SUN Dongbai()， XU Wenchao()， QIAO Lili()， PENG Rui( )， WU Di( )

1 National Center for Materials Service Safety， University of Science & Technology Beijing， Beijing 100083， China2 Donlinks School of Economics & Management， University of Science & Technology Beijing， Beijing 100083， China3 Shool of Management, Xi’an Jiaotong University, Xi’an 710049, China

Abstract： The research infrastructure is very crucial for the development of some fundamental research. However， it is costly to buy， install and operate the infrastructure. This paper analyzes the costs and benefits of research infrastructure using a concept termed as investment reliability. Both the costs and the outputs are represented by a cash flow diagram， and the investment reliability is modeled. Different types of outputs are taken into concern in the model formulation. Illustrative examples are proposed to show how to apply the model.

Key words： research infrastructure； benefit； cost； output； reliability

Introduction

Research infrastructure is significant to the development of scientific research. Typical research infrastructure includes the experimental device for different types of experiments[1]， such as the synchrotron radiation facilities worldwide. Moreover， the investment on research infrastructure can be expensive[2-3]， because of not only a big amount of money needed to buy and install the related devices， but also the possible high operational cost. Thus it makes sense to study whether the investment in research infrastructure is worth the money taking into account both the input and the output.

The performability of research infrastructure can be measured in several ways. In recent years， Heidler and Hallonsten[4]suggested to use the bibliometrical indicators， such as the number of publications， to measure the benefits of the research infrastructure. However， publication is not the only form of output for research infrastructure， and one should also consider other types of output， such as patent. Through estimating expected values of each type of output to the organization owning the research infrastructure， it is possible to convert both the amount of input and output into cash flow. Manager can judge whether the investment on a research infrastructure is worthwhile with the cash flow. In particular， this paper measures the costs and benefits of research infrastructure using a concept called investment reliability. In the field of engineering， reliability has often been used to characterize the probability that some pre-specified requirement can be satisfied under certain conditions. Pengetal.[5-6]analyzed different conditions in their works. In our case， investment reliability is used to characterize the probability for the investment on the research infrastructure to get a pre-specified parameter known as internal rate of return (IRR).

The rest part of the paper is formed as follows. Section 1 describes the specific problem under assumptions. Section 2 models the investment reliability where paper and patent are considered for the output. As the costs and benefits of research infrastructure usually need to be assessed before the life end of the infrastructure， some cost and output are unknown based on the assumption. Fuzzy numbers are used to represent the unknown cost and output， and the operations of fuzzy numbers are used to obtain the investment reliability. Section 3 presents the illustrative examples based on the investment reliability. Section 4 makes a conclusion and states some future directions.

1 Problem Description

Consider an investment on research infrastructure， which can support the research inNyears. The number of papers published in each yeariis assume to beO1i. The number of patents of the same infrastructure in each yeariis assumed to beO2i. We use parameterc0to denote the initial investment. During the operation overNyears， operational costs occur， and the cost in yeariis assumed to beci. All the money spent in a year is assumed to happen at the end of the year. AfterNyears， the infrastructure can be disposed and the investor can get back some money， denoted asmd. The expected contribution of each paper to society is assumed to bev1. The expected contribution of each patent to society is assumed to bev2.

Fig.1 Cash flow diagram representing the input and output of the investment

The cash flow which represents the input and output of the investment is depicted in Fig. 1. When the IRR is not smaller thanj， we regard the investment as a successful one. Also note that in this model we implicitly assume that the expected value of each paper to society remains the same with years， and some relaxation to the assumption which can be considered in the future. Moreover， it is hard to exactly estimate the expected value of each paper. Therefore， based on Dingetal.[7]， we estimatevas a fuzzy variable， instead of a crisp value. Specifically， we definevlas a triangular fuzzy variable (v11，v12，v13)， as shown in Fig. 2. For fuzzy variables， we can use the area between the sides of the triangle and an interval on horizontal axis to denote the membership value ofv1will fall inside the interval. Specifically， the membership value ofv1which betweenv11andv13is 1， and the membership value ofv1to be betweenAandBis the ratio between the area “ABGF” and the area of triangle “CDE” in Fig. 2. Similarly，v2here is defined as a triangular fuzzy variable (v21，v22，v23).

Fig.2 Expected value of a paper denoted as a fuzzy variable

2 Formulation of Investment Reliability

To be more general， we assume that the infrastructure has just run forM

(1)

Then， by ordering (p1～，p2～，p3～) in ascending order， we have

(2)

(3)

(4)

By calculating the membership value ofpto be bigger than 0， the investment reliability can be obtained. However， the formula for the investment reliability are different when the order between 0，p1，p2，p3are different.

For the case 0

(5)

(a) 0

(b) p1≤0

(c) p1

(d) p1

3 Illustrative Examples

Consider an investment on a research infrastructure which is supposed to run 30 years after construction. Assuming that the cost and output for year 0， and the first 15 years of operation are known deterministically， and those for the last 15 years are estimated as fuzzy variables and are all shown in Table 1.

Table 1 Parameters for illustrative example

The scrap valuemdis assumed to be 90 million, 100 million, and 110 million, respectively; the expected value of each paperv1is still assumed to be 0.1， 0.2， 0.3，respectively; the expected value of each patentv2is assumed to be 1， 2， 3, respectively. If the minimum requirement of IRR is 0.08， the NPV of the investment of the infrastructure can be obtained using Eq. (1) as

p=(-101.887， 383.838 8， 903.165 7).

(6)

Using (5)， the investment reliability can be obtained as

R=0.978 7.

(7)

4 Conclusions

This paper proposed a framework to analyze the costs and benefits of research infrastructure. In particular， the tradeoff between them is measured using investment reliability， which is modelled through four parameters: the initial cost， the operational cost， the output and the scrap value. The number and value of output in each category of each type is whether known or unknown based on different cases. Under the case when they are not known， they can be estimated as fuzzy variables. Framework is also proposed to evaluate the investment reliability.

Future researches can be devoted to figure out all types of output and classify them as detailed as possible. Moreover， data can be collected from real case of research infrastructure for further analysis and discussion.