Advertising for a new product introduction: A stochastic approach

We formulate a stochastic extension of the Nerlove and Arrow’s advertising model in order to analyze the problem of a new product introduction. The main idea is to introduce some uncertainty aspects in connection both with the advertising action and the goodwill decay, in order to represent the random consequences of the advertising messages and of the word-of-mouth publicity, respectively. The model is stated in terms of the stochastic optimal control theory and a general study is attempted using the stochastic Maximum Principle. Closed form solutions are obtained under linear quadratic assumptions for the cost and the reward functions. Such optimal policies suggest that the decision-maker considers both the above mentioned phenomena as opportunities to increase her/his final reward. After stating some general features of the optimal solutions, we analyze in detail three extreme cases, namely the deterministic model and the stochastic models with either the word-of-mouth effect only, or the lure/repulsion effect only. The optimal policies provide us with some insight on the general effects of the advertising action. Supported by MIUR and University of Padua.     

Optimal Expenditure Patterns of a Double-Path Engineering Project

The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.     

Optimal trajectory to overflow in a queue fed by a large number of sources

We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or optimal path) to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov fluid sources and periodic sources. Apart from a number of ramifications of this result, we present guidelines for the numerical evaluation of the optimal path.     

考虑消费者预期后悔的企业新产品推介策略

考虑消费者预期后悔因素,在分别提供新型、旧型产品的两个企业构成的市场中,建立了企业产品推介策略模型,分析了预期后悔对企业的产品推介和定价策略及利润的影响。消费者购买新产品后实际效用低于旧产品则产生转换后悔,购买旧产品后实际效用低于新产品则产生重复购买后悔。结果表明:消费者对转换后悔的厌恶程度越大,新企业的产品推介投资越多,两个企业的价格和利润越小,而重复购买后悔厌恶时的结论则相反。相比无后悔因素的情况,转换后悔和重复购买后悔的存在分别损害和增加两个企业的利润,后悔因素对新企业利润的影响比旧企业更大。此外,转换后悔的存在会促使新企业增加产品推介投资,而重复购买后悔的存在则导致相反结论。     

批量购买下免费商品赠送对新产品扩散的影响

在非耐用品的购买过程中,批量购买的消费行为较为普遍。本文基于Bass模型,将批量购买看作一个扩散过程,建立批量购买下含免费商品的产品扩散模型;然后在扩散模型中引入重复购买和价格策略等因素的影响,构建了优化模型群。对不同购买方式下的免费商品赠送进行仿真分析,同时对模型中重要参数进行优化后分析,计算分析表明:和单量购买情形一致,当存在批量购买时,免费商品的赠送同样会加快产品的扩散速度,但值得赠送更多的免费商品以达到利润最大化。消费者的批量购买量越大,就越有必要赠送更多的免费商品来让消费者了解该产品,甚至对每个消费者发放免费商品。同时,通过对赠送时期的对比分析,发现只有在产品引入初期赠送最佳,形成了“首期赠送效应”。最后,给出了参数对免费商品赠送水平的影响范围与趋势。     

Optimal harvesting of renewable resources

The aim of the paper is to investigate different types of calculus of variations solutions maximizing the present value of a renewable resource. It is found that there are two types of optimal stationary harvesting policies. For certain cost functions, bang-bang harvesting may be more profitable than either of these.     

用矩阵和积求最短路的一种新算法

先定义了矩阵和积的概念和运算,在求最短路中,这种方法和线性代数中的矩阵运算相似,通过这种方法,把求最短路转化为矩阵的运算,计算简便,有效.     

新产品设计前端的筛选与评价系统研究

本着重于新产品设计前端的筛选与评价系统研究。设计了若干准则，有社会环境准则、经济成本准则、技术准则、时间准则、价值准则等，对新产品构思进行筛选。运用模糊理论，确定隶属度函数，得到评价矩阵，最终得到综合评价；运用加权评分法，确定评判的各影响因素及其各自所占的权重，给每种构思进行评分，根据最后总得分的多少来评定构思的优劣。最后，阐述了评价系统在设计过程中的重要作用，评价系统贯穿于整个设计过程中。     

关于“一致有界的一族无穷小的积是无穷小”定理

针对微积分教材关于"无穷小的积是否是无穷小"的命题的模糊叙述,证明"一致有界的一族无穷小的积仍是无穷小".     

