Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model

We consider a manufacturer who sells both the new and remanufactured versions of a product over its life cycle. The manufacturer’s profit depends crucially on her ability to synchronize product returns with the sales of the remanufactured product. This gives rise to a challenging dynamic optimization problem where the size of both the market and the user pool are dynamic and their current values depend on the entire history. We provide an analytical characterization of the manufacturer’s optimal pricing, production, and inventory policies which lead to a practical threshold policy with a small optimality gap. In addition, our analysis offers a number of interesting insights. First, the timing of remanufacturing activity and its co-occurrence with new product manufacturing critically depends on remanufacturing cost benefits, attractiveness of the remanufactured product and product return rate. Second, there is a small upward jump in the price of the new product when remanufacturing is introduced. Third, the manufacturer keeps the new product longer on the market as the cost of remanufacturing decreases. Fourth, partially satisfying demand for the remanufactured item is never optimal, i.e., it is satisfied either fully or not at all. Finally, user pool and inventory of returned products are substitutes in ensuring the supply for future remanufacturing.     

Optimal pricing,production, and inventory for deteriorating items under demand uncertainty: The finite horizon case

This paper aims to investigate the joint dynamic pricing and production decisions of deteriorating items with uncertain demand over a finite selling season, where the demand is price sensitive and the potential demand is characterized by a stochastic process. The stocks deteriorate physically at a constant fraction of the on-hand inventory. A joint dynamic pricing and production problem to maximize the total expected profit is modeled as a stochastic optimal control problem. We derive the closed-form solutions, which are in time-dependent linear feedback form of the inventory level when it is either positive or negative. It is shown that the manufacturer always benefits from a reduction in the volatility of potential market demand. In addition, to highlight the effectiveness of the joint dynamic strategy, we also consider the case of optimal production with a static price. A numerical example is presented to illustrate the validity of the optimal control policy, and sensitivity analysis on major parameters is performed to provide more managerial insights into deteriorating items.     

A competitive dynamic pricing model when demand is interdependent over time

In this study, we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels. Customers can purchase and store the products, even if they do not need them at the time, in order to use them in future. The stockpile of the products generated by customers affects the demand in future periods. Therefore, the demand for each product not only is a function of prices and quality levels, but also of the products’ stockpile levels. In addition, the stockpile levels change the customers’ consumption behavior; more product in a stockpile leads to more consumption. Therefore, we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment.     

A jump-diffusion model for option pricing under fuzzy environments

Owing to fluctuations in the financial markets from time to time, the rate λ of Poisson process and jump sequence {V_i} in the Merton’s normal jump-diffusion model cannot be expected in a precise sense. Therefore, the fuzzy set theory proposed by Zadeh [Zadeh, L.A., 1965. Fuzzy sets. Inform. Control 8, 338-353] and the fuzzy random variable introduced by Kwakernaak [Kwakernaak, H., 1978. Fuzzy random variables I: Definitions and theorems. Inform. Sci. 15, 1-29] and Puri and Ralescu [Puri, M.L., Ralescu, D.A., 1986. Fuzzy random variables. J. Math. Anal. Appl. 114, 409-422] may be useful for modeling this kind of imprecise problem. In this paper, probability is applied to characterize the uncertainty as to whether jumps occur or not, and what the amplitudes are, while fuzziness is applied to characterize the uncertainty related to the exact number of jump times and the jump amplitudes, due to a lack of knowledge regarding financial markets. This paper presents a fuzzy normal jump-diffusion model for European option pricing, with uncertainty of both randomness and fuzziness in the jumps, which is a reasonable and a natural extension of the Merton [Merton, R.C., 1976. Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3, 125-144] normal jump-diffusion model. Based on the crisp weighted possibilistic mean values of the fuzzy variables in fuzzy normal jump-diffusion model, we also obtain the crisp weighted possibilistic mean normal jump-diffusion model. Numerical analysis shows that the fuzzy normal jump-diffusion model and the crisp weighted possibilistic mean normal jump-diffusion model proposed in this paper are reasonable, and can be taken as reference pricing tools for financial investors.     

The pricing of credit risky securities under stochastic interest rate model with default correlation

In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R.A. Jarrow and F.Yu (2001), S.Y.Leung and Y.K.Kwok (2005), A.Wang and Z.Ye (2011)). By using the method of change of measure and the technology (H. S.Park (2008), R.Hao and Z.Ye (2011)) of dealing with jump diffusion processes, we obtain the analytic pricing formulas of defaultable zero-coupon bonds. Moreover, by the “total hazard construction”, we give the analytic pricing formulas of credit default swap (CDS).     

