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.     

QUOPLAN: A System for Optimizing Sales Quota-Bonus Plans

This paper describes an IBM-PC menu-driven and user-friendly procedure which can help sales management in setting up optimal quota-bonus plans. For a given sales force, the resulting quotabonus plan maximizes the firm's current profits subject to (1) keeping every individual sales-force member at least at his/her current level of satisfaction (or eventually, increasing this level), and (2) being consistent and harmonious across sales representatives. The QUOPLAN system is composed of two submodels. The first submodel is used by salespersons for eliciting their own utility functions, and is essentially based upon the principles of conjoint analysis. The second submodel is used by management for reconciling all the individuals' judgements and the company's objectives into a consistent quota-bonus plan.     

激励销售与准确预测的薪酬机制设计

由于销售人员具有比厂商更多的销售信息，厂商在制定生产计划时需要参考来自销售人员的市场预测。传统的薪酬机制在引导销售人员如实上报预测量方面存在严重不足。Gonik机制虽然可以部分地弥补这一不足，但仍然要由厂商先提供参考定额和相应奖金数值。本发展了一种不需要厂商提供参考定额值而直接由销售人员自己参与提出定额确定奖金并努力销售的薪酬机制。章论证了它的有效性，并导出了在设计合同参数时，需要注意的一些规则和约束，对实际操作有一定的指导意义。     

Alternative Models of Salesmen's Response to Financial Incentives

The assumption underlying any sales force incentive compensation plan is that salesmen react to financial incentives according to some definite and consistent pattern. In order to influence salesmen's activities through financial compensation a manager must know the “rule” salesmen follow in reacting to money incentives. There is relatively little theoretical and empirical research in this area and the partial findings do not support the presence of a single behavioural pattern in response to financial incentives.This paper describes a model mainly based on a series of linear programs simulating salesmen's reactions to financial incentives under alternative basic behavioural hypotheses. By determining which hypothesis best explains actual data, a sales manager can possibly identify and infer the rule followed by his salesmen, and adjust the compensation scheme accordingly. The implications of such results for compensating salesmen are noted and a sample application of the model to an actual situation is described.     

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。     

产品销售相关环境下的提成率研究

以往多产品销售的最优提成率研究多基于多产品销售相互独立的假设之上。本文将一种多产品销售的合同模型拓展到产品销售相互影响的环境中,对不同的销售相关性情况下销售提成率的设置进行了分析,推出了不同情况下各产品提成率之间的关系特点和指导性结论。最后研究了当厂商兼顾短期利润和长期利润时对主副产品销售提成率的影响,提出了根据产品所处生命周期的不同阶段,用价值权重向量来动态调整、优化负责销售主、副产品的销售人员薪酬合同参数设计的方法。     

Stackelberg equilibria in managerial delegation games

Managerial compensation packages do not only influence managers’ behavior, but also have an impact on competing firms. In a managerial delegation game investigating the latter aspect, it is shown that the inherent prisoner’s dilemma situation can be resolved (without changing the normally studied setup or timing). In the first stage, owners choose an incentive function for their managers, in the second stage they choose the weights assigned to that function besides profits and in the third stage managers play a Cournot game. Solving this continuous optimization problem with the implicit function theorem shows that choosing an incentive from the set of “multiplicative incentives”, i.e. any generalized affine transformation of the product of both firms’ quantities, which includes e.g. relative profit, ensures that the Stackelberg outcome is among the set of equilibrium outcomes. Furthermore, it is the unique outcome if the rival owner opts for one of the well-known incentives like sales, revenue or market share. The general approach used allows demonstrating that with no other linear incentive a Stackelberg outcome results and that incentives like profit-to-cost ratio should be avoided. Selecting a multiplicative incentive is a dominant strategy of the game.     

Diversity of firm’s life cycle adapted from the firm’s technology investment decision

The stylized model presented is an optimal control model of technology investment decision of a single product firm. The firm’s technology investment does not have only a long-run positive effect but also a short-run adverse effect on its sales volume. We examine the case of high adverse investment effects where the firm finally leaves the market but we have observed different life cycles till this happens. Depending on the firm’s initial technology stock and sales volume, we compute different firm’s life cycles, which are driven by a trade-off between two strategies: technology versus sales focus strategy. Indifference curves, where managers are indifferent to apply initially technology or sales focus strategies, separate founding conditions of the firm to various classes distinguishable because of the firm’s life cycle.     

