Revenue management for remanufactured products

Revenue management for remanufactured products has not been addressed in literature so far. There could be more than one quality level of the recovered products, which would draw different prices in the secondary markets. In this paper, we develop a pricing model to maximize the expected revenue from the recovered products. Numerical examples are included for illustration.     

The value of acquisition price differentiation in reverse logistics

The quality of returned products may vary greatly, depending on their previous usage. Since the remanufacturing of products in good condition is more economically rewarding for the remanufacturer—and since even for non-remanufacturable products the value that can be extracted from their parts or materials may depend on the products’ quality—it seems logical to acquire used products of different quality levels at different prices. However, acquisition price differentiation requires the product quality to be revealed, i.e. the products are graded before their actual acquisition. We observe two different approaches in current practice. The first one is a decentralized system with several collection sites to which the customers can bring their used products. After a short grading procedure, they receive a specific acquisition price offer for their products, which they can accept or decline directly. The second setting is a reverse logistics system with a centralized grading facility. The final grading is conducted after shipping the used products to this specific facility. Motivated by these empirical observations, we compare the two strategies with the help of a continuous approximation model. We derive analytical expressions for the optimal pricing and network density decision and show that, in addition to the other factors discussed in the literature, acquisition price differentiation can be a reason for decentralizing the reverse logistics network, if the product quality is uncertain. Furthermore, we illustrate our results with a numerical example.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

基于晶格场理论和动态规划的国债期货定价研究

通过用一个二维量子场取代传统金融上的布朗运动,构建了可有效纳入国债远期利率在到期时间和日历时间两个维度上的不完全相关性的量子场理论模型,并离散化二维量子场,得到国债远期利率的晶格场理论模型,同时结合动态规划方法,将国债期货的所有交易交割规则纳入一个模型进行建模,实现在统一的模型框架下对国债期货及其内嵌的择时期权和质量期权进行定价。研究结果亦表明,所构建的国债期货定价模型的定价效果均显著优于传统的主流两因子HJM模型,且与真实市场结算价的贴合性均很强,特别地,在临近交割月份,其定价误差均降至0.05%以内。而各国债期货合约的质量期权价值都在其对应的国债期货面值的2%至6%之间,其择时期权价值大部分时间都在0附近徘徊,但随交割月份临近,择时期权价值开始迅速上升,最大时约为期货合约面值的0.6%。     

An Examination of the Effect of Continuous Quality Improvements on Optimal Pricing for Durable Goods*

This paper investigates the nature of optimal prices for a durable good in the presence of continuous quality improvements. The analysis of optimal prices is based on a nonlinear dynamic model of sales response that relates price, quality, average life of a product and the persistence of quality perceptions. Numerical solutions to the model are derived by employing the generalized reduced gradient algorithm. The results show that optimal price depends on the persistence of quality perceptions and the average life of a product (an aspect of quality). The analysis of optimal results affirms results based on other models and provides insights on the influence that quality has on optimal pricing. The implications of the results and suggestions for future research are discussed.     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.     

Open Source Development with a Commercial Complementary Product or Service

We examine optimal control decisions regarding pricing, network size, and hiring strategy in the context of open source software development. Opening the source code to a software product often implies that consumers would not pay for the software product itself. However, revenues may be generated from complementary products. A software firm may be willing to open the source code to its software if it stands to build a network for its complementary products. The rapid network growth is doubly crucial in open source development, in which the users of the firm's products are also contributors of code that translates to future quality improvements. To determine whether or not to open the source, a software firm must jointly optimize prices for its various products while simultaneously managing its product quality, network size, and employment strategy. Whether or not potential gains in product quality, network size, and labor savings are sufficient to justify opening the source code depends on product and demand characteristics of both the software and the complementary product, as well as on the cost and productivity of in‐house developers relative to open source contributors. This paper investigates these crucial elements to allow firms to reach the optimal decision in choosing between the open and closed source models.     

产能和需求不确定情形下ATO系统最优库存和生产决策研究

通过将产成品的最终组装环节延迟到观察到实际需求以后进行,按订单组装(Assemble-to-Order,ATO)策略能够有效避免按库存生产(Make-to-Stock)策略下因为生产过剩而带来的损失和风险。然而,在未来产能有限的情形下,生产商必须提前组装部分产成品,以最大化自身收益。本文考虑一个未来需求和组装产能同时具有不确定性的单周期ATO系统:在观察到实际需求以前,生产商必须准备好所有的零部件库存,并组装适量的产成品;观察到实际需求和实际可用组装能力以后,则根据需要进一步追加产成品产量,以尽可能满足客户需求,从而最大化自身利益。通过构建一个两阶段规划模型,我们研究了生产商的最优零部件库存和最优生产决策;并进一步考察了生产商可以通过紧急外包来获取额外组装产能时的最优决策。研究结果为随机环境下生产商合理采购零部件库存和合理安排生产提供了有益的管理启示。     

RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements

In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.     

