Determining Optimal Selling Price and Lot Size When the Supplier Offers All-Unit Quantity Discounts*

This paper is concerned with finding the optimal price and lot size for a retailer purchasing a product for which the supplier offers all-unit quantity discounts. Demand for the product is assumed to be a decreasing function of price, and a procedure is developed for finding the optimal price and lot size for a class of demand functions. The procedure then is applied to two common demand functions: (1) the constant price-elasticity function, and (2) the linear demand function.     

ASYMMETRIC LOSS FUNCTION AND OPTIMAL POLICY UNDER UNCERTAINTY: A SIMPLE PROOF

Given an asymmetric quasi-convex loss function and a symmetric quasi-concave probability density function, both continuous, an extremely simple proof is suggested that shows that a policy maker will minimize expected loss by choosing a policy value on the less-damaging side of the loss function. This proof, which is compatible with a wide variety of loss functions and probability density functions, is extended to include cases where a symmetric loss function is matched against an asymmetric probability density function and where an asymmetric loss is matched with an asymmetric probability density function.     

ON-LINE QUALITY MANAGEMENT: INTEGRATION OF PRODUCT INSPECTION AND PROCESS CONTROL

A growing recognition that quality management is an important factor in defining a firm's competitive position has led to renewed attention to this function and has resulted in implementation of elaborate systems for on-line quality control comprising product inspection and process control. Traditionally, these functions have been treated independently, with very little interaction. In this paper we examine, in detail, a scheme that integrates the two functions, and we demonstrate that such an approach can result in significant cost savings. The motivation for this work comes from our experience in a wafer fabrication facility that suggested that exchange of quality information between different stages of production could result in significant performance improvements. To illustrate this approach, we consider a specific environment characterized by a single-stage continuous production process whose status is monitored by an X̄ control chart. We assume that quality-related costs may be described as a function of the process output. This is analogous to Taguchi's quality loss function and may be interpreted as a generalization of conventional classification of process output as either acceptable or defective units. The integrative scheme essentially relies on utilization of the process status information (based on process control) in making product inspection decisions. For this system we derive a cost model and develop a solution procedure to determine optimal decision parameters. Limited computational results indicate that the scheme has significant potential for reducing quality-related costs.     

When to Offer Lower Quality or Remanufactured Versions of a Product

We investigate the profitability of adding a lower quality or remanufactured product to the product portfolio of a monopoly firm, both in single‐period and steady‐state settings. Consumer behavior is characterized by a deterministic utility function for the original product and a nonlinear relative utility function for the lower quality product. We find a threshold for the cost of the low‐quality product below which it is optimal to add it to the firm's portfolio, and show that while a cost advantage is necessary to make the lower quality offering profitable under linear or convex relative utility functions, market segmentation alone can justify the addition of the lower quality product under concave relative utility functions. In particular, we characterize (i) the new product cost under which it is optimal to offer a lower quality version of the product even if it is as costly to produce as the original product; and (ii) the weighted average of new and remanufactured product costs in the steady state under which it becomes cost effective to offer new products under the remanufactured label. Finally, we also identify the maximum possible profits from customer segmentation and the form of the relative utility function that achieves them. We discuss the implications for the common marketing practices of branding and generics.     

REGRESSION ANALYSIS WITH ASYMMETRIC LINEAR LOSS

Asymmetric loss functions often arise where regression estimates are used in management decision making. However, regression analysis has traditionally made use of a symmetric loss function in which the cost of underestimating equals the cost of overestimating. If the loss function is linear and the degree of asymmetry can be determined, the asymmetric regression method presented in this paper can be employed to find appropriate regression estimates. Asymmetric regression analysis requires no unusual data inputs other than an estimate of the cost asymmetry and can be performed efficiently using standard linear programming techniques.     

产品并行开发过程中的风险分析

风险是产品开发的固有特性,本文分析产品并行开发中的风险问题。首先基于上游演化度和下游灵敏度分别建立产品并行开发中的时间函数和成本函数,并结合相关的风险分析,建立产品并行开发的时间风险和成本风险函数,并且基于这两种风险的可转化性,追求其加权和最小,保证产品开发在时间和成本两方面达到预期目标。     

Development of Economic Consequence Methodology for Process Risk Analysis

A comprehensive methodology for economic consequence analysis with appropriate models for risk analysis of process systems is proposed. This methodology uses loss functions to relate process deviations in a given scenario to economic losses. It consists of four steps: definition of a scenario, identification of losses, quantification of losses, and integration of losses. In this methodology, the process deviations that contribute to a given accident scenario are identified and mapped to assess potential consequences. Losses are assessed with an appropriate loss function (revised Taguchi, modified inverted normal) for each type of loss. The total loss is quantified by integrating different loss functions. The proposed methodology has been examined on two industrial case studies. Implementation of this new economic consequence methodology in quantitative risk assessment will provide better understanding and quantification of risk. This will improve design, decision making, and risk management strategies.     