Optimal Compensation Plans for Salesmen Who Trade-off Leisure Time Against Income

This paper discusses the minimum requirements for an adequate salesmen's compensation plan structure to lead to profit maximization by inducing non-income maximizing salesmen (1) to deploy the highest profitable activity level, and (2) to optimally allocate their time among various selling activities. It is found that a commission-quota-bonus plan is such a structure. These results hold under a large set of plausible behavioral patterns of salesmen's responses to financial incentives. In addition, the analysis supports the use of challenging sales quotas for improved sales force efficiency.     

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.     

Experts' adjustment to model-based SKU-level forecasts: does the forecast horizon matter?

Experts (managers) may have domain-specific knowledge that is not included in a statistical model and that can improve short-run and long-run forecasts of SKU-level sales data. While one-step-ahead forecasts address the conditional mean of the variable, model-based forecasts for longer horizons have a tendency to convert to the unconditional mean of a time series variable. Analysing a large database concerning pharmaceutical sales forecasts for various products and adjusted by a range of experts, we examine whether the forecast horizon has an impact on what experts do and on how good they are once they adjust model-based forecasts. For this, we use regression-based methods and we obtain five innovative results. First, all horizons experience managerial intervention of forecasts. Second, the horizon that is most relevant to the managers shows greater overweighting of the expert adjustment. Third, for all horizons the expert adjusted forecasts have less accuracy than pure model-based forecasts, with distant horizons having the least deterioration. Fourth, when expert-adjusted forecasts are significantly better, they are best at those distant horizons. Fifth, when expert adjustment is down-weighted, expert forecast accuracy increases.     

An Expert System Framework for Economic Evaluation of Machining Operation Planning

Recognising the importance of combining manufacturing and management systems for machining operation planning, this paper presents a new methodology for the evaluation of economic aspects in an operation plan. To ensure that the quality of machined parts satisfies the required specifications, the manufacturing system acts as an alternative generator that provides meaningful and practical plans. Through cost analysis, the variable, fixed, and total costs associated with the machining operation are quantitatively determined. The management system, which functions as an evaluation mechanism, then selects the optimal plan based on the defined goal. The proposed methodology has been applied in the framework design of an expert system. The program establishes a sequence of machining operation planning and searches for the optimal plan. This optimal plan integrates considerations from both managers and production engineers, and balances their needs for efficient machining of a quality product.     

Optimizing a Two-Step Sales-Force Selection Process

This paper delineates the conditions whereby a sales manager would maximize long-run profits by using a typical two-step procedure to recruit salespersons. The procedure attempts to select the most able sales candidates from a flow of applicants, given the opportunity costs associated with the lack of validity and reliability of the procedure followed at each step. A computer algorithm (called SCRAP), based on the principles of Bayesian sequential sampling theory, makes the procedure operational. Required input data are generally available from existing personnel and accounting data, as well as from managerial judgements. The procedure is illustrated in a real situation and points the way towards more efficient recruiting practice.     

DEA-based production planning considering influencing factors

When planning production in a centralized decision-making environment using data envelopment analysis (DEA), previous researches usually plan for units by selecting best-practice points within the entire production possibility set or adhering to their original abilities so that potentials may not be fully explored. In practice, there often exist factors that influence units’ production abilities. Difficulties may occur when improving inefficient units’ performances or they can only be improved in a limited room. This paper takes these influencing factors into account to avoid new plans beyond units’ abilities or not fully exploring their potentials. Depending on performance variability, two DEA-based production planning approaches are proposed to optimize the total resource utilization assuming demand changes in the next production season can be forecasted. When performances are improvable, units are grouped according to the influencing factors they face. Simple numerical examples and a real world data set are used to illustrate the proposed approaches.     

