Method for simulating and estimating project research and development cost by utilizing Monte Carlo

Abstract

The invention discloses a method for estimating the research and development cost of a project through Monte Carlo simulation, and the method comprises the steps: constructing a corresponding mathematical model according to a research problem, and selecting a corresponding random variable as an input variable; correspondingly inputting partial observed values or parameters of the corresponding random variables, and determining specific probability distribution shapes of the random variables; taking a test item of which the cost is to be estimated as a statistical magnitude, and defining the statistical magnitude as an output variable of the mathematical model; according to random variables and statistics defined in a Monte Carlo simulation tool, the number of random simulation times is set, simulation random sampling and statistics fitting statistics sample values are carried out, and distribution formed by a plurality of statistics samples is obtained; and obtaining a corresponding statistical mean value, a variance and a confidence interval according to a result fitted by a Monte Carlo method, and further estimating the research and development cost. According to the method, the uncertainty in the project cost estimation process is considered, the statistical prediction result is given in a probability distribution mode, and higher accuracy and credibility are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of project cost estimation, and in particular to a method for estimating project R&D cost by using Monte Carlo simulation. Background Art

[0002] The existing estimation methods are complex and subject to human subjective influence. Yang Lei (2017) proposed a substation life cycle cost estimation model using particle swarm optimization fuzzy neural network. By decomposing and analyzing the life cycle cost of the substation, the influencing factors of various costs were summarized. The structure of the fuzzy neural network and the particle swarm optimization algorithm were analyzed, and the estimation model of the life cycle cost of the substation was established. The feasibility of the model was verified by an example, which provided a reference for the selection of substation construction plans. In order to overcome the influence of data missing and uncertain factors on the life cycle cost evaluation of construction projects, Liang Xi (2017) introduced fuzzy theory into the estimation and evaluation of the life cycle cost (LCC) of construction projects, constructed a calculation model based on the composition of the project LCC, and then used triangular fuzzy functions to fuzzify the variables. The Day-Stout-Warren (DSW) algorithm was used to plot the points to find the change trend of the LCC fuzzy function. Finally, MATLAB performed least squares curve fitting on the discrete data, clarified the estimation range of the construction project cost, solved such uncertainty problems, considered the subjectivity of decision makers, and made the decision of the plan simple and effective. In view of the highly nonlinear characteristics between the cost of engineering projects and their influencing factors and the small sample data in engineering practice, Du Zhida (2020) constructed a cost estimation model based on ABC-LS-SVM. The model is based on the LS-SVM algorithm and uses the artificial bee colony algorithm to tune the core parameters of the model. The results show that compared with traditional cost estimation methods, the model greatly improves the accuracy of estimation and the efficiency of modeling. On this basis, the cost control interval is delineated according to the cost estimate value and the test set error MAPE, and a cost control model is established to judge the status and management level of the project cost, ensure that the project achieves the predetermined economic goals and social benefits, and provide a reference for the effective control of project costs.

[0003] In most cases, a combination of qualitative and quantitative analysis is used to estimate project costs according to the characteristics of the project. At the same time, the impact of uncertainty factors on project cost estimation in the process of project cost estimation is also different. However, the current research on project cost estimation at home and abroad is still based on large-scale engineering and infrastructure projects or software projects as application scenarios, and rarely involves the cost estimation of new consumer electronics product development projects. Many uncertain factors and considerations of actual method application scenarios are also based on large-scale engineering and infrastructure projects or software development projects. This situation has led to the current research being unable to adapt well to the cost estimation scenario requirements in consumer electronics R&D and testing projects. Based on the trend of increasing corporate R&D investment, it is necessary to study how to improve the efficiency and accuracy of cost estimation of new consumer electronics product R&D and testing projects. Summary of the invention

[0004] In view of the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for estimating project R&D costs using Monte Carlo simulation, propose to analyze the main cost influencing factors and corresponding probability distribution in R&D project cost estimation, use the Monte Carlo method to conduct quantitative analysis and simulation experiments on the main R&D cost uncertainties, and simulate the corresponding mean and confidence intervals of different project cost estimates under the combined effect of the main cost uncertainties.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] A method for estimating project R&D costs using Monte Carlo simulation, comprising the following steps:

[0007] Construct a corresponding mathematical model according to the research problem, and select the corresponding random variables as input variables; input partial observation values ​​or parameters of the corresponding random variables accordingly to determine the specific probability distribution shape of the random variables; take the test items whose costs are to be estimated as statistics, and define the statistics as the output variables of the mathematical model based on the mathematical model;

[0008] According to the random variables and statistics defined in the Monte Carlo simulation tool, the number of random simulations is set, and simulated random sampling and statistical fitting of statistical sample values ​​are performed to obtain the distribution formed by multiple statistical samples;

[0009] According to the results of Monte Carlo method fitting, the corresponding statistical mean, variance and confidence interval are obtained, and then the R&D cost is estimated.

[0010] Furthermore, the method for estimating project R&D costs is based on the law of large numbers, generates random variables through tens of thousands of computer random simulations, constructs a function for R&D cost estimation from these random variables, and obtains the expected value of the R&D cost by solving the expected value of the random variables in the computer simulation.