Inventory management of multiple items with irregular demand: A case study

We present the case of a Greek commercial enterprise facing the problem of managing the inventories of thousands of different items, supplied by more than 20 European and Asian manufacturers and sold to a large number of different-type customers. A key feature of the problem is that the demand for the vast majority of items is intermittent and lumpy, thus not allowing the use of the usual normal or Poisson distributions. The paper describes the solutions given to several practical problems in the course of developing an easy-to-use yet effective and all-encompassing inventory control system. Emphasis is placed on the accurate modeling of demand by means of a gamma distribution with a probability mass at zero or a package Poisson distribution for very-slow-moving items. Using those models and simple quantitative tools we develop an efficient procedure for approximate but quite accurate determination of the base stock levels that achieve the desired fill rates in the proposed periodic review system. We briefly describe the computerized implementation of the new system and the very encouraging results.     

Urban dynamics and multiple-objective programming: A case study of Beijing

This study serves as a primary application of the integrated system dynamics and multiple-objective programming (ISDMOP) model for strategic planning of Beijing city, which is here divided into six subsystems as population, resources, energy, economy, environment and ecosystem, with the planning horizon spanning from 2003 to 2020. Comparison between the original system dynamics (ORSD) model based on the existing economic structure of Beijing and the optimized system dynamics (OPSD) model adjusted according to the solutions of the multiple-objective programming (MOP) are conducted. The developing trend of each subsystem is simulated and illuminated, based on which constructive suggestions are provided for urban strategic planning of Beijing. The ISDMOP model is proved effective for investigating urban dynamics and realizing the multiple-objective programming.     

A simple recourse model for power dispatch under uncertain demand

Optimal power dispatch under uncertainty of power demand is tackled via a stochastic programming model with simple recourse. The decision variables correspond to generation policies of a system comprising thermal units, pumped storage plants and energy contracts. The paper is a case study to test the kernel estimation method in the context of stochastic programming. Kernel estimates are used to approximate the unknown probability distribution of power demand. General stability results from stochastic programming yield the asymptotic stability of optimal solutions. Kernel estimates lead to favourable numerical properties of the recourse model (no numerical integration, the optimization problem is smooth convex and of moderate dimension). Test runs based on real-life data are reported. We compute the value of the stochastic solution for different problem instances and compare the stochastic programming solution with deterministic solutions involving adjusted demand portions.This research is supported by the Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung of the Deutsche Forschungsgemeinschaft.     

Dynamic dairy facility location and supply chain planning under traffic congestion and demand uncertainty: A case study of Tehran

In this paper, dynamic dairy facility location and supply chain planning are studied through minimizing the costs of facility location, traffic congestion and transportation of raw/processed milk and dairy products under demand uncertainty. The proposed model dynamically incorporates possible changes in transportation network, facility investment costs, monetary value of time and changes in production process. In addition, the time variation and the demand uncertainty for dairy products in each period of the planning horizon is taken into account to determine the optimal facility location and the optimal production volumes. Computational results are presented for the model on a number of test problems. Also, an empirical case study is conducted in order to investigate the dynamic effects of traffic congestion and demand uncertainty on facility location design and total system costs.     

A computational study on fill rate expressions for single-stage periodic review under normal demand and constant lead time

This paper reviews fill rate expressions for a single stage periodic review inventory system under normal demand and constant lead time, discusses the relationship among all expressions in the literature, and evaluates their robustness and accuracy. Monte Carlo simulation is used to numerically compare all expressions. We present conditions under which some expressions produce higher values than others.     

A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study

This study presents a hybrid fuzzy integral decision-making model that integrates factor analysis, interpretive structural modeling, Markov chain, fuzzy integral and the simple additive weighted method for selecting locations of high-tech manufacturing centers in China. The analytical results of this case study demonstrate the feasibility of the proposed model for solving fuzzy multiple attribute decision-making problems, especially when criteria are interdependent. Further, the empirical study brings out some properties that are crucial for high-tech manufacturing centers to invest in China.     

A new fourth-order numerical scheme for option pricing under the CEV model

The empirically observed negative relationship between a stock price and its return volatility can be captured by the constant elasticity of variance option pricing model. For European options, closed form expressions involve the non-central chi-square distribution whose computation can be slow when the elasticity factor is close to one, volatility is low or time to maturity is small. We present a fast numerical scheme based on a high-order compact discretisation which accurately computes the option price. Various numerical examples indicate that for comparable computational times, the option price computed with the scheme has higher accuracy than the Crank–Nicolson numerical solution. The scheme accurately computes the hedging parameters and is stable for strongly negative values of the elasticity factor.     

