Optimal Expenditure Patterns of a Double-Path Engineering Project

The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.     

Technological change,population dynamics,and natural resource depletion

In this paper, we integrate fertility and educational choices into a scale-invariant model of directed technological change with non-renewable natural resources, in order to reveal the interaction between population dynamics, technological change, and natural resource depletion. In line with empirical regularities, skill-biased technological change induces a decline in population growth and a transitory increase in the depletion rate of natural resources. In the long-run, the depletion rate also declines in the skill intensity. A decline in population growth is harmful for long-run productivity growth, if R&D is subject to diminishing technological opportunities. The effectiveness of economic policies aimed at sustained economic growth thus hinges on its impact on long-run population growth given the sign of intertemporal spillovers in R&D with respect to existing technological knowledge. We demonstrate that an increase in relative research productivities or an education subsidy enhances long-run growth, if R&D is subject to diminishing technological opportunities, while an increase in the teacher–student ratio is preferable in terms of positive intertemporal knowledge spillovers.     

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.     

R&D pipeline management: Task interdependencies and risk management

Maintaining a rich research and development (R&D) pipeline is the key to remaining competitive in many industrial sectors. Due to its nature, R&D activities are subject to multiple sources of uncertainty, the modeling of which is compounded by the ability of the decision maker to alter the underlying process. In this paper, we present a multi-stage stochastic programming framework for R&D pipeline management, which demonstrates how essential considerations can be modeled in an efficient manner including: (i) the selection and scheduling of R&D tasks with general precedence constraints under pass/fail uncertainty, and (ii) resource planning decisions (expansion/contraction and outsourcing) for multiple resource types. Furthermore, we study interdependencies between tasks in terms of probability of success, resource usage and market impact. Finally, we explore risk management approaches, including novel formulations for value at risk and conditional value at risk.     

Comparative evaluation of performance of national R&D programs with heterogeneous objectives: A DEA approach

The strategic importance of performance evaluation of national R&D programs is highlighted as the resource allocation draws more attention in R&D policy agenda. Due to the heterogeneity of national R&D programs’ objectives, however, it is intractably difficult to relatively evaluate multiple programs and, consequently, few studies have been conducted on the performance comparison of the R&D programs. This study measures and compares the performance of national R&D programs using data envelopment analysis (DEA). Since DEA allows each DMU to choose the optimal weights of inputs and outputs which maximize its efficiency, it can mirror R&D programs’ unique characteristics by assigning relatively high weights to the variables in which each program has strength. Every project in every R&D program is evaluated together based on the DEA model for comparison of efficiency among different systems. Kruskal–Wallis test with a post hoc Mann–Whitney U test is then run to compare performance of R&D programs. Two alternative approaches to incorporating the importance of variables, the AR model and output integration, are also introduced. The results are expected to provide policy implications for effectively formulating and implementing national R&D programs.     

A multiobjective evolutionary approach for linearly constrained project selection under uncertainty

In the project selection problem a decision maker is required to allocate limited resources among an available set of competing projects. These projects could arise, although not exclusively, in an R&D, information technology or capital budgeting context. We propose an evolutionary method for project selection problems with partially funded projects, multiple (stochastic) objectives, project interdependencies (in the objectives), and a linear structure for resource constraints. The method is based on posterior articulation of preferences and is able to approximate the efficient frontier composed of stochastically nondominated solutions. We compared the method with the stochastic parameter space investigation method (PSI) and illustrate it by means of an R&D portfolio problem under uncertainty based on Monte Carlo simulation.     

Optimal Dynamics of Innovation in Models of Economic Growth

A nonlinear model of economic growth which involves production, technology stock, and their rates as the main variables is considered. Two trends (growth and decline) in the interaction between the production and R&D investment are examined in the balanced dynamics. The optimal control problem of R&D investment is studied for the balanced dynamics and the utility function with the discounted consumption. The Pontryagin optimality principle is applied for designing the optimal nonlinear dynamics. An existence and uniqueness result is proved for an equilibrium of the saddle type and the convergence property of the optimal trajectories is shown. Quasioptimal feedbacks of the rational type for balancing the dynamical system are proposed. The growth properties of the production rate, R&D, and technology intensities are examined on the generated trajectories.     

Strategic optimization in R&D investment

We use d'Aspremont and Jacquemin's strategic optimal R&D investment in a duopoly Cournot competition model to construct myopic optimal discrete and continuous R&D dynamics. We show that for some high initial production costs, the success or failure of a firm is very sensitive to small variations in its initial R&D investment strategies.     

