Risk assessment method for project combination based on improved BPNN and DEA integration

Abstract

The invention relates to the technical field of project combination risk management, in particular to a project combination risk assessment method based on improved BPNN and DEA integration. The method comprises the following steps: identifying project combination risk factors, and constructing a PPR factor set from six dimensions based on a dependency relationship between projects; an IGA-BPNN model is constructed, and training and testing are carried out; on the basis of the trained IGA-BPNN model, PPR value changes before and after risk response measures are implemented are calculated to serve as risk response effects; and constructing a DEA-BCC model, and evaluating the efficiency of each risk coping strategy. According to the project combination risk assessment method based on improved BPNN and DEA integration provided by the invention, the interdependence relationship between projects is analyzed; constructing a PPR evaluation model by using the IGA-BPNN, and measuring and calculating PPR values before and after the implementation of the risk response measures; the risk coping cost and the PPR reduction effect serve as input and output parameters of a DEA model, and the efficiency of a risk coping strategy is evaluated; and finally, screening out an optimal risk coping strategy by comprehensively considering the effectiveness and efficiency of PPR response.

Description

Technical Field

[0001] This invention relates to the field of portfolio risk management technology, and in particular to a portfolio risk assessment method based on an improved integration of BPNN and DEA. Background Technology

[0002] With the increasing project-based and procedural nature of enterprises, project portfolios (PPs) are being used more and more widely in organizations to enhance flexibility and competitiveness. However, project portfolios operate in a dynamic environment and therefore often face various internal and external uncertainties. Uncontrollable environmental and organizational uncertainties can trigger project portfolio risk (PPR), which can not only hinder the smooth execution of the portfolio but ultimately threaten its overall success. Once such risks materialize, they can have positive or negative impacts on one or more strategic objectives of the portfolio. Given the significant impact of PPR on strategic objectives, organizations should proactively address these risks to mitigate potential threats and seize emerging opportunities. Addressing PPR requires identifying, assessing, and managing risk factors. An effective project portfolio response mechanism ensures that the portfolio drives strategic objectives while effectively mitigating the negative impacts of uncertainty and threats. By enabling organizations to identify, prioritize, and respond to risks in a timely and systematic manner, they can not only mitigate negative impacts but also transform risk challenges into opportunities, thereby improving overall performance and competitiveness. Therefore, an effective PPR response is not merely a support function but a strategic enabler, crucial for aligning project plans with organizational goals and for dynamically responding to market changes.

[0003] Given its importance, existing research employs various methods to plan portfolio risk response (PPR), such as probabilistic modeling methods like Bayesian networks and mathematical optimization methods like linear programming and integer programming. While these methods are helpful in developing risk response plans and providing decision-making insights for managers, they share a common limitation: most existing research methods focus on the independent response design of single risks, failing to adequately consider the correlation and complex nonlinear characteristics of risks within a portfolio (PP). Therefore, they cannot meet the systematic decision-making requirements of portfolio risk management (PPRM). Furthermore, existing research generally emphasizes the effectiveness of the selected risk response plan—that is, whether the strategic objectives are ultimately achieved—while neglecting the efficiency of these strategies, which may affect the reliability of their practical application. Efficiency here can be understood as the degree of impact per unit of input on the effectiveness of risk response actions; higher efficiency means more efficient utilization of organizational reserve resources. It is worth noting that neglecting efficiency may lead to inappropriate resource allocation, i.e., excessive input failing to produce a proportional risk reduction effect, thereby weakening the sustainability and applicability of the response strategy in real-world scenarios. Therefore, given that risk response strategies must simultaneously consider both efficiency and effectiveness, there is an urgent need to propose a more adaptive PPR response planning method to provide managers with scientific decision support.

[0004] The effectiveness of risk response measures can be assessed by the difference in PPR values ​​before and after implementation. In other words, a suitable PPR assessment model needs to be established to calculate the PPR values ​​before and after the risk response. In dynamic environments, the relationship between PPR and risk factors exhibits complex nonlinear characteristics. Backpropagation neural networks (BPNNs) are favored for their ability to fit nonlinear relationships. However, BPNNs are prone to getting trapped in local optima and converge slowly, resulting in poor assessment performance. These limitations in PPR effectiveness assessment need to be addressed. Summary of the Invention

[0005] Therefore, it is necessary to provide a risk assessment method for project portfolio based on an improved BPNN and DEA integration to address the aforementioned technical issues.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The risk assessment method for project portfolios based on the improved integration of BPNN and DEA involves the following steps: Step S1: Identify project portfolio risk factors and construct a PPR factor set based on inter-project dependencies from six dimensions: organizational operations, time management, cost management, quality management, human resource management, and stakeholder management. Step S2: Construct an improved genetic algorithm-optimized backpropagation neural network model, namely the IGA-BPNN model, to evaluate the portfolio risk value; Step S3: Train and test the IGA-BPNN model; Step S4: Based on the trained IGA-BPNN model, calculate the change in PPR value before and after the implementation of risk response measures, as the risk response effect; Step S5: Construct the DEA-BCC model to evaluate the efficiency of each risk response strategy.

