存在替代关系,销售商以自身利润最大化为目标确定两产品的订货量,得到其最优订货量及一些性质.研究结果表明:在允许退货的背景下,替代策略的采用将会进一步提高销售商利润.     

企业单一产品在不同市场条件下的利润最大化分析

针对企业单一产品在不同市场条件下 ,采取不同的定价和不同的销售数量取得利润最大问题进行研究 ,为企业产品的生产和销售决策提供分析方法 .     

供应商两种捆绑销售策略的供应链分析

捆绑销售是供应链中占主导地位的供应商常用的产品销售手段,对供应链有利有弊.现有研究仅仅关注零售商的捆绑销售行为,文章创新性地研究了供应商的捆绑销售策略:纯捆绑销售、混合捆绑销售.研究发现:供应商的捆绑销售行为对供应链有重要影响,其影响效果与捆绑策略有密切关系.相比于单独销售策略,纯捆绑销售对整个供应链是不利的,使供应商零售商利润均下降;混合捆绑销售策略下零售商销售量会明显增加,供应商零售商利润均上升,是一种"双赢"的策略.     

双公平关切下第三方回收再制造闭环供应链的动态演进

第三方回收再制造闭环供应链中的零售商通常认为制造商销售利润的实现依赖于其产品销售努力,第三方回收商则认为制造商再制造利润的实现与其废旧产品回收直接相关,因而两者都会十分关注收益分配的公平性.利用博弈理论对双公平关切下再制造闭环供应链定价决策、效率及公平度的动态演进问题进行了研究,揭示了公平关切强度对定价决策、效率及公平度的影响规律,并基于影响规律给出了相应的管理建议.     

多产品公司创建平台邀请竞争对手进行联合销售的策略研究

由于资金分配或生产规模的限制,多产品公司的某类产品与专门销售此类产品的专业产品公司相比,会有一定的不足.以两个产品公司为对象,研究了两个竞争性公司的联合销售模式,即多产品公司投资建设平台,邀请销售单一产品的专业公司在平台上共同销售某类产品.运用主从博弈建立联合销售的基础模型,探讨不同销售模式下的相关投资,并利用数值计算进行决策分析.研究表明,通过创建平台进行联合销售,一方面,消除了消费者的额外购物成本;另一方面,在平台进行联合销售使得两个公司由单纯的竞争关系转化为相互补充,不仅能够吸引更多有不同产品需求的客户,而且能够在一定程度上提高两个产品公司的利润.     

再制造产品销售渠道决策分析

再制造产品的出现,引出了销售渠道决策的新问题。基于博弈理论,分析比较新制造产品和再制造产品五种渠道结构,得到了五种结构下新制造产品和再制造产品均衡产量和零售价格,以及制造商和零售商的均衡利润。研究结果表明,一般情况下,制造商可以凭借零售商之间的竞争提升自身在供应链的权重,使自己获利。然而当制造商通过两个零售商分开销售新制造产品和再制造产品时,制造商并不能因此而增加自己的利润。对于零售商而言,双边垄断使零售商地位提升,而新制造产品或者再制造产品分开销售都会伤及零售商。数值结果表明,零售商之间的竞争缓和了供应链上下游的双重边际效应,增加了供应链的总利润,同时也提高消费者剩余和社会福利。     

On Setting Optimal Sales Commissions

This paper treats the problem of determining the commission rates a company should choose to establish for each of n products sold by a salesman. It has been shown that a sales commission plan based on paying equal commission rates on the gross margins of the salesman's product lines is optimal under the assumption that sales generated as a function of time spent on a product is a deterministic increasing function of time. This paper explores a similar problem with relaxation of the deterministic assumption. It considers a stochastic sales function in order to show differences in preference functions between a company and salesman in determining optimal commissions.     

Fair vs Optimal Salesmen's Compensation Plans

This paper suggests that a "fair" compensation plan (i.e. a compensation plan which remunerates salesmen proportionally to their efforts and competence) should include commissions on sales and bonuses pending on sales increases over a reference period. It also shows that under general conditions, a straight commission plan is not a fair compensation structure to the salesmen. Finally, it discusses the conditions under which the proposed fair compensation structure can lead to a jointly optimal allocation of a salesman's time among selling activities.     