短期电价预测的组合混沌方法

电力市场中,电价的变化呈现的是一种非线性的、动态开放的过程,传统的方法已很难提高其预测精度。为此,本文提出一种基于小波变换、计量经济学模型和径向基函数网络的组合混沌预测方法。首先利用小波变换将原电价序列分解、重构成概貌序列和细节序列;在此基础上,针对不同的子序列建立不同的模型,并进行预测;最后将所有子序列的预测结果求和,作为最终的预测值。对西班牙电力市场短期电价的预测表明,该方法具有很高的预测精度。     

Hedging through index-based price contracts in commodity-based supply chains

This paper studies the optimal hedging strategy of risk-neutral firms in supply chain settings. We model a retailer procuring goods through index-based price contracts from two commodity processors. The processors’ input commodity prices are random and correlated. The retailer faces price-sensitive demand curves; therefore, it controls product demand through retail pricing in the final product market. We characterize the optimal contracting terms for the processors and show that they prefer to hedge part of their exposure to the commodity price risk. The optimal contract for processor comprises a processing margin independent of the commodity price volatility and a hedge ratio that is a function of the commodity price volatility and the products substitution factor. We uncover a new rationale for hedging in settings where downstream firms have pricing power; both processors and the retailer benefit from the retailer’s pricing power when their margins are linked to input prices; an index-based price contract is a means to link the processors’ and the retailer’s margins. We further investigate how different market parameters affect the optimal hedge ratios and extend our model to settings with random market sizes and asymmetric substitution for final products.     

Forecasting the market demand for waste paper

In a recent article in this journal, Livesey and Barcena supplied an interesting but necessarily superficial analysis of the market for waste paper. Their essential conclusion was that, faced with future shortages, and hence increased prices of wood pulp, the paper and board industry would be forced to rely more heavily on secondary fibre. In turn, they felt that ‘in order to ensure an adequate supply of waste paper, governments may need to exert a greater degree of influence over the market than they do at present’.This paper seeks to provide a more rigorous analysis of the ‘waste paper problem’ in terms of future demand and fluctuations in that demand. It also corrects some misconceptions in the paper by Livesey and Barcena as to the likely sources of future supply and the economics of securing those supplies.     

Optimal lot sizing under continuous price decrease

An important characteristic of high-tech industries is decreasing component prices over time. In the personal computer industry, some component prices decline at a rate of 1% per week. This paper develops an inventory model for products experiencing continuous decrease in unit price. We develop an accurate closed-form approximate solution to the model. Our results indicate that declining prices lead to substantial decrease in the optimal cycle time and much frequent ordering. This explains the heavy emphasis on just-in-time inventory management practiced by successful companies in high-tech industries. While previous models attributed the success of just-in-time policies to reduced holding cost and improved quality, under declining prices a substantial source of savings becomes lower costs of raw materials which is significant part of cost in these industries. We illustrate the results of the model with a numerical example and perform sensitivity analysis.     

考虑顾客策略行为和产品质量的闭环供应链决策模型

策略型的顾客对于不同质量的产品以及不同时间的产品会有不同的估值和支付意愿,企业在进行决策时应当考虑顾客的策略性行为。建立了由一个制造商(即原始设备制造商)和一个独立的再制造商以及一组策略型顾客组成的闭环供应链模型,利用动态博弈理论分析了当由独立的再制造商负责回收旧产品并进行再制造时顾客策略行为和再制造品的质量水平对闭环供应链的产品价格、利润、消费者剩余的影响。研究结果表明,当顾客的策略程度增加时,制造商的利润减少,再制造商的利润和消费者剩余增加。当再制造品的质量水平增加时,制造商的利润降低,再制造商的利润先增加后降低,消费者剩余增加。     

顾客策略行为下差异产品两阶段定价模型研究

互联网和信息技术的发展,为零售商收集顾客信息带来方便的同时,也使得消费者变得越来越具有策略性和选择性。首先,构建零售商只销售一种高质量产品的情形,研究其两阶段的定价策略,并分析产品的跨期折扣因子对产品的零售价格、销售量和零售商利润的影响。然后,考虑零售商可提供高质量和低质量两种产品的情形,顾客在第一销售期、第二销售期都可以选择两种产品。构建两阶段的定价决策模型,并分析产品的跨期折扣因子、顾客对低质量产品的接受度等参数对产品两阶段的零售价格、销售量的影响。最后,用数值算例分析了第二种模型下顾客对低质量产品的接受度等模型参数对零售商两阶段总利润的影响,然后比较了第一种和第二种模型下高质量产品的零售价格和销售量。研究结论较全面的分析了顾客策略行为对差异产品两阶段销售期的定价决策的影响,为零售商进行定价优化决策提供了十分重要的参考。     

