Optimal Salesmen's Compensation Plans: A Multiperiod Approach

Conditions to induce an income maximizing salesman to allocate his time among product lines so as to maximize the firm's long-run profits are derived. These conditions highlight the need to take explicitly into account the carryover effects of salesmen's activities in determining the relative importance of the commission rates to be paid for the various product lines.     

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.     

Heston随机方差模型下确定缴费型养老金的最优投资

本文对确定缴费计划养老金的最终财富期望指数效用最大的最优投资组合进行研究.假设养老金计划的基金可以投资于无风险资产和风险资产,并且风险资产的方差服从Heston模型,得到最优投资和最大期望指数效用的明确表达式.此外,通过数值计算还得到最优投资与各个参数之间的关系.     

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 Dynamic Control for the Defined Benefit Pension Plans with Stochastic Benefit Outgo

Abstract

This work is devoted to a continuous time dynamic pension funding model in a defined benefit plan of an employment system. We extend the analysis of some standard models by incorporating a source of uncertainty in the benefit outgo. The key assumption is that the random benefits increase on average at an exponential rate. We model the preference of the manager with the main objective of minimizing both the contribution rate risk and the solvency risk. Two different situations are studied regarding the investment decisions. In the first case, the fund is invested at a constant, risk-free rate of interests; in the second case, the promoter invests in a portfolio with a risky asset and a risk-free bond. We provide, in both cases, explicit expressions for the actuarial liability, normal costs, value function, and the supplementary contribution rate.     

考虑返回补偿策略的制造与再制造的最优决策

作为减少成本的一种有效方式,近年来,再制造获得了企业越来越多的关注.对于再制造企业,如何有效地返回产品是一个基本的问题,为此,考虑了一个返回补偿策略,即企业支付给愿意返回产品的消费者一个价格补偿.在这个策略下,回收数量是随机需求的一个比例.研究了一个两周期的库存系统,企业需要在每周期初决策新材料的采购数量以及分配给制造和再制造方式的生产数量.通过建立一个三级随机动态规划模型,给出了制造和再制造混合系统对于已实现需求的最优生产策略,同时证明了每个周期的目标函数对于库存补充数量是凸的,进而证明基本的库存策略仍然是最优的.最后从管理者的角度进行了数值分析.     

股权激励下的高管冒险决策与最优或有薪酬

股权类薪酬可导致高管冒险决策,而“内部债”是解决这个问题的可行方案。或有薪酬作为一种新型的“内部债”模式得到了实务界的重视,但如何设计或有薪酬以缓解股权激励下的高管冒险决策尚无理论研究。本文利用动态规划方法,得到高管薪酬价值及企业证券价值的显式解;构建委托代理模型,给出薪酬合同激励相容的一个充分条件;并给出了最优合同的数值结果及定量分析。分析表明:与单纯的股权薪酬相比,或有薪酬有效缓解了高管的冒险决策,促使其顾及社会总福利、注重企业长期发展。     

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。     

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.     

公平汇率

随着世界与中国的经贸关系变得更加复杂,汇率政策调整产生的净影响远不是那么简单。     

部分纯净主效应设计

纯净效应准则是选择最优设计的一个重要准则,实际中往往部分二阶交互效应是可忽略的,此时对主效应的估计,可以允许主效应与可忽略二阶交互效应混杂.文章首先回顾了部分纯净主效应设计的相关理论、进展、以及二水平情形下的结果.然后以三水平为例,给出了高水平下部分纯净主效应设计的若干结果.相比二水平情形,其存在更多类的高水平部分纯净主效应设计.最后通过随机模拟比较,验证了三水平部分纯净主效应设计在估计参数上的优势.     

Fair 1-Factorizations and Fair Holey 1-Factorizations of Complete Multipartite Graphs

A k-factor of a graph G is a k-regular spanning subgraph of G. A k-factorization is a partition of E(G) into k-factors. Let K(n, p) be the complete multipartite graph with p parts, each of size n. If \(V_{1},\ldots , V_{p}\) are the p parts of V(K(n, p)), then a holey k -factor of deficiency \(V_{i}\) of K(n, p) is a k-factor of \(K(n,p)-V_{i}\) for some i satisfying \(1\le i \le p\). Hence a holey k -factorization is a set of holey k-factors whose edges partition E(K(n, p)). Representing each (holey) k-factor as a color class in an edge-coloring, a (holey) k-factorization of K(n, p) is said to be fair if between each pair of parts the color classes have size within one of each other (so the edges are shared “evenly” among the permitted (holey) factors). In this paper the existence of fair 1-factorizations of K(n, p) is completely settled, as is the existence of fair holey 1-factorizations of K(n, p). The latter result can be used to provide a new construction for symmetric quasigroups of order np with holes of size n. Such quasigroups have the additional property that the permitted symbols are shared as evenly as possible among the cells in each \(n \times n\) “box”. These quasigroups are in some sense as far from frames produced by direct products as possible.     

Fair colorful k-center clustering

Mathematical Programming - An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The...