Predicting the long-run profit impact of a contemplated sales force compensation plan

Analytical sales force compensation research offers only limited answers to sales managers who try to devise effective compensation plans, because it often rests on restrictive assumptions, and it considers only simple compensation plan structures. In practice, sales managers need to predict how alternative and relatively complex compensation schemes would affect sales revenues and profits, as well as their likely impacts on sales force morale and turnover. This is why they typically obtain key salespeople’s prior reactions to a new scheme, or pretest the new plan on a limited scale. These procedures, however, may not provide accurate long-run predictions, and they can be applied to only one or two schemes at a time. The paper proposes the application of a simple Markovian model for assessing the long-run impacts of alternative compensation plans on sales and profits, taking into account the associated benefits and/or costs of variations in sales force motivation and turnover. A simple application is provided and implementation issues are discussed.     

Setting Commission Rates for the Control of the Salesperson's Client-prospect Effort Allocation

The literature on setting optimal commission rates for decentralized controls over salespeople's time allocations has used the sales of various product lines as the relevant selling activities. When the time allocation is between calls to prospects versus customers, the problem should account for specific aspects, such as: (1) the conversion pattern of prospects for the various product lines; (2) the attrition rate in the sales force; (3) the salespeople's attitudes toward delayed income. These variables recognize that several calls over some period of time are typically needed for converting prospects, and that salespeople will be able to cash commissions only at the conversion time and provided they are still in charge of the same accounts. Using a simple Markovian structure, this paper shows that under typical conditions, commissions on sales to prospects during the conversion period should always be larger than commissions on sales to customers. Managerial implications and implementation issues are discussed.     

Optimal sales force compensation plans: an operational procedure

This paper describes an operational procedure for identifying optimal sales force compensation plans featuring salary, commissions and/or quota/bonus. Utility-maximising salespeople's behaviours and reactions to given compensation plans are simulated, and the resulting sales, costs and long-term expected profits are assessed. Then, a search technique attempts to identify the long-term profit-maximising compensation plan structure. Operationally, the simulation model parameters are calibrated so as to reflect those of an actual sales force, and consequently the optimal compensation scheme for this specific sales force can be identified. The concept is illustrated in an actual case study.     

Retail replenishment models with display-space elastic demand

We study a single store multi-product inventory problem in which product sales are a composite function of shelf space. Since sales tend to deplete the amount of product on display, the effective shelf space assigned to the product diminishes with time unless replenishment occurs. We consider the problem of optimal replenishment times under these conditions. We assume a linear dependence of sales rate to effective shelf space in all our analysis. We present exact and approximate solutions for the single product and multi-product cases. For the single product case, we study the effect of space elasticity, cross elasticity and empty space elasticity on the optimal replenishment period. For the multi-product case we present a computationally attractive method using matrix exponentials and develop error bounds for this method.     

The Impact of Risk Attitude on the Optimal Compensation Plan in a Multi-product Situation

This paper examines the role of uncertainty and risk in determining the optimal commission rates a company should choose for each product of a salesman's product line. We assume that sales for each product are a stochastic function of the time (sales effort) allocated to that product. When sales are assumed to be deterministic, we achieve optimality when each product's commission is the same fraction of its gross margin. However, we determine here that when sales are stochastic this may no longer be true. Optimality conditions require explicit consideration of the utility function of the salesman and the moments of the sales response function.     

供应链互补产品广告投入和捆绑销售联合决策研究

以一个制造商和一个零售商的供应链为研究对象,制造商生产两种互补产品,零售商可选择分开或捆绑两种销售策略。考虑互补品的负交叉弹性和广告外部性的特点,构建基于溢出效应的需求模型,运用博弈论的方法,求解零售商采取分开和捆绑两种销售策略时的均衡结果。通过比较不同销售策略下的均衡结果及利润关系,探讨在分散式和集中式两种情况下,零售商的最优广告投入和捆绑销售的联合决策问题。最后,通过数值算例,讨论产品互补程度和广告成本系数对决策结果的影响。研究结果表明,无论是在分散式还是集中式决策下,当产品互补程度较高或广告成本系数低时,分开销售是占优策略而广告费用较高;当产品互补程度较低且广告成本系数高时,捆绑销售是占优策略且广告费用较低。     

考虑平台优惠券的不同线上销售决策研究

本文以第三方电商平台是否发放优惠券和线上销售商是否进行集成销售(现售与预售并存)为标准构建四种Stackelberg模型,分析了平台佣金率、商品估值差异系数以及优惠券兑换率对供应链成员的决策与利润影响。结果表明,随着佣金率的提高,商品(现售和预售)的销售价及优惠券面值也随之增加;当预售成本足够低时,开展预售活动以及缩小估值差异可以提高线上销售商的收益;在一定条件下,提高优惠券兑换率可以增加供应链成员的收益,电商平台发放优惠券使其收益增加,却损害了销售商利润;相比其他销售方案,供应链系统利润在集成销售方案下最优。