The research and development (R&D) processes influence the economic development of a company, because in an industry that is changing fast, firms must continually revise their projects and range of products. Therefore in order to determine the specific costs of research and development activity we have to highlight the efforts and effects of these activities and to calculate some indicators of economic efficiency. In the cost calculation process in R & D we have emphasized the identification of the components of cost and the duration of the R & D processes, as a component of the R&D cost, that is why as a new method we used Monte Carlo simulation. The novelty of the paper is that it focuses on determining components of cost and the duration of the R & D processes in its cost calculation procedure. The originality of this work is the use of Monte Carlo simulation to determine the average length of producing a new product

Aurelian, Sarbu Flavius

Gavrila, Calefariu

Monika, Moga

Smarandache, Florentin

English

University of New Mexico

University of New Mexico 
UNM Digital Repository 
Mathematics and Statistics Faculty and Staff 
Publications Academic Department Resources 
4-2014 
Determining the Duration of R&D Processes through Monte Carlo 
Simulation 
Florentin Smarandache 
Moga Monika 
Calefariu Gavrila 
Sarbu Flavius Aurelian 
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Determining the Duration of R&D Processes 
 through Monte Carlo Simulation 
MOGA Monika1,a, CALEFARIU Gavrilă1,b, SMARANDACHE Florentin2,c, 
SÂRBU Flavius Aurelian1,d and BOGDAN Laura3,e 
1 Transilvania University, Faculty of Technological Engineering and Industrial Management, 
 Colina Universitatii nr. 1 corp A, Brașov 500036, Romania. 
2 University of New Mexico, 705 Gurley Ave., Gallup, New Mexico 87301, USA. 
3 Babes-Bolyai University, Faculty of Economics and Business Administration, 
 Str. Teodor Mihali, Nr.58-60, Cluj-Napoca 400591, Romania. 
amoga_monika@yahoo.com, bgcalefariu@unitbv.ro, c fsmarandache@gmail.com, 
dsflavius@unitbv.ro, eby_laura99@yahoo.com 
Keywords: R&D, R&D cost calculation, R&D process duration, and Monte Carlo simulation. 
Abstract. The research and development (R&D) processes influence the economic development of 
a company, because in an industry that is changing fast, firms must continually revise their projects 
and range of products. Therefore in order to determine the specific costs of research and 
development activity we have to highlight the efforts and effects of these activities and to calculate 
some indicators of economic efficiency. In the cost calculation process in R & D we have 
emphasized the identification of the components of cost and the duration of the R & D processes, as 
a component of the R&D cost, that is why as a new method we used Monte Carlo simulation. The 
novelty of the paper is that it focuses on determining components of cost and the duration of the R 
& D processes in its cost calculation procedure. The originality of this work is the use of Monte 
Carlo simulation to determine the average length of producing a new product. 
Introduction 
After [1] the R & D function of a firm can be defined as a whole of activities of the industrial 
organization by which it is conceived and implemented its technical and scientific progress, 
considering the minimization of deviations between targets and results on the market. Determining 
the specific costs of R&D activity consist of highlighting the efforts and effects of these activities 
and the calculating some indicators of economic 
efficiency. Discrete event simulation is used to simulate 
situations in which there are identified different events 
that change the status of the studied system. Events are 
discrete because it is believed that between two events, 
the system state does not change. Monte Carlo method 
is an important component of discrete event simulation 
to generate random intervals between two successive 
events, duration of service, etc. [2]. Time points of the 
events are random. Due to the dynamic nature of the 
discrete event simulation models, the simulation time is 
necessary to know the value of the simulated time and 
it is also a need for a simulated progress of time from 
one value to another. The purpose and applicability of 
the simulation is not limited only to assist managerial decision-making processes. Simulation has 
important uses in: computer aided design, virtual reality systems, for computer game industry, 
training of professionals (pilots, surgeons) or military applications [3]. Among the objectives of the 
Fig. 1. Stages of the research 
Applied Mechanics and Materials Online: 2014-10-08
ISSN: 1662-7482, Vol. 657, pp 886-890
doi:10.4028/www.scientific.net/AMM.657.886
© 2014 Trans Tech Publications, Switzerland
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
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paper we list the better sizing of the research team and needs, presentation of the methodology for 
obtaining the input data, which will be introduced in the Monte-Carlo model, and also validating the 
methodology through a study case. 
Research Stages 
Our research referring to the determination of the cost components and duration of a research 
consists of the stages presented in Fig. 1. 
Presentation of the Methodology for Obtaining Input Data. Because of the importance of 
creativity in the process of R&D appeared the issue of its stimulation. The number practical 
methods existing in the world today, used   to stimulate creativity is of the hundreds. The general 
classification divides two important 
methods of stimulating creativity: 
intuitive methods and analytical methods. 
Intuitive methods are called so because it 
is based on the use of intuitive thinking, 
particular focus on the imagination, freed 
from the constraints of reality. 
The main intuitive methods are: 
Brainstorming can be defined as a way to 
get in a short time, a large number of 
ideas from a group of people. Sinectica is 
the rival of brainstorming. Thinking Hats 
method, is based on the interpretation of 
roles depending on the color of the 
chosen hat. Delphi method, the goal is to 
obtain guidance, forecasts and solutions 
to complex problems using a group of 
experts. Mind-mapping method involves 
building a graphical diagram suggesting 
how ideas arise from each other [4]. Analytical methods are based on the predominant use of logical 
thinking in order to stimulate the process of combining the real plan using information directly 
related to the problem. The main analytical methods are: Osborn's interrogative method is a list of 
60 questions grouped into 9 categories. Attribute listing technique: to get new ideas, identify and list 
as many of the attributes of a problem, then work, in turn, to each of them. Morphological analysis, 
its principle is to describe analytically and systematically, all solutions of the problem, than choose 
the best. Multiple criteria analysis has 5 stages: establish criteria, determination of the weight of 
each criterion, identifying all variants, granting a grade N, calculate the product of the N notes and 
the weighting coefficients. The "ETECTRE" method, aims to examine a number (m) of possible 
options in terms of (n) selection criteria through a simple procedure for estimating the "effect". 
PINDAR technique, is a successful combination of morphological analysis with the criteria analysis  
The stages of product development are presented in Fig. 2 after [5].  
Cost calculation is made for the first 8 stages of development, including the final draft. 
Sometimes, for complex projects, after the first eight stages, there is still a prototype development 
phase. For the input stage in current manufacture, cost issues will be treated in a forthcoming paper. 
Direct costs are in direct contact with the innovation and development of a new product. Indirect 
costs are general operating cost of the R & D department. Their highlighting separate from the 
direct makes sense, especially if the department runs several projects simultaneously.  
Fig. 2. Stages of product developing 
Applied Mechanics and Materials Vol. 657 887
 