A MIXED CONTROL PROBLEM OF THE MANAGEMENT OF NATURAL RESOURCES

In this paper, we study the optimal solutions of a model of natural resource management which allows for both impulse and continuous harvesting policies. This type of model is known in the literature as mixed optimal control problem. In the resource management context, each type of control represents a different harvesting technology, which has a different cost. In particular, we want to know when the following conjecture made by Clark is an optimal solution to this mixed optimal control problem: if the harvesting capacity is unlimited, it is optimal to jump immediately to the steady state of the continuous time problem and then to stay there. We show that under a particular relationship between the continuous and the impulse profit function, the conjecture made by Clark is true. In other cases, however, it is either better to use only continuous control variables or to jump to resource levels which are smaller than the steady state and then let the resource grow back to the steady state. These results emphasize the importance of the cost functions in the modeling of natural resource management.     

Expenditure patterns and timing of patent protection in a competitive R&D environment

In this paper we consider a stochastic R&D decision model for a single firm operating in a competitive environment. The study focuses on the firm's optimal policy which maximizes the expected discounted net return from the project. The firm's policy is composed of two ingredients: a stopping time which determines when the developed technology should be introduced and protected by a patent, and an investment strategy which specifies the expenditure rate throughout the R&D program. The main findings of the study are:

• (a) 

  Under a constant expenditure rate strategy, the optimal stopping time of the project is a control limit policy of the following form: stop whenever the project's state exceeds a fixed critical value, or when a similar technology is introduced and protected by one of the firm's rivals, whichever occurs first.

• (b) 

  For a R&D race model in which the winner-takes-all competition and the loser's return is zero, we show that the firm's optimal expenditure rate throughout the R&D program increases monotonically as a function of the project's state.

In order to gain a better insight regarding optimal R&D programs in competitive markets we examine the effect of key economic parameters on the firm's optimal policy.     

Real R&;D options with time-to-learn and learning-by-doing

We model R&D efforts to enhance the value of a product or technology before final development. Such efforts may be directed towards improving quality, adding new features, or adopting technological innovations. They are implemented as optional, costly and interacting control actions expected to enhance value but with uncertain outcome. We examine the interesting issues of the optimal timing of R&D, the impact of lags in the realization of the R&D outcome, and the choice between accelerated versus staged (sequential) R&D. These issues are also especially interesting since the history of decisions affects future decisions and the distributions of asset prices and induces path-dependency. We show that the existence of optional R&D efforts enhances the investment option value significantly. The impact of a dividend-like payout rate or of project volatility on optimal R&D decisions may be different with R&D timing flexibility than without. The attractiveness of sequential strategies is enhanced in the presence of learning-by-doing and decreasing marginal reversibility of capital effects.     

合作研发中项目的搜寻与项目的状态价值

本将Pissarides模型的思想应用于合作研发中项目的搜寻，讨论合作研发过程中研发体和投资体的资源互补性，以及研发体项目资金获得的影响因素，和项目价值在搜寻过程中的决定因素。     

A generalized real option pricing method of R&D investments: jump diffusion and external competition

ABSTRACT

Numerous studies have assessed Research and Development (R&D) investment using the real option pricing approach. This paper proposes a more general real option pricing method that both considers the specificity of R&D investment (such as uncertainty) and the R&D investment opportunity of a business in a market environment with external competitors. Specifically, we adopt a jump diffusion model to evaluate R&D investments that incorporate the uncertainties of these activities. The model values a pioneer's R&D investment opportunity allowing the chance that competitors may enter the market and the project value may vary with time. By construction and analysis of the model, we then analyse the optimal timing to realize profit on an investment. Overall, this model should facilitate a more comprehensive evaluation for R&D investments.     

R&;D Equilibrium Strategies with Surfers

A typical assumption in the game-theoretic literature on research and development (R&D) is that all firms belonging to the industry under investigation pursue R&D activities. In this paper, we assume that the industry is composed of two groups; the first (the investors) is made of firms that have R&D facilities and are involved in this type of activity. The second group corresponds to firms that are inactive in R&D (the surfers). The latter group benefits from its competitors’ R&D efforts, thanks to involuntary spillovers. This division of the industry is in line with actual practice, where indeed not all firms are engaged in costly and risky R&D. We adopt a two-stage game formalism where, in the first stage investors decide on their levels of investment in R&D, and in the second stage all firms compete à la Cournot in the product market. We characterize and analyze the unique subgame perfect Nash equilibrium. Research supported by NSERC, Canada. F. Ben Abdelaziz is on leave at The College of Engineering, American University of Sharjah, UAE.     

Climate change and optimal energy technology R&D policy

Public policy response to global climate change presents a classic problem of decision making under uncertainty. Theoretical work has shown that explicitly accounting for uncertainty and learning in climate change can have a large impact on optimal policy, especially technology policy. However, theory also shows that the specific impacts of uncertainty are ambiguous. In this paper, we provide a framework that combines economics and decision analysis to implement probabilistic data on energy technology research and development (R&D) policy in response to global climate change. We find that, given a budget constraint, the composition of the optimal R&D portfolio is highly diversified and robust to risk in climate damages. The overall optimal investment into technical change, however, does depend (in a non-monotonic way) on the risk in climate damages. Finally, we show that in order to properly value R&D, abatement must be included as a recourse decision.     