Contract design for risk sharing partnerships in manufacturing

The development of extensive partnerships with suppliers has become a characteristic of manufacturing, particularly in the aircraft and automobile industries. This paper considers the development of appropriate contracts that enable market risks to be shared between the lead manufacturer and the partners. It is shown that it is usually appropriate to have threshold contracts, i.e., contracts where a partner only shares in profits if sales exceed a value determined by risk tolerance and target return. The value of having financial partners as well as manufacturing partners is demonstrated, although it is also shown that financial partner contributions to the project should be limited. We also consider the situation where partners have pre-existing commitments to other projects, perhaps with competitors. The producers sales may be correlated with the partners profits on pre-existing commitments so the impact on contract structure is explored. It is shown that even if a partner had preexisting commitments whose profit is positively correlated with product sales then it is often beneficial to use such a partner.     

An application of support vector machines to sales forecasting under promotions

This paper deals with sales forecasting of a given commodity in a retail store of large distribution. For many years statistical methods such as ARIMA and Exponential Smoothing have been used to this aim. However the statistical methods could fail if high irregularity of sales are present, as happens for instance in case of promotions, because they are not well suited to model the nonlinear behaviors of the sales process. In recent years new methods based on machine learning are being employed for forecasting applications. A preliminary investigation indicates that methods based on the support vector machine (SVM) are more promising than other machine learning methods for the case considered. The paper assesses the application of SVM to sales forecasting under promotion impacts, compares SVM with other statistical methods, and tackles two real case studies.     

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.     

The shelf space and pricing strategies for a retailer-dominated supply chain with consignment based revenue sharing contracts

Consider a two-echelon supply chain consisting of two manufacturers and a dominant retailer, such as big supermarkets like Walmart. Under a consignment contract with revenue sharing, the two manufacturers sell through the retailer two substitutable products whose demands are dependent on their shelf space and sales prices. The two manufacturers may compete horizontally for shelf space and pricing by three scenarios: Nash game, Stackelberg game, and collusion, and play vertically the retailer-Stackelberg game with the retailer. For each of these horizontal scenarios, we present all participators’ equilibrium strategies and their corresponding profits, based on which the impacts of manufacturers’ cost difference and moving sequence are investigated. Additionally, we discuss whether a horizontal collusion among manufacturers occurs when they choose their scenarios and whether centralization is always beneficial for the entire chain under the considered consignment contract. The study reveals the following results: (i) When the manufacturers compete horizontally, the high-cost manufacturer always sets a high-price and less shelf space strategy, while the low-cost manufacturer always adopts a low-price and more shelf space strategy, which is not affected by their moving sequence. If they collude horizontally, it is just reverse. (ii) When the two manufacturers compete horizontally, all participators’ equilibrium strategies and their corresponding profits are significantly influenced by manufacturers’ moving sequence. (iii) A horizontal collusion between the manufacturers can occur only when their cost difference is relatively small; this finding supplements existing literature. (iv) When the cost difference between manufacturers is relatively big, then centralization may be detrimental to the entire chain, which can explain why several supply chains adopt vertical competition strategies in practice. In addition, we find that these results still hold for the limited shelf space scenario and shelf-space limitation enhances the horizontal and vertical competition intensity by increasing shelf space fee.     

基于经销商再制造的闭环供应链政府补贴策略及效果分析

针对制造商负责再制造设计,经销商负责再制造的闭环供应链系统,建立政府无补贴、补贴经销商再制造和补贴制造商再制造设计3种策略下的Stackelberg博弈模型,分析不同补贴策略对供应链成员企业决策的影响。同时,应用数值仿真方法研究相同补贴支出下两种补贴策略的优劣。结果表明:相对于无补贴策略,两种补贴策略均会降低再制品和新产品的销售价格,提高再制品销售量,提升再制造设计水平,并且在再制品需求量小于新产品需求量时均会降低新产品销售量,在再制品和新产品的需求量相等时均会提高新产品销售量;另外,在相同的补贴支出下,当新产品需求量大于再制品需求量时,补贴经销商更能降低两种产品的销售价格和新产品的销售量,提高再制品销售量和制造商与经销商的利润,补贴制造商则更能提升再制造设计水平。     

Compensation plan for competing salespersons under asymmetric information

We investigate the optimal compensation scheme involving one firm and two competing salespersons deployed in different territories under asymmetric information. The problem is analyzed using a two-stage game. In the first stage, the firm announces the compensation plans. The two salespersons, who are closer to customers, have superior market information and then simultaneously but independently decide which plans to sign. The firm decides the production quantity and the salespersons independently make effort decisions. In the second stage, sales volumes are realized and the associate payments are made.