A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

Project options valuation with net present value and decision tree analysis

Real options analysis (ROA) has been developed to correctly value projects with inherent flexibility, including the possibility to abandon, defer, expand, contract or switch to a different project. ROA allows computing the correct discount rate using the replicating portfolio technique or risk-neutral probability method. We propose an alternative approach for valuing Real Options based on the certainty-equivalent version of the net present value formula, which eliminates the need to identify market-priced twin securities. In addition, our approach can be extended to the case of multinomial trees, a useful tool for modeling uncertainty in projects. We introduce within decision tree analysis (DTA) a method to derive the different discount rates that prevail at different chance nodes. We illustrate the valuation method with an application presented in “A Scenario Approach to Capacity Planning” [Eppen, G.D., Martin, R.K., Schrage, L.E., 1989. A scenario approach to capacity planning. Operations Research, 37 (4)], in which the authors state that for the capacity configuration investment decision studied at General Motors, “… there is no scientific way to determine the appropriate discount rate based on estimated demand.” Our method allows deriving the scientifically correct discount rates. A major result of the analysis is that the discount rates are endogenously derived from the project structure and its behavior in light of prevailing market conditions, instead of being exogenously imposed.     

Problem-based optimal scenario generation and reduction in stochastic programming

Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear two-stage stochastic programs we show that the problem-based approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semi-infinite program. We show that the latter is convex if either right-hand sides or costs are random and can be transformed into a semi-infinite program in a number of cases. We also consider problem-based optimal scenario reduction for two-stage models and optimal scenario generation for chance constrained programs. Finally, we discuss problem-based scenario generation for the classical newsvendor problem.

     

Applying Local Rescheduling in response to schedule disruptions

In realistic scenarios of disruption management the high number of potential options makes the provision of decision support—on how to get back on track—complex. It is thus desirable to reduce the size of the regarded problems by applying methods of partial rescheduling. As existing approaches (such as Affected Operations Rescheduling or Matchup Scheduling) mainly focus on production-specific problems, we propose Local Rescheduling (LRS) as a generic approach to partial rescheduling in this paper. It integrates previous research on partial rescheduling and local search in the context of complex project scheduling problems. LRS is based on the bidirectional incremental extension of a time window regarded for potential schedule modifications. Experiments show that LRS outperforms previous approaches.     

A real options approach for entering the Internet securities trading businesses with start‐up time

This paper uses a real options approach to establish a new evaluation model under uncertainty of both the volume of Internet securities transactions and the total transaction volume of a securities firm. The proposed approach can assist securities firms in evaluating the optimal thresholds for entering the Internet securities trading business and withdrawing from the conventional securities trading business. This paper assumes that the annual number of Internet securities transactions and the total annual number of securities transactions both follow a geometric Brownian motion. Besides, this model considers a start‐up time to complete the entry project's procedure. Accordingly, a decision model based on the real options approach is introduced, and the closed form solutions for the optimal threshold values of the entry or withdrawal models are determined. The conclusions provide some valuable references to help strategic managers of securities firms in making decisions on entering the Internet securities trading business or withdrawing from the conventional trading business. Copyright © 2003 John Wiley & Sons, Ltd.     

A GPU based iteration approach to efficiently evaluate radiation symmetry for laser driven inertial confinement fusion

Radiation computation is very important for high energy density experiments design in the laser-driven Inertial Confinement Fusion. The view-factor based models are often used to calculate the radiation on the capsule inside a hohlraum. However, it usually takes much time to solve them when the number of equations is very large.In this paper, an efficient iteration approach GPU is presented. The core idea is: (1) guaranteed symmetry, strictly diagonally dominant, and positive definite properties underlying the models are described, (2) a preconditioned conjugate gradient iteration approach is presented to compute the radiation based on such guaranteed properties, and (3) such approach is then parallelized and implemented for GPU so that the large scale models, especially for the non-linear model, can be efficiently solved in reasonable time.Finally, two experimental targets for Shenguang laser facilities built in China are demonstrated and compared to validate the efficiency of the presented approach. The results show that, the models’ computation (1) can be speeded up with successive over-relax iteration method by eight times as compared with Cholesky factorization based direct approach, (2) can be accelerated more with the preconditioned conjugate gradient iteration approach by almost eight times, and (3) can be further accelerated about 2 to 4 times as it parallelized and run on the GPU, which enables the large scale models, can be efficiently solved in reasonable time on the usual desktop computers.     

