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.     

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.     

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。     

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。     

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.     

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.     

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。     

A Cutting Planes Algorithm for the <Emphasis Type="Italic">m</Emphasis>-Salesmen Problem

The existence of reliable and flexible FORTRAN programs for integer linear programming has recently enabled the development of very efficient algorithms for the travelling salesman problem. The main characteristic of these algorithms is the relaxation of most of the constraints of the problem during its solution. The same approach can be used for the solution of the m-salesmen problem in which m salesmen starting from the same city must visit only once n cities at minimum cost. The number of salesmen can be fixed in advance or allowed to vary, upper and lower bounds set on the number of salesmen and even fixed costs associated with the salesmen. The results obtained so far are very encouraging. Problems of up to 100 cities have been solved optimally for the m-travelling salesmen case and other more complex problems are currently under study.     

Sales Commission for Multiproduct Sales Forces

In the early 1970s several papers computed commission rateswith the criterion that they be chosen so that the optimal timeallocations for salesmen were the same as the optimal timesfor the firm. Recent papers have considered a principal-agentmodel for a single-product firm in which the firm sets commissionrates knowing how the sales force will allocate time for anygiven rates. These papers assume that the probability distributionof sales is a function of sales effort. In this paper, we alsoconsider a principal-agent model, but for deterministic salesof a multiproduct firm. A computational procedure is illustrated.     

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.     

Competitive travelling salesmen problem: A hyper-heuristic approach

We introduce a novel variant of the travelling salesmen problem and propose a hyper-heuristic methodology in order to solve it. In a competitive travelling salesmen problem (CTSP), m travelling salesmen are to visit n cities and the relationship between the travelling salesmen is non-cooperative. The salesmen will receive a payoff if they are the first one to visit a city and they pay a cost for any distance travelled. The objective of each salesman is to visit as many unvisited cities as possible, with a minimum travelling distance. Due to the competitive element, each salesman needs to consider the tours of other salesman when planning their own tour. Since equilibrium analysis is difficult in the CTSP, a hyper-heuristic methodology is developed. The model assumes that each agent adopts a heuristic (or set of heuristics) to choose their moves (or tour) and each agent knows that the moves/tours of all agents are not necessarily optimal. The hyper-heuristic consists of a number of low-level heuristics, each of which can be used to create a move/tour given the heuristics of the other agents, together with a high-level heuristic that is used to select from the low-level heuristics at each decision point. Several computational examples are given to illustrate the effectiveness of the proposed approach.     

基于最优让步均衡协调策略的供应链差价补偿机制研究

制造商为了激励零售商订购更多数量的产品,会在产品零售价下调时提供给零售商一定的补偿,如何制定最优补偿机制是提高供应链收益的关键问题。为此,建立了两阶段销售差价补偿机制下制造商与零售商的博弈模型,分析了纳什均衡解和Stackelberg均衡解下制造商对零售商的差价补偿机制的决策行为,导出了在最优让步均衡策略下差价补偿机制定量关系,并提出了求解给定差价补偿系数下的近似最优让步均衡策略的算法。通过智能产品算例的分析,表明差价补偿机制能提高供应链的期望收益,增加零售商的订购量,进一步,说明差价补偿机制可以有效地改善零供关系。     

基于风险偏好和公平偏好的PPP项目政府补偿机制研究

本文在综合考虑社会资本风险偏好和公平偏好的基础上,构建了政府与社会资本之间的Stackelberg博弈模型,分析了社会资本风险偏好和公平偏好影响下PPP项目政府补偿机制的最优设计。研究表明:社会资本的最优投资水平随风险规避度的增高而降低,随公平偏好程度的增高而增高;政府补偿机制的最优设计应是在考虑单期风险及公平溢价成本的基础上,估计单期期望运营收益的高低,进而协调年建设成本补偿及运营期补偿系数两者的相对关系,设计最优的年建设成本补偿和运营期补偿系数。     

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.     

Mimetic trust and intra‐organizational network dynamics

Dynamic network models based on the homophily principle are criticized for neglecting organizational context conditions and the impact of role structures on the evolution of intra‐organizational trust networks. Using a neo‐institutional framework it is argued that individuals in competitive environments will attempt to reduce uncertainty about the trustworthiness of potential trustees by imitating the sociometric choice behavior of persons in similar network positions. Three hypotheses are developed. The positional trust hypothesis predicts that individuals tend to trust other actors who occupy a similar network position as themselves. The mimetic trust hypothesis argues that individuals trust actors who are trusted by persons in their own network position. Finally, the advisory trust hypothesis claims that individuals prefer to maintain trust relations to persons occupying a position of third party intermediary than to persons in other positions. An exploratory empirical test of the hypotheses is carried out by reanalyzing a longitudinal network study of the relationships among 25 salesmen in the furniture department of a North American retail sales store during the 1950s. Blockmodelling procedures are used to identify structural positions in the networks, and log‐linear analysis is applied to determine stability of choices within and between structural positions. The results support the mimetic trust and the advisory trust hypothesis.     

A linear programming approach for determining optimal advertising policy

^** Email: wkc{at}maths.hku.hk In this paper, we propose a new advertising model which cancapture the advertising wear out phenomenon. The objective hereis to maximize overall sales. We show how to derive the optimalpulsation advertising strategy. The optimization problem canbe formulated as a linear programming problem. Closed-form optimalsolution can also be obtained under some conditions. We presentnumerical examples to illustrate the proposed model and applythe model to practical sales data.     

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.     

基于公平关切的双渠道低碳供应链博弈分析

以制造商为主导的双渠道低碳供应链中,在制造商、零售商为公平中性、零售商具有公平关切以及制造商具有公平关切3种情形下,分别对比分析单位低碳产品碳减排量、零售商销售努力程度、公平关切程度对制造商、零售商决策及效用的影响.研究发现:在制造商主导的供应链中,无论哪一方具有公平关切,也不论公平关切程度大小,制造商大多是获利方;公平关切行为不会带来定价变动趋势的变化;单位碳减排量越大或者零售商销售努力程度越高,则制造商对零售商的批发价格越高,如果零售商具有一定的公平关切,则批发价格上涨幅度会得到一定程度的有效控制;制造商、零售商的效益相互依赖,当零售商销售努力程度上升时,制造商的效用也会增加;当零售商不愿为低碳产品的销售付出努力时,制造商具有公平关切情形下零售商的损失反而较小.     

Estimating demand by using sales information: inaccuracies encountered

Demand data is integral to a company’s overall information requirement. This is particularly true for manufacturers and retailers with regard to capacity, production, and inventory planning. Notwithstanding the implicit inaccuracies encountered, companies are predisposed to employ sales data as a primary source of information for estimating future demand.In this paper, by adopting a two-product setting, we measure inventory cost inaccuracies that arise from using sales data in estimating demand. By analyzing these costs, we also explore the conditions under which the resulting inaccuracies are either “lessened” or become “acute.” In this context, the determining rule of an induced substitution structure between the two products during stockout occasions is explicitly analyzed.We use a newsboy framework, in a two product environment, wherein one product may be taken as a direct substitute for the other. We provide necessary and sufficient optimality conditions and an extensive computational study to illustrate and support our findings and to provide additional insights on the conditions characterizing optimal stocking policies.