Coordinating a three level supply chain with flexible return policies

This paper studies the coordination issue of a three level supply chain selling short life cycle products in a single period model. The manufacturer first negotiates the trade contract with the retailer, then with the supplier. We construct the so-called flexible return policy by setting the rules of pricing while postponing the determination of the final contract prices. With return policies between each pair of adjacent firms, unsold products or used modules dissembled from the unsold products are returned level by level from the retailer to the upstream firms and each firm shares in the loss due to the overstock. We show that the three level supply chain can be fully coordinated with appropriate contracts and the total profit of the channel can be allocated with any specified ratios among the firms.     

Integrated production strategy and reuse scenario: A CoFAQ model and case study of mail server system development

One of the core problems in software product family (SPF) is the coordination of product building and core asset development, specifically the integration of production strategy decision and core asset scenario selection. In the current paper, a model of Cost Optimization under Functional And Quality (CoFAQ) goal satisfaction constraints is developed. It provides a systematic mechanism for management to analyze all possible products and evaluate various reuse alternatives at the organizational level. The CoFAQ model facilitates decision-makers to optimize the SPF development process by determining which products are involved in the SPF (i.e. production strategy) and which reuse scenario for each module should be selected to implement the SPF toward minimum total developing cost under the constraints of satisfying functional and quality goals. A two-phase algorithm with heuristic (TPA) is developed to solve the model efficiently. Based on the TPA, the CoFAQ is reduced to a weighted set-covering problem for production strategy decision and a knapsack problem for the reuse scenario selection. An application of the model in mail server domain development is presented to illustrate how it has been used in practice.     

A SIMULATION MODEL OF THE HIGHER EDUCATION SYSTEM OF A STATE1

This paper describes a simulation model to estimate the enrollments and expenditures associated with various policy alternatives for the post-secondary education system of a state, with Indiana as an example. Enrollments, operating expenditures, and construction costs are predicted for every public and private school for each year until 1985. The basic model-building technique employed is regression analysis on historical data, but it is supplemented by other quantitative techniques and by experts' predictions. The model may be used to predict “most likely” future enrollments and costs, to perform sensitivity analyses to better understand the impact of various exogenous variables upon the system, and to evaluate possible policy alternatives. Including all of the schools in a state makes possible the evaluation of policy alternatives such as possible configurations of new two-year public schools, the effect of tuition changes, and the effect of enrollment ceilings for larger state universities.     

基于GARCH-EWMA原理的期货交易保证金随动调整模型

在EWMA模型和GARCH模型思想的基础上,结合SPAN系统的思想,以保证金在期货交易中可以弥补最大损失额和保证交易的正常进行等作用为考虑因素,运用数理统计和VaR等风险管理方法,建立了保证金随动调整模型。在满足给定风险系数和置信水平的前提下,制定合理的保证金的收取比例,为期货交易的保证金水平的确定提供了新的计算方法。本模型的特点一是利用GARCH模型对EWMA模型中的关键参数-衰减因子进行测定,解决了以往使用EWMA模型时,对该参数人为赋值而导致模型人为因素过强的问题。二是在模型中引入波动函数,用来确定随时点t而不断变化的波动系数值。并采用大量的历史数据对大豆、豆粕两种期货品种的波动函数进行线性拟合,得到时点t与波动系数之间的连续线性函数,以代替以往波动系数与时点t之间所采用的极为粗糙的分段函数,从而大大提高了模型的灵敏性。三是采用近4500个合约价格的历史数据,对大豆和豆粕两种期货合约价格的涨跌停情况进行统计分析,得到这两类期货品种的涨跌停情况的概率分布。并分别考虑各种可能发生的情况综合计算最终单位保证金,使得保证金的计算更具全面性。     

Bipolar value-driven joint product costing

There exists a joint-cost allocation problem in the public sector, particularly highlighted by the cost-based national pricing of blood products in England, supposedly derived using volume-driven activity-based costing (ABC): an approach criticised by the implementation criteria propounded for ABC within the academic literature. In contrast, we believe that the contributions of quality-associated operations-based drivers, described within ABC, together with the net realisable value method, usually recommended as the optimal joint-cost allocation method, provide the beginnings of a solution. This paper sets out a methodological development from this platform that links allocation decisions with the issue of value. The bipolar nature of the model is based upon the combination of two types of allocation. One allocates joint costs according to the altered value of source material when competing non-joint alternative products exist. The other allocates joint costs according to product outcome values ascertained separately for the physical specification elements that comprise each of the range of joint products. The overall emphases are on academic context, model generalisation, the facilitation of cost-effective choices between joint products and non-joint alternatives, and possible future trends in the application of the method.