Table 1. The direct cost of the R&D process 
Cost of 
determining the 
parameters of 
innovation 
CPI = EMR+PP+EKH+ES 
[unit/project],(1)                
EMR is the expenditure with market research; EP is the expenditure 
with patents; EKH is the expenditure with the Know –how; Es is the 
expenditure with the specialized software. 
Cost of materials 
∑ ×=
=
N
k
mkckm pnC
1
 
[unit/project],(2)                
N is the number of components and subassemblies; nck is the norm 
of the material consumption for reference k; Pmk is the unit price of 
the material or of the subassemblies.  
Cost of 
technological 
acquisition – CTA 
CTA = CE+CTE+CDCT 
[unit/project],(3)                
CUT is the expenditure with equipment; CTE is the expenditure with 
technological equipment; CCDT is the expenditure with the special 
dispositive checker tools. 
Cost of utilities CU =CE+CTF+CIW 
[unit/project],(4)                
CE is the expenditure with electricity; CTF is the expenditure with 
technological fuel; CIW is the expenditure with industrial water used 
in the manufacture, testing and improvement of the experimental 
model.  
Total costs of 
directly 
productive staff  
Cemp/year=  
Ns (Sd/month+IS/month)T  
[unit/project],(5) 
Direct productive staff means who is involved in the 8 stages of 
development. NS is the average number of employees involved in 
the 8 stages; Sd is the average gross hourly salary; IS is the average 
monthly charges; T is the total project time in months. This 
duration is determined by the Monte Carlo method.  
Total direct costs Summing the above elements. 
 