A Stochastic Programming Model for Currency Option Hedging

In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors, we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our examples also illustrate stochastic programming as a practical computational tool for realistic hedging problems.     

Particle methods for stochastic optimal control problems

When dealing with numerical solution of stochastic optimal control problems, stochastic dynamic programming is the natural framework. In order to try to overcome the so-called curse of dimensionality, the stochastic programming school promoted another approach based on scenario trees which can be seen as the combination of Monte Carlo sampling ideas on the one hand, and of a heuristic technique to handle causality (or nonanticipativeness) constraints on the other hand. However, if one considers that the solution of a stochastic optimal control problem is a feedback law which relates control to state variables, the numerical resolution of the optimization problem over a scenario tree should be completed by a feedback synthesis stage in which, at each time step of the scenario tree, control values at nodes are plotted against corresponding state values to provide a first discrete shape of this feedback law from which a continuous function can be finally inferred. From this point of view, the scenario tree approach faces an important difficulty: at the first time stages (close to the tree root), there are a few nodes (or Monte-Carlo particles), and therefore a relatively scarce amount of information to guess a feedback law, but this information is generally of a good quality (that is, viewed as a set of control value estimates for some particular state values, it has a small variance because the future of those nodes is rich enough); on the contrary, at the final time stages (near the tree leaves), the number of nodes increases but the variance gets large because the future of each node gets poor (and sometimes even deterministic). After this dilemma has been confirmed by numerical experiments, we have tried to derive new variational approaches. First of all, two different formulations of the essential constraint of nonanticipativeness are considered: one is called algebraic and the other one is called functional. Next, in both settings, we obtain optimality conditions for the corresponding optimal control problem. For the numerical resolution of those optimality conditions, an adaptive mesh discretization method is used in the state space in order to provide information for feedback synthesis. This mesh is naturally derived from a bunch of sample noise trajectories which need not to be put into the form of a tree prior to numerical resolution. In particular, an important consequence of this discrepancy with the scenario tree approach is that the same number of nodes (or points) are available from the beginning to the end of the time horizon. And this will be obtained without sacrifying the quality of the results (that is, the variance of the estimates). Results of experiments with a hydro-electric dam production management problem will be presented and will demonstrate the claimed improvements. A more realistic problem will also be presented in order to demonstrate the effectiveness of the method for high dimensional problems.     

Fixed versus flexible production systems: A real options analysis

In this work, we address investment decisions in production systems by using real options. As is standard in literature, the stochastic variable is assumed to be normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. The methodology establishes a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case) and then, computes the project value. We have developed and implemented stochastic dynamic programming models both for fixed and flexible capacity systems. In the former case, we consider three standard options: the option to postpone investment, the option to abandon investment, and the option to temporarily shut-down production. For the latter case, we introduce the option of corrective action, in terms of production capacity, that the management can take during the project by considering the existence of one of the following: (i) a capacity expansion option; (ii) a capacity contraction option; or (iii) an option considering both expansion and contraction. The full flexible capacity model, where both the contraction and expansion options exist, leads, as expected, to a better project predicted value and thus, investment policy. However, we have also found that the capacity strategy obtained from the flexible capacity model, when applied to specific demand data series, often does not lead to a better investment decision. This might seem surprising, at first, but it can be explained by the inaccuracy of the binomial model. The binomial model tends to undervalue future decreases in the stochastic variable (demand), while at the same time tending to overvalue an increase in future demand values.     

The just-in-time scheduling problem in a flow-shop scheduling system

We study the problem of maximizing the weighted number of just-in-time (JIT) jobs in a flow-shop scheduling system under four different scenarios. The first scenario is where the flow-shop includes only two machines and all the jobs have the same gain for being completed JIT. For this scenario, we provide an O(n³) time optimization algorithm which is faster than the best known algorithm in the literature. The second scenario is where the job processing times are machine-independent. For this scenario, the scheduling system is commonly referred to as a proportionate flow-shop. We show that in this case, the problem of maximizing the weighted number of JIT jobs is NP-hard in the ordinary sense for any arbitrary number of machines. Moreover, we provide a fully polynomial time approximation scheme (FPTAS) for its solution and a polynomial time algorithm to solve the special case for which all the jobs have the same gain for being completed JIT. The third scenario is where a set of identical jobs is to be produced for different customers. For this scenario, we provide an O(n³) time optimization algorithm which is independent of the number of machines. We also show that the time complexity can be reduced to O(n log n) if all the jobs have the same gain for being completed JIT. In the last scenario, we study the JIT scheduling problem on m machines with a no-wait restriction and provide an O(mn²) time optimization algorithm.     