[0007] As a preferred embodiment of the risk assessment method for project portfolios based on the improved BPNN and DEA integration provided by the present invention, step S2 includes the following steps: S2.1: Construct a three-layer BPNN structure with an input layer, a hidden layer, and an output layer. The number of nodes in the input layer is the same as the number of PPR factors, and the output layer is the PPR value. S2.2: According to Determine the initial range for the number of neurons in the hidden layer, where, For neurons in the input layer, For neurons in the output layer, For neurons in the hidden layer, 'a' is a constant. ; S2.3: An improved genetic algorithm is used to optimize the initial weights and thresholds of the BPNN; S2.4: Using root mean square error as the training performance indicator, determine the optimal number of hidden layer neurons through trial and error to complete the construction of the IGA-BPNN model.

[0008] As a preferred embodiment of the risk assessment method for project portfolio based on the improved BPNN and DEA integration provided by the present invention, the improved genetic algorithm in step S2.3 adopts a specific crossover and mutation operation strategy to enhance the global search capability and convergence speed of the BPNN.

[0009] As a preferred embodiment of the risk assessment method for project portfolio based on the improved BPNN and DEA integration provided by the present invention, the network structure of the IGA-BPNN model is 21-11-1, corresponding to 21 input PPR factors, 11 hidden layer neurons and 1 PPR output value.

[0010] As a preferred embodiment of the risk assessment method for project portfolios based on the improved BPNN and DEA integration provided by the present invention, step S3 includes the following steps: S3.1: Use fuzzy logic to obtain training data, including designing a language assessment scale for risk probability and impact, and converting it into trapezoidal fuzzy numbers; S3.2: Collect PPR factor assessment data through questionnaires. Calculate the fuzzy values ​​of each risk factor and convert them into numerical data using a defuzzification formula; S3.3: Divide the data into training and testing sets, and set the training parameters, including the maximum number of iterations, learning rate, target error, and activation function; S3.4: After completing model training, use the test set to verify the model accuracy, calculate MAPE and RMSE metrics, and evaluate the model's predictive ability.

[0011] As a preferred embodiment of the risk assessment method for project portfolios based on the improved BPNN and DEA integration provided by this invention, in step S3.1, the linguistic variables of risk probability and impact are mapped to trapezoidal fuzzy numbers, and then... Defuzzification is performed, where a, b, c, and d are constants in the trapezoidal fuzzy number.

[0012] As a preferred embodiment of the risk assessment method for project portfolios based on the improved BPNN and DEA integration provided by the present invention, step S5 includes the following steps: S5.1: Use different combinations of risk response measures as the decision-making unit, with the cost of each measure as the input variable and the reduction in PPR as the output variable; S5.2: Establish an input-oriented DEA-BCC model to calculate the overall efficiency, pure technical efficiency, and scale efficiency of each decision-making unit; S5.3: Select the optimal combination of risk response strategies based on efficiency scores.

[0013] It is clear without a doubt that the technical solution described above in this application can solve the technical problem that this application aims to address.

[0014] Meanwhile, through the above technical solutions, the present invention has at least the following beneficial effects: 1. The risk assessment method for project portfolios based on the improved BPNN and DEA integration provided by this invention identifies risk factors from six dimensions by analyzing the interdependencies between projects using the improved IGA-BPNN-DEA. Then, a PPR assessment model is constructed using IGA-BPNN to calculate the PPR value before and after the implementation of risk response measures. On this basis, the risk response cost and PPR reduction effect are used as input and output parameters of the DEA model to evaluate the efficiency of the risk response strategy. Finally, by comprehensively considering the effectiveness and efficiency of the PPR response, the optimal risk response strategy is selected.

[0015] 2. This invention accurately assesses portfolio risk through an improved IGA-BPNN model and combines it with a DEA model to quantify the efficiency of risk response strategies, achieving dual optimization of risk response plans in terms of effectiveness and cost efficiency. At the same time, the IGA-BPNN model achieves an average assessment accuracy of 96.6% in testing, which is significantly better than the traditional GA-BPNN model, with an error reduction of more than 63%, faster convergence, and more robust prediction.