     
Table 2. The indirect cost of the R&D process 
Expenses for maintenance and repair CMR/year [unit/project] 
Material expenses DCT normal and special CDCT/year [unit/project] 
Energy expenditure, 
other than that used in 
the process, including 
lighting departments, 
offices etc. 
CEE2/year= 
(NTSP - NTMS) · pUE T 
[unit/project], (6) 
 
NTPS [kW] is the total power used by the entire system of 
production; NTMS [kW] is the total power used by the manufacturing 
system; T is the effective time of functioning in one, two or three 
shifts; pUE [mu / kWh] is the unit price of electricity. 
Fuel costs for heating 
and for preparing 
domestic hot water 
CGM2/year=(NGMH+ 
NGMW) · pUG T 
[unit/project], (7) 
NGMH [m
3] is the volume of gas used for heating purposes; NGMW 
[m3] is the volume of gas consumed for hot water; pUG [unit/m
3] is 
the unit price of natural gas. 
Annual expenses for 
amortization of fixed 
assets 
∑
=
=
q
i iA
iMF
yearA
T
C
C
1
/
[unit/project], (8) 
 
q is the number of fixed assets of the company; CMFi is the expense 
recorded with the i [unit] asset purchase including transportation 
charges, installation, commissioning, and so on; TAi is the normal 
duration of operation of the i[years] asset, based on that given in 
the catalog of normal duration of fixed assets. 
Expenses with the  
indirectly productive 
employees  
CeIP [unit/project] 
 
 Calculated similarly as those with the direct productive personnel, 
taking into consideration the number of people, average salary, and 
duration. 
Total annual indirect 
costs 
Summing the above elements. 
 
Monte Carlo Simulation. The relative probability and the cumulative probability was calculated 
according. Than in a two axes coordinate system we presented the durations and the cumulative 
probabilities. On each interval associated with a duration a vertical bar was built having an equal 
height to the corresponding cumulative probability of that duration. Next it was generated a set of N 
random numbers uniformly distributed in the interval [0, 1] using a random number generator. Then 
these numbers were represented by a point on the horizontal axis, from that point a parallel was led 
to the vertical axis until it meets the vertical front and the length of the base bar was read. Finally, 
the average of duration was calculated, its standard deviation, and the confidence interval of the 
mean. 
The Validation of the Methodology through a Case Study. This paper serves on determining 
the financial projections from step 4 (Fig. 2). It should be also noted that the Monte Carlo method 
can be used for determining total duration of the development process based on accumulated 
experiments from firms and other developments that they made. 
888 Engineering Solutions and Technologies in Manufacturing
 
Fig. 3. Representation of the durations 
and the cumulative probabilities 
 
 
 
 
 
 
 
 
 
 
 
 
 
