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.     

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.     

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.     

基于大型商场销售采集系统的营销模型

针对零售行业企业管理的合理性,基于某大型商场销售采集系统数据,构建适合零售运营商精准营销的FRLMC模型,实现零售行业的精准营销,优化会员管理制度.应用K-Means聚类分析方法构建合理实用的结构体系,精准识别会员消费特征,实现对会员消费行为画像描绘.通过实际应用说明模型的准确率,在其他行业经过验证可推广应用.     

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.     

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.     

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.     

Contract type and decision right of sales promotion in supply chain management with a capital constrained retailer

From the practices of Chinese consumer electronics market, we find there are two key issues in supply chain management: The first issue is the contract type of either wholesale price contracts or consignment contracts with revenue sharing, and the second issue is the decision right of sales promotion (such as advertising, on-site shopping assistance, rebates, and post-sales service) owned by either manufacturers or retailers. We model a supply chain with one manufacturer and one retailer who has limited capital and faces deterministic demand depending on retail price and sales promotion. The two issues interact with each other. We show that only the combination (called as chain business mode) of a consignment contract with the manufacturer’s right of sales promotion or a wholesale price contract with the retailer’s right of sales promotion is better for both members. Moreover, the latter chain business mode is realized only when the retailer has more power in the chain and has enough capital, otherwise the former one is realized. But which one is preferred by customers? We find that the former is preferred by customers who mainly enjoy low price, while the latter is preferred by those who enjoy high sales promotion level.     

Cointegration analysis of brand and category sales: Stationarity and long‐run equilibrium in market shares

The present study uses modern time series methodology to understand long‐run equilibrium in markets and provides additional evidence of the frequent existence of stationary market shares for frequently purchased consumer products. Dekimpe and Hanssens, Marketing Science 1995; 14(2):G109–121 using a database of over 400 prior studies, found that 78 per cent of the market share series they studied were stationary, but that 68 per cent of the sales series were evolving. Our findings reconcile these results. A major contribution of this paper is its demonstration that the prior empirical evidence that a majority of sales series is in evolution is consistent with stationary market shares, if brand sales and category sales are cointegrated. To the extent that competitive activities have an effect on market share, an implication of our findings is that these activities may, in general, only have a temporary effect on market share. Finally, we distinguish, from a strategic perspective, between sales and share response at the primary‐demand level (category sales), selective‐demand level (brand sales) and relative‐position level (market share) and identify strategic scenarios depending upon their stable/evolving nature. Copyright © 2000 John Wiley & Sons, Ltd.     

Qualifying for a government’s scrappage program to stimulate consumers’ trade-in transactions? Analysis of an automobile supply chain involving a manufacturer and a retailer

We investigate an automobile supply chain where a manufacturer and a retailer serve a market with a fuel-efficient automobile under a scrappage program by the government. The program awards a subsidy to each consumer who trades in his or her used automobile with a new fuel-efficient automobile, if the manufacturer’s suggested retail price (MSRP) for the new one does not exceed a cutoff level. We derive the conditions assuring that the manufacturer has an incentive to qualify for the program, and find that when the cutoff level is low, the manufacturer may be unwilling to qualify for the program even if the subsidy is high. We also show that when the manufacturer qualifies for the program, increasing the MSRP cutoff level would raise the manufacturer’s expected profit but may decrease the expected sales. A moderate cutoff level can maximize the effectiveness of the program in stimulating the sales of fuel-efficient automobiles, whereas a sufficiently high cutoff level can result in the largest profit for the manufacturer. The retailer’s profit always increases when the manufacturer chooses to qualify for the program. Furthermore, we compute the government’s optimal MSRP cutoff level and subsidy for a given sales target, and find that as the program budget increases, the government should raise the subsidy but reduce the MSRP cutoff level to maximize sales.     

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.     

Value at risk and inventory control

The purposes of this paper are two-fold. On the one hand, we shall provide a decision analysis justification for the Value at Risk (VaR) approach based on ex-post, disappointment decision making arguments. We shall show that the VaR approach is justified by a disappointment criterion. In other words, the asymmetric valuation between ex-ante expected returns above an appropriate target return and the expected returns below that same target level, provide an explanation for the VaR criterion when it is used as a tool for VaR efficiency design. Second, this paper provides applications to inventory management based on VaR risk exposure. Although the mathematical problems arising from an application of the VaR approach, tuned to current practice in financial risk management, are difficult to solve analytically, solutions can be found by application of standard computational and simulation techniques. A number of cases are solved and formulated to demonstrate the paper's applicability.     