基于价值损耗的生鲜农产品供应链协调

生鲜农产品属于变质产品,但是变质库存管理是针对产品本身的变质属性发展起来的,不能解决生鲜农产品的非变质性价值损耗问题。由此,本文针对现有文献对损耗尚停留在定性描述阶段,构造了一个指数形式的新鲜度衰减函数,尝试用新鲜度表征价值损耗,在此基础上定量研究两级生鲜农产品供应链协调问题。研究发现,考虑价值损耗的情况下,集中式决策不能使生鲜农产品供应链达成协调。     

基于消费者损失效用的概率销售策略研究

随着网络信息技术的迅猛发展，概率销售作为一种新颖的销售策略广泛应用于旅游业。在双寡头销售商竞争销售背景下，两销售商分别向损失中性和损失厌恶型消费者销售高档产品和概率产品（中低档产品打包成概率产品）。本文首先运用博弈方法建立了损失中性下的概率销售模型，揭示了产品质量对销售商策略的影响。考虑到消费者在购买概率产品后存在期望损失，我们进一步构建了损失厌恶下的概率销售模型，研究了期望损失对概率销售策略的影响。研究表明期望损失为概率销售商实施概率销售提供了可能性，同时可以增加概率销售商的利润，但可能会损害其竞争者的利益；销售商是否采用概率销售策略主要取决于消费者对购买损失和选择损失的敏感度。最后给出了数值应用结果及管理学启示。     

基于顾客分类的生鲜农产品二次补货策略

零售商为弥补生鲜农产品新鲜度降低造成的顾客流失,选择在单销售期内二次补货,将新鲜产品和初始订货的非新鲜产品同时销售。但二次补货的新鲜产品会对初始订货产品形成需求挤兑。将顾客划分为三种类型:只购买新鲜产品、只够买折扣产品和两种产品都愿意购买,引入需求挤兑因子的概念,讨论了不同顾客类型下需求挤兑效应对零售商订货决策和利润的影响,并与单次订货策略做比较。结论表明,随着顾客对产品品质和新鲜度要求不断提高,二次补货策略能有效降低订货总量,提升零售商利润水平;不但优化了经济效益,更具有减少产品损耗和节约社会资源、增加消费者福利水平的社会效益。     

ECONOMIC PROCESS CONTROL UNDER UNCERTAINTY

The future of the global industry lies in the continuous improvement of both products and processes, a renewed commitment to competition, and an aggressive approach to satisfying customers needs in quality, quantity, and timing. In quality management, the degree of customer satisfaction for a given product may be measured in the form of the loss to society. This loss is formulated as a function of the deviation from the target for each of the product's quality characteristics. The greater the variability of uncontrolled factors during manufacturing or production the larger will be that loss. In this paper, we develop a form of the loss function that takes into account the variability of a production process, the decision loss, and the costs of sampling and inspection. Specifically, we consider monitoring a production process, which may undergo continuous mean shift and variance deterioration during a production run. We then examine decision rules for continuing production or stopping and adjusting the production process.     

Fusion Product Planning: A Market Offering Perspective*

Devices that integrate multiple functions together are popular in consumer electronic markets. We describe these multifunction devices as fusion products as they fuse together products that traditionally stand alone in the marketplace. In this article, we investigate the manufacturer's fusion product planning decision, adopting a market offering perspective that allows us to address the design and product portfolio decisions simultaneously. The general approach adopted is to develop and analyze a profit‐maximizing model for a single firm that integrates product substitution effects in identifying an optimal market offering. In the general model, we demonstrate that the product design and portfolio decisions are analytically difficult to characterize because the number of possible portfolios can be extremely large. The managerial insight from a stylized all‐in‐one model and numerical analysis is that the manufacturer should, in most cases, select only a subset of fusion and single‐function products to satisfy the market's multidimension needs. This may explain why the function compositions available in certain product markets are limited. In particular, one of the key factors driving the product portfolio decision is the margin associated with the fusion products. If a single all‐in‐one fusion product has relatively high margins, then this product likely dominates the product portfolio. Also, the congruency of the constituent single‐function products is an important factor. When substitution effects are relatively high (i.e., the product set is more congruent), a portfolio containing a smaller number of products is more likely to be optimal.     