太阳图与路的笛卡儿积图的任意可分性（英文）

一个阶为n的图G称为是任意可分的(简作AP),如果对于任一正整数序列τ=(n₁,n₂,…,n_k)满足n=n₁+n₂+…+n_k,总是存在顶点集V(G)的一个划分(V₁,V₂,…,V_k)满足:对于i∈[1,k],|V_i|=n_i,且子图G|V_i|是图G的V_i导出的一个连通子图.我们用S~*=S(n;m₁,m₂,…,m_n)来表示最大度△(S~*)=3的太阳图.本文讨论了图S~*P_m(m≥3)的任意可分性.     

Optimal impulsive transfers between real planetary orbits

This study presents the derivation of the equations necessary to establish a practical method for computing optimal transfers in the real case. It makes it possible to compute and use actual optimal transfers for advanced planning of preliminary mission analysis in place of the standard Hohmann transfers. This realizable solution includes the effects of the inclination and eccentricity of the orbits of the planets. It applies directly to cases in which a two-impulse transfer is the optimal solution and presents the results as functions of the corresponding idealized Hohmann transfers.     

Γ‐convergence: a tool to investigate physical phenomena across scales

De Giorgi's Γ‐convergence is a variational theory modelled upon the convergence of families of (perturbed) minimum problems and of the corresponding minimizers. In these notes, after reviewing briefly the basic theory and accounting for some recent new insights, we discuss three examples of static mechanical models, which can be analysed by means of Γ‐convergence arguments. Copyright © 2012 John Wiley & Sons, Ltd.     

技术不确定环境下新产品策略的设计应用

技术的动态发展和企业间的竞争对企业新产品策略有很大影响,直接决定新产品的引进周期。本文在产业技术动态变化的随机环境下构建随机动态规划模型,关注产业技术进步、投资成本和产品市场竞争等影响因素,探讨企业进行新产品引进的周期选择,对新产品引进的周期和质量决策进行方法设计和应用举例。利用随机动态规划模型得出新产品引进的最优时间周期,用算例分析技术进步和产品研发成本对企业引进周期策略的影响,采取策略迭代的方法进行求解,发现技术进步较快时企业的新产品引进步伐也较快,研发成本的提高使企业的新产品引入步伐降低。     

Optimal steady-state versus periodic operation in discrete systems

The problem of improving the optimal steady state of a discrete system by means of a suitable cyclic operation is discussed. Two sufficient conditions are found by negating a necessary condition and by following a frequency-domain approach, respectively. The connection between the two conditions is also shown.This work has been supported by the Consiglio Nazionale delle Ricerche, Rome, Italy.     

Optimal design of structures with unspecified loading distribution

The problem of the optimal distribution of loading on a structure that corresponds to the minimum of the elastic compliance or the maximum of the safety factor for plastic collapse is considered. Optimality criteria are derived, and their applicability is illustrated in the case of beams. Besides the optimally varying cross section, also the support positions and the load distribution are determined from the optimal solution.     

公共信息产品与最佳完全契约

委托-代理理论对于建立完全契约,防治机会主义行为具有重要意义.讨论了三种参数化的委托-代理模型,通过比较分析得出:在委托代理契约中,若代理人在职消费的信息以及所有公司平均净资产报酬率的信息能体现在契约条款中,并以现金为基础来评价代理人的经营业绩,则代理契约的完全程度将增加,其激励程度也将增强,代理成本将降低.但所有公司的平均净资产报酬率是一个公共信息产品,只有政府提供才具有权威性.因此只要政府提供了相关的公共信息产品,完善了相关的制度环境,最佳完全契约是可以实现的.     

On a class of logarithmic integrals

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.     

On the existence in a problem of the calculus of variations without convexity assumptions

Summary We obtain new sufficient conditions for the existence in a problem of the calculus of variations without convexity assumptions.     

A New Derivation of the Inner Product Formula for the Macdonald Symmetric Polynomials

We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type A_n-1. As a special case, the corresponding constant term conjecture is also proved.