Stochastic programming with random processes

Three possible approaches to stochastic programming problems defined in time (so that they contain random processes) are described in this paper: (1) an application of the extremal theory of random processes; (2) an exponential penalty model approach related to scenario analysis; (3) a modification of the entropic penalty approach. Explicit results are derived for some special cases.     

基于实物期权定价方法的林业碳汇项目投资决策仿真研究

文章针对林业碳汇项目投资决策的复杂性、动态性和不确定性过程,利用林业—碳汇共同经营决策模型计算林业碳汇项目在投资期内的期望价值,采用实物期权定价方法对不同阶段不同策略下的林业碳汇项目价值进行评估,同时提出了多主体仿真建模方法,利用NetLogo仿真软件对林业碳汇项目投资决策过程进行动态模拟。仿真系统中涉及到的主体有林地、CO₂和投资者,投资者主要是作为观察者的身份,在不同阶段会做出不同的投资策略。模拟仿真三种不同状态下投资者的决策变化:一是传统林业投资动态模拟,不包含碳汇和期权因素动态模拟;二是引入碳汇市场后的林业投资动态模拟;三是引入碳汇市场和期权后林业投资动态模拟。NetLogo仿真分析结果表明引入碳汇市场可以提高投资者的收益并改变投资者的经营策略,同时引入期权,不仅增加了投资者的积极性而进行扩张投资,还可以更好地发挥林木碳汇功能,体现林业的生态价值及经济价值。     

On pricing arithmetic average reset options with multiple reset dates in a lattice framework

We develop a straightforward algorithm to price arithmetic average reset options with multiple reset dates in a Cox et al. (CRR) (1979) [10] framework. The use of a lattice approach is due to its adaptability and flexibility in managing arithmetic average reset options, as already evidenced by Kim et al. (2003) [9]. Their model is based on the Hull and White (1993) [5] bucketing algorithm and uses an exogenous exponential function to manage the averaging feature, but their choice of fictitious values does not guarantee the algorithm’s convergence (cfr., Forsyth et al. (2002) [11]). We propose to overcome this drawback by selecting a limited number of trajectories among the ones reaching each node of the lattice, where we compute effective averages. In this way, the computational cost of the pricing problem is reduced, and the convergence of the discrete time model to the corresponding continuous time one is guaranteed.     

Updating a credit-scoring model based on new attributes without realization of actual data

Funding small and medium-sized enterprises (SMEs) to support technological innovation is critical for national competitiveness. Technology credit scoring models are required for the selection of appropriate funding beneficiaries. Typically, a technology credit-scoring model consists of several attributes and new models must be derived every time these attributes are updated. However, it is not feasible to develop new models until sufficient historical evaluation data based on these new attributes will have accumulated. In order to resolve this limitation, we suggest the framework to update the technology credit scoring model. This framework consists of ways to construct new technology credit-scoring model by comparing alternative scenarios for various relationships between existing and new attributes based on explanatory factor analysis, analysis of variance, and logistic regression. Our approach can contribute to find the optimal scenario for updating a scoring model.     

Robust option pricing

In this paper, we combine robust optimization and the idea of ?$?$-arbitrage to propose a tractable approach to price a wide variety of options. Rather than assuming a probabilistic model for the stock price dynamics, we assume that the conclusions of probability theory, such as the central limit theorem, hold deterministically on the underlying returns. This gives rise to an uncertainty set that the underlying asset returns satisfy. We then formulate the option pricing problem as a robust optimization problem that identifies the portfolio which minimizes the worst case replication error for a given uncertainty set defined on the underlying asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-asset, American and Asian options using linear optimization; and thus the computational complexity of our approach scales polynomially with the number of assets and with time to expiry and (b) modeling flexibility illustrated by our ability to model different kinds of options, various levels of risk aversion among investors, transaction costs, shorting constraints and replication via option portfolios.     