基于模糊规划的QFD 系统参数确定方法

针对QFD 系统的内在模糊性,运用带有对称三角形模糊系数的模糊规划理论,提出了一 种确定QFD 系统参数的方法. 并通过工程特性目标值的规范化,定义产品开发总成本函数、工 程特性改进成本函数及改进成本系数等概念,建立了一个QFD 规划模型. 仿真结果表明,该模 型能够帮助开发人员在不确定的、模糊条件下有效确定关联函数及自相关函数,优化顾客需求 的满意水平,确定工程特性目标值,使新开发/ 改进的产品顾客满意度赶上或超过目标市场上 的竞争企业,并满足开发预算约束.     

Effects of Product Structure Complexity on Multi-level Lot Sizing*

As an input to the materials requirement planning (MRP) process, the product structure interacts with the lot-sizing rules to affect inventories, materials flow, and production costs. Despite engineering constraints, considerable latitude is still available to construct alternate product structures for the same product. An important concern of MRP managers and designers is the impact of product structure complexity on the cost performance of the lot-sizing rules. To date, there exists no detailed research that provides managers with guidelines that relate the lot-sizing rules to individual product structure parameters. We report on an extensive experiment to test the effects of individual product structure parameters on the relative cost performance of 11 lot-sizing rules. Three parameters—the number of items, number of levels, and commonality index—are proposed to characterise product structure complexity and used as factors in an experiment involving a large variety of product structures. The results indicate that all three parameters affect the relative cost differences but not the ranking of the rules. The overall best lot-sizing rule is Bookbinder and Koch's [11] rule.     

A Comprehensive Model for Managing Credit Risk on Home Mortgage Portfolios*

Managing credit risk in financial institutions requires the ability to forecast aggregate losses on existing loans, predict the length of time that loans will be on the books before prepayment or default, analyze the expected performance of particular segments in the existing portfolio, and project payment patterns of new loans. Described in this paper are tools created for these functions in a large California financial institution. A forecasting model with Markovian structure and nonstationary transition probabilities is used to model the life of a mortgage. Logistic and regression models are used to estimate severity of losses. These models are integrated into a system that allows analysts and managers to depict the expected performance of individual loans and portfolio segments under different economic scenarios. With this information, analysts and managers can establish appropriate loss reserves, suggest pricing differentials to compensate for risk, and make strategic lending decisions.     

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.     

Separable Preferences,Strategyproofness, and Decomposability

We consider strategyproof social choice functions defined over product domains. If preferences are strict orderings and separable, then strategyproof social choice functions must be decomposable provided that the domain of preferences is rich. We provide several characterization results in the case where preferences are separable only with respect to the elements of some partition of the set of components and these partitions vary across individuals. We characterize the libertarian social choice function and show that no superset of the tops separable domain admits strategyproof nondictatorial social choice functions.     

一类具有生存/危险特征的生鲜品价格策略研究

研究了一个周期内零售商对一种易变质生鲜品的订购和价格决策问题。引入价格转折点概念,变质率具有三参数生存/危险特征的Weibull分布,需求率依赖于变质率和价格,建立利润最大化的目标函数,将求解最优价格的问题转化为带有控制的Bolza问题,得到最优价格表达式。通过算例,研究了价格敏感度和价格转折点变化对利润的影响,进一步给出了灵敏度分析和价格弹性分析;对于生鲜品,随着时间的推移,销售价格越来越低;对销售价格敏感的顾客,销售量随着价格转折点的滞后而降低,但在整个销售阶段的1/2到3/5附近进行价格调整有助于增加利润。     

功能性IT产品首次试用和重复试用对消费者态度的影响有什么不同？

随着技术的发展，许多创新型IT产品的功能，消费者很难一看便知。对于这些产品而言，产品试用被看作一种十分有效的市场推广手段。但是，以往的研究主要关注消费者初次试用产品的情境，并没有分析当消费者重复进行产品试用时，影响他们产品态度的内在因素有何不同。因此，针对这一研究缺口，论文采用现场研究方法，分析消费者初次试用和重复试用时的行为特征以及消费者态度变化的不同内在机制。本文的研究结果弥补了以往研究主要关注消费者初次试用产品，对重复试用研究不足的缺陷，并对厂商产品试用的营销设计提供了建议。     

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.