[0011] Furthermore, the random variable is a cost estimate value for each test item.

[0012] Furthermore, the probability distribution is Beta-PERT distribution.

[0013] Due to the adoption of the above technical solution, the present invention has the following advantages and positive effects compared with the prior art:

[0014] (1) The Monte Carlo simulation results were compared with those obtained by traditional cost estimation methods and the actual total equipment expenditure of product A's testing project. It was found that the results obtained by the Monte Carlo method were more accurate than those obtained by simple expert judgment and the WBS method. At the same time, the time required for cost estimation using Monte Carlo simulation was much less than that required by the WBS method.

[0015] (2) Monte Carlo simulation takes into account the uncertainty in the project cost estimation process and gives statistical prediction results through probability distribution. Therefore, it has higher accuracy and credibility than traditional cost estimation methods.

[0016] (3) Monte Carlo simulation can be based on the data obtained by analogy and simple expert judgment, and can be used with a variety of computer simulation software such as CrystalBall to simulate project cost estimation, which is more efficient than the traditional WBS method. It provides a new way to estimate costs at the project management practice level, with higher data processing efficiency and higher estimation accuracy. It can not only assist project managers in project budget approval, but also provide a scientific reference for subsequent project cost management work. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of the method framework for estimating project R&D costs using Monte Carlo simulation;

[0018] Figure 2 Flowchart of the method for estimating project R&D costs using Monte Carlo simulation. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and features of the present invention more clearly understood, the present invention is described in detail below in conjunction with the accompanying drawings and implementation examples. The specific embodiments described here are only used to explain the technical solution of the present invention and are not limited to the present invention.

[0020] Embodiment 1:

[0021] See also Figure 1 and Figure 2When estimating the R&D cost of a project, the first thing to do is to build a corresponding mathematical model for the problem being studied and select the corresponding random variables as input variables.

[0022] First of all, after clarifying the problem to be studied, it is necessary to construct the corresponding mathematical model and define the corresponding input variables according to the target value. It should be noted that the input variables here should be independent random variables. The construction of these models and the determination of random variables can be based on theoretical research foundations or from practical summaries. As long as the constructed model can meet the solution of the final problem and the defined input variables are also independent random variables, it will be fine. When using the Monte Carlo method to estimate the cost of R&D test projects, since the cost estimate is an uncertain value, it is particularly affected by various factors in the R&D process. Therefore, as long as we can determine which main factors in the R&D process will affect the cost of R&D test projects, and how these main influencing factors themselves change, we can roughly construct a mathematical model related to the cost of R&D test projects and the corresponding input variables.

[0023] Analyze and determine the probability distribution of each random variable. After defining the corresponding mathematical model and random variables, it is also necessary to determine the probability distribution of each random variable. Common probability distributions include uniform distribution, Weibull distribution, normal distribution, exponential distribution, and triangular distribution. Among them, triangular distribution and beta distribution are more commonly used in uncertainty estimation applications in engineering project management. In the commonly used Monte Carlo simulation tools, the general probability distribution of random variables is generally determined. As long as the partial observation values ​​or parameters of the corresponding random variables are input accordingly, the specific probability distribution shape of the random variables can be determined.

[0024] Based on the defined mathematical model, the statistic is defined as the model output variable. In the first step, the mathematical model for the problem under study has been determined. Here, the previously defined model statistics need to be input into the corresponding Monte Carlo simulation tool and defined as the predicted value. In this way, the mathematical model in the first step is truly established in the Monte Carlo simulation tool. When the Monte Carlo method is used to estimate the cost of the R&D test project, the overall R&D test project cost becomes the predicted value, that is, the model output.

[0025] Set the number of computer simulations and perform simulated random sampling and statistical fitting estimation. In this step, the number of computer random simulations is set based on the random variables and statistics previously defined in the Monte Carlo simulation tool. Generally speaking, the more Monte Carlo simulations are performed, the more accurate the simulation results will be. This is because, with other conditions remaining unchanged, as the number of simulations increases, the probability distribution of the statistic will gradually approach the actual probability distribution. Currently, most Monte Carlo simulation tools can achieve tens of thousands of simulations in a short period of time, but if the number of Monte Carlo simulations is set too high, it will increase the computational burden of the computer and reduce the efficiency of the simulation process. Therefore, you can choose an appropriate number of simulations based on the problem being studied, or you can choose a relatively suitable number of simulations by setting different levels of simulations to compare the statistical fitting results. After setting the number of simulations n, each random variable will be randomly sampled according to the set probability distribution to obtain the corresponding statistical sample value. After n rounds of such sampling, the computer will fit the distribution formed by the n statistical samples. The central limit theorem mentioned above shows that when n tends to infinity, the probability distribution of the n statistical samples will be infinitely close to the normal distribution. The general process of this fitting can also be expressed as follows.

[0026] The Monte Carlo method result report is output and analyzed and interpreted. Finally, the corresponding statistical mean, variance and confidence interval are obtained for the results fitted by the Monte Carlo method, the reliability of the judgment results is tested and combined with analysis such as sensitivity analysis to apply to actual work needs.