Next it was determined for a company with Monte Carlo simulation the total duration of the 
development process based on accumulated experiments from the company of middle size from the 
domain of rubber roller construction with relative low complexity products with a medium size, 
owning 30% of the local market with the intention of increasing its market share. It should be noted 
that these values are for incremental innovation. For determining the time required there were 
carried 18 experiments with the results 
presented in Table 3. 
Because the determination of the 
average duration with a good accuracy 
requires a large number of experiments, 
which are time, energy, materials and not 
least human resource consuming, we use 
the Monte Carlo method that can generate 
simulated observations. 
1.  The relative and the cumulative 
probability was calculated: 
2. In a two axes coordinate system we 
presented vertically the durations and 
horizontally the cumulative probabilities. On each interval associated with a duration a vertical 
bar was built having the height of the corresponding cumulative probability of that duration. 
3. After that it was generated a set of 50 N random numbers distributed in the interval [0, 1] using a 
random number generator. 
4. Each generated number was represented by a point on the horizontal axis, from that point a 
parallel was led to the vertical axis until it meets the vertical front and the length of the base bar 
was read. This resulted a series of N simulated durations as in [6,7]. 
5. Finally, it was calculated the average of duration m = 5.13 months and its standard deviation = 
5.09 and the confidence interval of the mean, which is about 5.2 months.  
 
 
Fig. 4. Representation of the random numbers and N simulated durations 
Table 3. The duration of the operations and the number 
of experiments 
The duration of the 
operation (xi) months 
 The number of the 
experiments(ni) 
3.5 1 
4 3 
4.5 3 
5 4 
6.5 5 
7 2 
 
Table 4. The relative and the cumulated 
probability 
Relative Prob. Cumulated Prob. 
0.06 0.06 
0.17 0.22 
0.17 0.39 
0.22 0.61 
0.28 0.89 
0.11 1.00 
 
Applied Mechanics and Materials Vol. 657 889
 
Research Method 
In the process of the cost calculation in R & D, the presented study was focused on determining 
components of cost and the duration of the R & D processes, as an important component of the 
R&D cost. A new method Monte Carlo simulation was used. Determination of average duration 
with good accuracy requires a large number of experiments that consumes much time, energy, 
materials and human resources. Therefore the Monte Carlo method was used for generate simulated 
observations with the help of cumulative distribution of the duration of realizing a new product and 
a generator of random numbers uniformly distributed in [0, 1]. 
Conclusions 
The major novelty of the work is that it emphasizes the components of cost and also the duration 
of R&D processes. The calculation of costs was realized through Monte Carlo simulation. This 
method can be defined as a random variable modeling method for the calculation of the 
characteristics of their distributions. Thus by using the Monte Carlo simulation it could be forecast 
the research cost and the duration of achievement. The validation of the methodology was realized 
through a case study. In a future work it is possible to discuss a comparative study, applying full 
method. Then, for different industries or for groups of companies producing similar goods, it is 
possible to obtain forecast of R&D costs and time. Furthermore, by using the fuzzy matrices it is 
possible to determine the optimum parameters in R&D. 
Acknowledgment 
This paper is supported by the Sectoral Operational Programme Human Resources Development 
(SOP HRD), ID134378 financed from the European Social Fund and by the Romanian Government. 
References 
[1] R.D. Marinescu, M. Iliescu, I. Grecu, The economic analyze in the industrial organizations from 
the domain of classic and nonconventional technological systems (in Romanian), BREN Publishing 
House, București, 2003. 
[2] D.P. Landau, K. Binder, A guide to Monte Carlo simulations in statistical physics, Cambridge 
University Press, Cambridge, New-York, 2000. 
[3] C. Doydum, N. D. Perreira, Use of Monte Carlo Simulation to Select Dimensions, Tolerances, 
and Precision for Automated Assembly. Journal of Manufacturing Systems. 10 (1991) 209-222. 
[4] G. Paicu, Creativity (in Romanian). PIM Publishing House, Iaşi, 2011. 
[5] L. Gorchels, Product manager’s guide, III. edition (in Romanian), Rosetti Educational 
Publishing House, Bucuresti, 2006. 
[6] H. Barreto, F. Howland, Introductory Econometrics: Using Monte Carlo Simulation with 
Microsoft Excel, Cambridge University Press, Cambridge, New-York, 2005. 
[7] S. E. Perez, G. Zachrich, M. Cockburn, Monte Carlo Simulation for Determination of the 
Stream Function. Computer Applications in Engineering Education. 8 (2000) 38-42. 
890 Engineering Solutions and Technologies in Manufacturing


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