随机需求环境下联产品系统价格与产量决策研究

基于固定比例生产技术和多产品随机需求的情形,研究了联产品制造商的两阶段产量和价格联合优化模型。通过反向倒推的优化求解,得到了联产品制造商的最优产量和价格决策以及变化规律。同时研究了需求服从均匀分布时,需求波动对均衡的影响。研究结果表明,在订货成本较低和一种产品的需求波动性较大时,当另外一种产品的波动增大,则该产品的最优订货量增大,同时价格下降。借助数值仿真,分析了价格敏感度和产出比例对最优决策和利润的影响。结果表明,在给定一种产品的价格敏感度时,另外一种的价格敏感度越大,那么该产品的价格就越低,制造商的订货量就下降。当一种产品的产出比例固定时,另一种产品的产出比例上升时,则该产品的价格下降,制造商的订货量下降,总利润上升。     

审计定价管制与交易剩余——2010年审计定价管制失效的自然实验

在经济下行压力加大、资本市场进一步开放的新形势下,厘清审计市场交易——监管机制,完善审计服务市场尤为必要。借由2010 年审计定价管制政策失效的自然实验,本文通过嵌入双边随机边界模型,得到审计双方的定价交易剩余指标,运用双重差分模型解析价格管制与交易定价的作用机制。研究发现,定价管制失效的原因不在于规制俘获,而在于价格管制与当前的市场效率不匹配。下限管制尽管能够提高审计师剩余,但同时会放大交易定价风险,增加剩余的错配,扰乱交易秩序。上限管制则进一步固化市场的低价竞争。进一步研究发现审计师剩余与盈余质量显著相关,2014年的放开定价管制政策提高了审计师剩余。研究厘清了审计市场交易机制,有利于未来研究审计交易机制的微观影响及与盈余质量的关联,为在新时代把握审计市场交易——监管规律、培育自发良性交易的审计市场提供有益借鉴。     

金融期权定价模型与金融风险管理

金融期货是一种具有独特功能的非常重要的衍生金融工具 ,对规避金融风险有重要意义 ,其作为一种金融资产表现为一种特定的权利。B -S期权模型开创性地表达了这种期权定价理论 ,二项式模型则将各种金融期权定价模型推向简化和实用化。     

Independent attributes control chart for Markov-dependent processes

Statistical process monitoring (SPM) is a very efficient tool to maintain and to improve the quality of a product. In many industrial processes, end product has two or more attribute-type quality characteristics. Some of them are independent, but the observations are Markovian dependent. It is essential to develop a control chart for such situations. In this article, we develop an Independent Attributes Control Chart for Markov Dependent Processes based on error probabilities criterion under the assumption of one-step Markov dependency. Implementation of the chart is similar to that of Shewhart-type chart. Performance of the chart has been studied using probability of detecting shift criterion. A procedure to identify the attribute(s) responsible for out-of-control status of the process is given.     

On the statistical computation of the sample multiple correlation moefficient

Based on the recursive formulas of Lee (1988) and Singh and Relyea (1992) for computing the noncentral F distribution, a numerical algorithm for evaluating the distributional values of the sample squared multiple correlation coefficient is proposed. The distributional function of this statistic is usually represented as an infinite weighted sum of the iterative form of incomplete beta integral. So an effective algorithm for the incomplete beta integral is crucial to the numerical evaluation of various distribution values. Let a and b denote two shape parameters shown in the incomplete beta integral and hence formed in the sampling distribution functionn be the sample size, and p be the number of random variates. Then both 2a = p - 1 and 2b = n - p are positive integers in sampling situations so that the proposed numerical procedures in this paper are greatly simplified by recursively formulating the incomplete beta integral. By doing this, it can jointly compute the distributional values of probability dens function (pdf) and cumulative distribution function (cdf) for which the distributional value of quantile can be more efficiently obtained by Newton's method. In addition, computer codes in C are developed for demonstration and performance evaluation. For the less precision required, the implemented method can achieve the exact value with respect to the jnite significant digit desired. In general, the numerical results are apparently better than those by various approximations and interpolations of Gurland and Asiribo (1991),Gurland and Milton (1970), and Lee (1971, 1972). When b = (1/2)(n -p) is an integer in particular, the finite series formulation of Gurland (1968) is used to evaluate the pdf/cdf values without truncation errors, which are served as the pivotal one. By setting the implemented codes with double precisions, the infinite series form of derived method can achieve the pivotal values for almost all cases under study. Related comparisons and illustrations are also presented     

Joint product assortment,inventory and price optimization to attract loyal and non-loyal customers

In this paper, we analyze the emerging retail practice of carrying a combined product assortment consisting of both regular “standard” products and more fashionable and short-lived “special” products. The purpose of this practice is to increase store traffic by attracting heterogeneous classes of customers, which drives up sales of standard products due to the potential cross-selling effect. Customers who are primarily attracted by special products will also buy some standard products. In this context, we analyze three decisions that are crucial for a retailer׳s commercial success: the product assortment, the inventory levels and the pricing. We propose an optimization model and an iterative heuristic to analyze the trade-offs between the combined product assortment, the inventory level and the price per product when there is limited shelf space. Using numerical experiments, we show that our heuristic can be trusted and that its accuracy improves when the number of products increases. Our findings indicate that to attract more customers for standard products, a retailer may benefit from carrying low priced special products which, if considered in isolation, would be non-profitable. As the cross-selling effect decreases, a retailer should focus more on the standard assortment by increasing its size and decreasing the prices. However, introducing special products and ignoring the cross-selling effect may decrease a retailer׳s profitability. We show that the introduction of special products involves more than just choosing the right specials for non-loyal customers but impacts the global assortment planning, the standard products and the products pricing.     

Self-validated Computations for the Probabilities of the Central Bivariate Chi-square Distribution and a Bivariate F Distribution. This work partially supported by National Science Foundation grant DMS-9500831

Self-validated computations using interval analysis produce results with a guaranteed error bound. This article presents methods for self-validated computation of probabilities and percentile points of the bivariate chi-square distribution and a bivariate F distribution. For the computation of critical points (c ₁,c ₂) in the equation P(Y ₁ @ c ₁, Y ₂ ≤ c ₂) = 1 ? α, the case c ₁ = c ₂ is considered. A combination of interval secant and bisection algorithms is developed for finding enclosures of the percentile points of the distribution. Results are compared to previously published tables.     

A note on “Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract”

In this short note, we first improve the proof in Zhang et al. [1] to show the strict concavity of the unit time total profit of the whole supply chain with respect to preservation technology investment without approximation. We then generalize the model of Zhang et al. [1] to a broader class of market demand functions. Additionally, theoretical results are provided to illustrate the features of the proposed model.     

Optimal Digital Rights Management with Uncertain Piracy

Many firms that sell digital copies of copyrighted materials online face a common dilemma: the use of digital rights management (DRM) to impede pirates can impose restrictions on legitimate use. We introduce a two‐period model in which the use of DRM in the first period affects the probability that a consumer finds a pirated copy in the second period; the threat of legal action reduces consumers’ consumption of pirated copies; and firms choose whether to sell, and at what prices, either strongly or weakly DRM‐protected products, or both. Furthermore, we incorporate the role of uncertainty concerning future levels of piracy. Using a two‐period model with uncertainty, we investigate a firm's optimal DRM strategies and present the optimal pricing strategy as well as product launch strategy under different market conditions. We find that one important characteristic of the optimal strategy is that it is optimal to maintain the same product line configuration strategy for both periods. We also characterize the conditions under which each strategy is optimal.