[0027] Embodiment 2:

[0028] Compare the Monte Carlo simulation results with the traditional cost estimation results, and compare the total test project equipment cost value obtained using the traditional cost estimation method with the cost valuation under Monte Carlo simulation. It can be seen that the total test project equipment cost value estimated by the expert judgment method is approximately: 4.620*10^6; the cost estimate value obtained using the WBS work breakdown structure method is approximately: 5.408*10^6; the cost estimate value obtained using Monte Carlo simulation is approximately: 6.027*10^6. Among them, the cost value estimated by the WBS method is relatively closer to the result of Monte Carlo simulation.

[0029] In terms of the actual total expenditure of the equipment for the product A test project, the actual total expenditure is approximately: 5.768*10^6 USD. Comparing the prediction results obtained by various methods with the actual total expenditure, it can be found that the difference between the cost estimate obtained by the expert judgment method and the actual total expenditure is about 1.148*10^6 USD, the difference between the cost estimated by the WBS method and the actual expenditure is 0.359*10^6 USD, and the difference between the cost valuation simulated by the Monte Carlo method and the actual expenditure is 0.259*10^6 USD. In general, the cost estimate obtained by the Monte Carlo simulation is relatively accurate, and the cost estimate by the WBS method is second in accuracy, but the cost valuation obtained by the simple expert judgment method is quite different from the actual expenditure.

[0030] Through communication with the corresponding project managers, we analyzed the reasons why the actual expenses of the expert judgment method are quite different. We learned that the expert judgment method is easily affected by the subjectivity of the evaluators, and because of the control of project costs, the project must be completed at the lowest cost, which leads to the generally low cost valuation obtained by simple expert judgment. At the same time, in simple expert judgment, some cost changes caused by other factors such as technology, products or markets are not fully considered, and some places where the reserved costs should be missed. Therefore, by comparing the results of the three methods, it can be seen that the cost valuation obtained under the Monte Carlo simulation based on the random variable Beta-PERT is more accurate.

[0031] Because the Monte Carlo simulation not only fits the overall distribution of the statistic based on the sample value, but also calculates the mean of the overall distribution, the mean of the sample, the variance of the overall distribution, and the variance of the sample, it can provide comparative information about the overall trend and dispersion of statistical predictions, and the Monte Carlo method obtains the overall distribution with probability, and the project manager can compare and select the valuation of the statistic based on the corresponding confidence interval. It is also flexible to use the Monte Carlo simulation to estimate the project cost.

[0032] What is more worth mentioning is that according to the investigation within the project manager team of S Company, it is generally known that it takes one day to use the simple expert judgment method for cost estimation, which includes consulting historical data and meeting with various core technical experts to estimate the approximate test equipment cost required for each technical module. The WBS method needs to be refined to the details of each part used in each test module, and it is also necessary to negotiate with experts of each technical module to agree on a rough test implementation plan, search for historical data, and inquire about the latest market price information. Therefore, it generally takes about one month to complete a complete test project equipment cost estimation using the WBS method. The Monte Carlo method does not involve the details of specific technical modules, and the minimum, maximum and most likely values ​​are all obtained based on the company's historical database and the evaluation of module technical experts. Therefore, the time spent under the Monte Carlo simulation method is about the same as that of the simple expert judgment method, which is also about one day. Then it can be seen that the third advantage of the Monte Carlo method is high efficiency.

[0033] It should be noted that, in the present invention, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0034] The above only expresses the preferred embodiments of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for ordinary technicians in this field, several modifications, improvements and substitutions can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.

Claims

1. A method for estimating project R&D costs using Monte Carlo simulation, characterized in that: The following steps are involved: Construct a corresponding mathematical model according to the research problem, and select the corresponding random variables as input variables; input partial observation values ​​or parameters of the corresponding random variables accordingly to determine the specific probability distribution shape of the random variables; take the test items whose costs are to be estimated as statistics, and define the statistics as the output variables of the mathematical model based on the mathematical model; According to the random variables and statistics defined in the Monte Carlo simulation tool, the number of random simulations is set, and simulated random sampling and statistical fitting of statistical sample values ​​are performed to obtain the distribution formed by multiple statistical samples; According to the results of Monte Carlo method fitting, the corresponding statistical mean, variance and confidence interval are obtained, and then the R&D cost is estimated.

2. The method for estimating project R&D costs using Monte Carlo simulation according to claim 1, characterized in that: The method for estimating project R&D costs is based on the law of large numbers. Random variables are generated through tens of thousands of computer random simulations. Functions for R&D cost estimation are constructed from these random variables. The expected value of the R&D cost is obtained by solving the expected value of the random variables in the computer simulation.

3. The method for estimating project R&D costs using Monte Carlo simulation according to claim 1, characterized in that: The random variable is the cost estimate for each test item.

4. The method for estimating project R&D costs using Monte Carlo simulation according to claim 1, characterized in that: The probability distribution is Beta-PERT distribution.

Images