Large deviations and estimation in infinite-dimensional models

Consider a random sample from a statistical model with an unknown, and possibly infinite-dimensional, parameter - e.g., a nonparametric or semiparametric model - and a real-valued functional T of this parameter which is to be estimated. The objective is to develop bounds on the (negative) exponential rate at which consistent estimates converge in probability to T, or, equivalently, lower bounds for the asymptotic effective standard deviation of such estimates - that is, to extend work of R.R. Bahadur from parametric models to more general (semiparametric and nonparametric) models. The approach is to define a finite-dimensional submodel, determine Bahadur's bounds for a finite-dimensional model, and then ‘sup’ or ‘inf’ the bounds with respect to ways of defining the submodels; this can be construed as a ‘directional approach’, the submodels being in a specified ‘direction’ from a specific model. Extension is made to the estimation of vector-valued and infinite-dimensional functionals T, by expressing consistency in terms of a distance, or, alternatively, by treating classes of real functionals of T. Several examples are presented.     

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.     

The Effect of Acceptance Sampling and Risk Aversion on the Quality Delivered by Suppliers

Firms often use acceptance sampling to monitor the quality of the raw materials and components delivered by suppliers. In this paper, we use numerical methods to examine how a risk averse supplier reacts to the acceptance sampling plan used by a customer. We assume that the supplier produces and delivers a quality level that maximizes the supplier's expected utility. We examine the sensitivity of the optimal delivered quality to changes in the price, to changes in the supplier's level of risk aversion, and to changes in the parameters of the customer's sampling plan. We conclude that risk averse suppliers deliver higher quality, that higher capability suppliers do not necessarily deliver higher quality, and that the optimal quality is sensitive to the lot size. We also conclude that since the risk of rejection motivates suppliers to improve quality, customers have an economic justification for using acceptance sampling even when there is no statistical justification.     

Clinical decision support system for dental treatment

BackgroundIn this research, a decision making system, based on fuzzy inference mechanism as proposed by Mamdani, is presented. Literature suggests that there is a lack of consistency among dentists in choosing treatment plan(s). So, this research work aims to facilitate the dentist decide the treatment plan(s) of the broken tooth.MethodsAn expert system based on fuzzy logic has been designed to accept inaccurate and vague values of dental signs and symptoms associated with the broken tooth. We designed a knowledge base with 60 rules and used Mamdani inference algorithm to decide the possible one or more treatment(s) and suggest the same to the dentist.ResultsThe results proposed by the system are compared with the dentists’ suggestions. The Chi-square test of homogeneity is conducted on 100 randomly generated sample cases with the help of three professional dentists. It is found that the results produced by the system are consistent with the treatment plan(s) proposed by the dentists. Chi-square value of the test is 3.843565 which is less than the critical value which is 12.592. Hence, we are unable to reject the null hypothesis that assumes the two populations are homogeneous with respect to treatments.ConclusionsThe accuracy of the proposed decision support system for the treatment of broken tooth enhances the confidence level of the dentists while making decision regarding the treatment plan(s). Simple and interactive GUI makes it easy to use.     

The rise,current position and future direction of asset management in utility industries

Ensuring the fitness for purpose of the UK's utility networks is vital to both the country and the network owners. Replacing these networks would cost many hundreds if not thousands of billions of pounds. As these assets age, high levels of investment are now required to maintain a satisfactory performance level. For example, the annual investment needed for the UK's electricity distribution network is over £1 billion. Hence, efficiently managing these assets is extremely important and ‘asset management’ is the core of the infrastructure companies' businesses. This paper reviews what is meant by the term ‘asset management’ and why it has risen in importance over the last few decades. The current position of asset management modelling is then described before the likely key future developments are considered.     

The impact of supervisory monitoring on high-end retail sales productivity

Based on a two-stage analysis of a panel of data on 12 outlets of a high-end retailer for 24 months, we investigate how the level of supervisory monitoring affects retail sales productivity. In the first stage, we use Data Envelopment Analysis (DEA) to compute the relative productivity of retail outlets in using their labor and capital resources to generate store sales. In the second stage, we regress the logarithm of DEA scores on contextual variables to obtain consistent estimators of the impact of contextual variables on productivity (Banker and Natarajan in Operation Research 56:48–58, 2008). Contrary to agency theoretic prediction that supervisory monitoring leads to an increase in retail sales productivity, our empirical results indicate that the higher the level of supervisory monitoring, the lower is the retail sales productivity for high-end retail outlets.     

Salespeople's management of customer information: Impact on optimal territory and sales force sizes

Collecting and processing territory and account information are major aspects of a salesperson's task. To a large extent, salespeople's effectiveness depends on the amount and quality of the market information available to them (such as their customers' needs and potential, the likelihood of getting an order after some contact time, etc.). Although they are not always easy to disentangle, these information gathering and processing activities on one hand, and the effective contact time devoted to selling to clients and prospects on the other, vie for the limited time resources available to a salesperson. This paper provides a simple statistical procedure for estimating the costs of information gathering and processing by a salesperson. The model can be used by management for estimating the most profitable territory size to be assigned to each salesperson, and consequently for estimating the optimal sales force size.     

Optimum step-stress accelerated degradation test for Wiener degradation process under constraints

To assess a product's reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.