Forecasting demand for single-period products: A case study in the apparel industry

The problem considered is that of forecasting demand for single-period products before the period starts. We study this problem for the case of a mail order apparel company that needs to order its products pre-season. The lack of historical demand data implies that other sources of data are needed. Advance order data can be obtained by allowing a selected group of customers to pre-order at a discount from a preview catalogue. Judgments can be obtained from purchase managers or other company experts. In this paper, we compare several existing and new forecasting methods for both sources of data. The methods are generic and can be used in any single-period problem in the apparel or fashion industries. Among the pre-order based methods, a novel ‘top-flop’ approach provides promising results. For a small group of products from the case company, expert judgment methods perform better than the methods based on advance demand information. The comparative results are obviously restricted to the specific case study, and additional testing is required to determine whether they are valid in general.     

Emergy-based urban ecosystem health assessment: A case study of Baotou,China

Ecosystem health has been a hot topic of ecosystem management research for years. Considering the urban area as a complex ecosystem consisted of natural, societal and economic entities, urban ecosystem health assessment is necessary to be conducted for the scientific management and proper ecological restoration. Combining with the ecosystem service function of the urban ecosystem, theoretical framework and methodology of the urban ecosystem health assessment based on emergy are proposed and the temporal variation of the health level of the city are also outlined in this paper. Following the principle of ecosystem health assessment, four major factors, including vigor (V), organizational structure (O), resilience (R) and function maintenance (F), are integrated to construct a novel emergy-based urban ecosystem health index (EUEHI). Based on the EUEHI and comparing with those of five other typical Chinese cities, the case study of Baotou city shows that its urban ecosystem health level is steadily arising despite the year 2001 as a turning point. Due to the emphasis on the resource structure adjustment and utilization efficiency, Baotou has obtained a better organizational structure and service function for the total urban ecosystem.     

Integrative fuzzy hierarchical model for river health assessment: A case study of Yong River in Ningbo City,China

Due to the increasingly serious ecological degradation of river systems, the river health research has attracted more and more attention of the researchers and decision-makers. This paper aims to integrate the fuzzy assessment method with analytic hierarchy process to establish the integrative fuzzy hierarchical assessment model, thus combing qualitative analysis and quantitative assessment and overcoming the disadvantages of subjectivity of the previous evaluation methods. The results show that the proposed assessment method is able to reveal how the river system is disturbed by human activities. Finally, the integrative fuzzy hierarchical method is validated and applied to the case study of Yong River in Ningbo City, China.     

A semi-analytic pricing formula for lookback options under a general stochastic volatility model

In general, the pricing problems of exotic options in finance do not have analytic solutions under stochastic volatility and so it is hard to compute the option prices or at least it requires much of time to compute them. This paper investigates a semi-analytic pricing method for lookback options in a general stochastic volatility framework. The resultant formula is well connected to the Black–Scholes price that is the first term of a series expansion, which makes computing the option prices relatively efficient. Further, a convergence condition for the expansion is provided with an error bound.     

A pricing model for secondary market yield based floating rate notes subject to default risk

The purpose of this article is to price secondary market yield based floating rate notes (SMY-FRNs) subject to default risk. SMY-FRNs are derivatives on the default-free term structure of interest rates, on the term structures for default-risky credit classes, and on the structure of a determined pool of bonds. The main problem in SMY-FRN pricing (as compared to the pricing of standard interest rate or credit derivatives) is market incompleteness, which makes traditional no-arbitrage pricing by replication fail. In general, SMY-FRNs are subject to two types of default risk. First, the SMY-FRN issuer may go bankrupt (direct default risk). Second, the possibility of the bankruptcy of the issuers in the underlying pool has an influence on the SMY-FRN coupons (indirect default risk). This article is the first one which provides a no-arbitrage pricing model for SMY-FRNs with direct and indirect default risks. It is also the first article applying incomplete market pricing methodology to SMY-FRNs.     

非线性Black-Scholes模型下阶梯期权定价

在非线性Black-Scholes模型下,研究了阶梯期权定价问题.首先利用多尺度方法,将阶梯期权适合的偏微分方程分解成一系列常系数抛物方程;其次通过计算这些常系数抛物型方程的解,给出了修正障碍期权的近似定价公式;最后利用Feymann-Kac公式分析了近似结论的误差估计.     

非线性Black-Scholes模型下Bala期权定价

在非线性Black-Scholes模型下,研究了Bala期权定价问题.首先利用双参数摄动方法,将Bala期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了Bala期权的近似定价公式.最后利用Green函数分析了近似结论的误差估计.