OPTIMAL R&D FOR NONRENEWABLE RESOURCES: THE CASE OF COST REDUCING TECHNOLOGY

A model is developed to determine optimal R&D spending and completion time when R&D results in lower extraction costs of a nonrenewable resource deposit. Examples of R&D projects for which the model is designed are in-situ leaching for mining and carbon dioxide injection in petroleum. The model is a combined R&D/nonrenewable resource model (CM). Results from the CM are compared to simulations of an R&D model which ignores the nonrenewable resource. The comparison demonstrates the importance of including resource parameters in the R&D spending model. The CM extends the literature by considering R&D spending and exhaustible natural resource production simultaneously. It demonstrates the importance of including the resource deposit when R&D affects the deposit. This is important because more accurate models of R&D will increase the profitability of the R&D projects.     

On the prisoner’s dilemma in R&D with input spillovers and incentives for R&D cooperation

This paper considers a standard model of strategic R&D with spillovers in R&D inputs, and extends the result that duopoly firms engaged in a standard two-stage game of R&D and Cournot competition end up in a prisoner’s dilemma situation for their R&D decisions, whenever spillover effects and R&D costs are relatively low. In terms of social welfare, this prisoner’s dilemma always works to the advantage of both consumers and society. This result allows a novel and enlightening perspective on some issues of substantial interest in the innovation literature. In particular, the incentive firms face towards R&D cooperation in the form of an R&D cartel is shown to be maximal for the case of zero spillovers, which is when the prisoner’s dilemma has the largest scope.     

Effects of asymmetric knowledge spillovers on the stability of horizontal and vertical R&D cooperation

In order to investigate the role of asymmetric spillovers in the stability of R&D cooperation, this paper distinguishes two different types of cooperative partners, and uses a game theory approach to reveal the relationship between asymmetric spillovers and R&D investment in the horizontally and vertically related R&D cooperation. In the horizontal R&D cooperation, higher incoming spillovers and lower outgoing spillovers induce firms to invest on R&D efforts as agreed. However, it is the contradiction between horizontal firms’ attitudes towards asymmetric spillovers that leads to the inherent instability of the cooperation. In the vertical R&D cooperation, our results question the usually held opinion about the effects of asymmetric spillovers on the decision of R&D investment. The incoming spillovers are less important in the innovation process for vertically related R&D cooperation. A firm tends to under-invest on the arranged level of R&D efforts when its incoming spillovers increase. Our results also show that efficient mechanisms to restrain firms’ non-cooperative behavior are essential to improve the stability of horizontal and vertical R&D cooperation.     

The impact of delaying an investment decision on R&D projects in real option game

In a research and development (R&D) investment, the cost and the project value of such an investment are usually uncertain, which thus increases its complexity. Correspondingly, the NPV (Net Present Value) rule fails to evaluate the value of this project exactly, because this method does not take into account the market uncertainty, irreversibility of investment and ability of delay entry. In this paper, we employ the real option theory to evaluate the project value of a R&D investment. Since the cost of a R&D investment is very high and the flow of the information is crowded, an investor cannot make an immediate decision every time. So, the proposed real option model is an exchange option. At the same time, combining the real option and the game theory, we can find the Nash equilibrium which is the optimal strategy. Moreover, we also study how the delayed time influences the price of the project investment and how the different delayed times effect the choice of the optimal strategies.     

Can R&D expenditure avoid corporate bankruptcy? Comparison between Japanese machinery and electric equipment industries using DEA–discriminant analysis

This study compares data envelopment analysis–discriminant analysis (DEA–DA) with Altman’s financial ratio analysis to identify the position of DEA–DA in financial performance analysis. Then, this study applies DEA–DA to examine whether Research and Development (R&D) expenditure influences the financial performance of Japanese machinery industry and electric equipment industry. The investigation of DEA–DA identifies that the R&D expenditure makes a positive impact on the financial performance of Japanese machinery industry, but it yields a negative impact on Japanese electric equipment industry. The result implies that the influence of R&D expenditure on financial performance (including the avoidance of bankruptcy) depends upon the type of a manufacturing industry. A rationale regarding why such a discrepancy has occurred between the two Japanese manufacturing industries is because the life cycle of electric equipments is shorter than that of the machinery products. Furthermore, the electric equipment industry faces more fierce competition than the machinery industry. This study suggests that the Japanese electric equipment industry needs R&D expenditure for competition in its global market. However, it is a high risk and high return investment. In contrast, the Japanese machinery is a technologically mature industry where the R&D expenditure influences positively its financial performance. In this sense, the R&D expenditure is a low risk and necessary investment.