Valuation of project portfolios: An endogenously discounted method

Real options analysis (ROA) has been developed to value assets in which managerial flexibilities create significant value. The methodology is ideal for the valuation of projects in which frequent adjustments (e.g. investment deferral, project scope changes, etc) are necessary in response to the realization of market and technological uncertainties. However, ROA has no practical application when valuing portfolios of multiple concurrent projects sharing resources, as the size of the problem grows exponentially with the number of projects and the length of the time horizon. In this paper an extension of ROA suitable for the valuation of project portfolios with substantial technological uncertainty (e.g. R&D portfolios) is proposed. The method exploits the distributed decision making strategy encountered in most organizations to decompose the portfolio valuation problem into a decision-making sub-problem and a set of single project valuation sub-problems that can be sequentially solved. Discrete event simulation is used for the first sub-problem, while a tailored ROA based strategy is used for the set of valuation sub-problems. A case study from the pharmaceutical industry is used to compare the decision tree analysis (DTA) method and the proposed method.     

Stochastic lot-sizing with backlogging: computational complexity analysis

For a multi-stage stochastic programming problem, one approach is to explore a scenario tree based formulation for the problem and solve the formulation efficiently. There has been significant research progress on how to generate scenario trees in the literature. However, there is limited work on analyzing the computational complexity of the scenario-tree based formulation that considers the number of tree nodes as the input size. In this paper, we use stochastic lot-sizing problems as examples to study the computational complexity issues for the scenario-tree based formulations. We develop production path properties and a general dynamic programming framework based on these properties. The dynamic programming framework allows us to show that the optimal value function is piecewise linear and continuous, which enables us to develop polynomial time algorithms for several different problems, including those with backlogging and varying capacities under certain conditions. As special cases, we develop polynomial time algorithms that run in O(n²){\mathcal{O}(n^2)} and O(n²T log n){\mathcal{O}(n^2T\,{\rm log}\,n)} times, respectively for stochastic uncapacitated and constant capacitated lot-sizing problems with backlogging, regardless of the scenario tree structure.     

CORO,a modeling and an algorithmic framework for oil supply,transformation and distribution optimization under uncertainty

We present a modeling framework for the optimization of a multiperiod Supply, Transformation and Distribution (STD) scheduling problem under uncertainty on the product demand, spot supply cost and spot selling price. The Hydrocarbon and Chemical sector has been chosen as the pilot area, but the approach has a far more reaching application. A deterministic treatment of the problem provides unsatisfactory results. We use a 2-stage scenario analysis based on a partial recourse approach, where the STD policy can be implemented for a given set of initial time periods, such that the solution for the other periods does not need to be anticipated and, then, it depends on the scenario to occur. In any case, it takes into consideration all the given scenarios. Novel schemes are presented for modeling multiperiod linking constraints, such that they are satisfied through the scenario tree; they are modeled by using a splitting variable scheme, via a reduntant circular linking representation.     

Model‐based quantification of the volatility of options at transaction level with extended count regression models

In this paper, we elaborate how Poisson regression models of different complexity can be used in order to model absolute transaction price changes of an exchange‐traded security. When combined with an adequate autoregressive conditional duration model, our modelling approach can be used to construct a complete modelling framework for a security's absolute returns at transaction level, and thus for a model‐based quantification of intraday volatility and risk. We apply our approach to absolute price changes of an option on the XETRA DAX index based on quote‐by‐quote data from the EUREX exchange and find that within our Bayesian framework a Poisson generalized linear model (GLM) with a latent AR(1) process in the mean is the best model for our data according to the deviance information criterion (DIC). While, according to our modelling results, the price development of the underlying, the intrinsic value of the option at the time of the trade, the number of new quotations between two price changes, the time between two price changes and the Bid–Ask spread have significant effects on the size of the price changes, this is not the case for the remaining time to maturity of the option. Copyright © 2006 John Wiley & Sons, Ltd.     

基于混合支持向量机的国防R&D项目中止决策方法

由于RD活动的高风险性,对国防RD项目开展中止决策研究具有重要的理论和现实意义.将传统RD项目中止决策的解决途径分为两类:分类型和回归型.在分析这两种解决途径存在不足的情况下,考虑到国防RD项目自身的特点,提出一种基于混合支持向量机(support vector machine,SVM)的项目中止决策方法;同时,针对模型的建立问题,提出采用交叉验证的方法,通过粒子群优化(particle swarm optimization,PSO)算法实现模型的优化选择.通过建立混合决策模型,可以得出项目中止决策的明确结论.应用分析表明,该方法能够同时实现对项目的分类和排序,较常用方法利用信息更为全面,得出结论更为细致,对实践中的项目中止决策具有较好的适应性.