[0016] 3. This invention supports dynamic adjustment of risk factors and countermeasures, and is applicable to project portfolio environments with multiple projects and multiple indicators. It enhances the organization's flexibility in risk response and the scientific nature of decision-making in complex environments. At the same time, it identifies the optimal combination of risk response strategies through the DEA-BCC model, avoids resource waste, improves the utilization efficiency of the organization's reserve resources, and enhances the overall risk management capability of the project portfolio. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the construction process of the PPR response plan of the present invention. Figure 2This is a flowchart of the IGA-BPNN model of the present invention; Figure 3 This is a schematic diagram of the RMSE curves of the training samples of this invention. Figure 4 This is a schematic diagram showing the distribution of the actual and expected output of the present invention; Figure 5 This is a schematic diagram illustrating the prediction results of different models in this invention; Figure 6 This is a schematic diagram comparing the efficiency results of the present invention; Figure 7 This is a schematic diagram of the input-output quadrant analysis of the present invention; Figure 8 This is a schematic diagram comparing the effectiveness of the risk response of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0021] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the embodiments of the present invention can be combined with each other.

[0022] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0023] Example 1: Reference Figures 1-5 A risk assessment method for project portfolios based on an improved integration of BPNN and DEA.

[0024] To address this, this invention enhances the global search capability of BPNN by improving the crossover and mutation operations of the Integral Genetic Algorithm (IGA), thus constructing a specialized PPR response analysis and evaluation system. Furthermore, selecting an appropriate risk response efficiency calculation method is crucial. This invention defines risk response efficiency as the intensity of the effect produced by risk response measures per unit cost, thereby effectively reflecting the relative efficiency of cost input and risk mitigation results. PPR essentially involves implementing multiple different risk response measures, each of which may incur costs measured in heterogeneous units (e.g., man-hours, material quantities, monetary expenditures). This multi-input characteristic, with costs quantified in various non-equivalent units, presents a significant challenge to integrating inputs into a single efficiency ratio. Data Envelopment Analysis (DEA), as a mainstream methodology, was developed precisely to address this unique challenge. DEA uses linear programming to evaluate the relative efficiency of comparable decision units (DMUs), directly calculating the ratio of multiple inputs to outputs. The core advantage of this method lies in its ability to accurately handle scenarios involving multiple inputs and outputs with different dimensions, without needing to convert them to a unified unit (such as monetary value). This inherent characteristic makes DEA particularly suitable for calculating PPR response efficiency—a scenario where multiple cost types constitute the inputs, and risk mitigation effect serves as the output metric. This is due to its applicability to multidimensional, heterogeneous unit efficiency problems and its wide range of applications across various fields.

[0025] 1. Proposed Method The process includes the following steps: First, based on the interdependencies between projects, PPR (Portfolio Risk) factors are identified from six dimensions; second, a PPR assessment model is constructed using the IGA-BPNN algorithm, and then trained and tested to calculate the PPR value; finally, the cost of risk response measures and the PPR response effect (PPR reduction) are used as input and output parameters of DEA (Data Envelopment Analysis) to evaluate the efficiency of risk response strategies. Figure 1 The construction steps of this method are shown.

[0026] The six dimensions are the dependencies between projects, from organizational operations, time management, cost management, quality management, human resource management, and stakeholder management; 1.1 Risk Factor Identification In the implementation of Project Portfolio Risk (PPR), in addition to the risks of individual projects, new risks arise due to the interdependencies between projects. Therefore, the complex inter-project dependencies need to be comprehensively considered when identifying project risk processes. It is worth noting that existing project risk process assessment criteria systematically identify assessment factors that reflect inter-project dependencies, laying the foundation for the assessment and analysis of project risk processes. These assessment criteria are also used as the basis for the project risk process assessment in this invention.

[0027] 1.2 Development of Risk Assessment Model 1.2.1 Model Construction Backpropagation Neural Networks (BPNNs) possess powerful nonlinear mapping capabilities, effectively fitting the nonlinear relationship between risk factors and portfolio risk (PPR), thereby achieving PPR assessment. Its core idea is to use risk factors and PPR as input and output parameters, and establish a nonlinear relationship model between them through data training. Therefore, this invention uses BPNNs to construct a PPR assessment model. The model construction process is briefly described below, with a detailed flowchart shown below. Figure 2 As shown.

[0028] (1). Constructing different BPNN models. This model adopts a three-layer network architecture, with the number of neurons in the input layer matching the number of PPR factors, and the output layer corresponding to PPR(Fn). Since there is currently a lack of standardized and mature methods for determining the number of neurons in the hidden layer, a trial-and-error method was adopted. This method gradually determines the optimal network structure within a specific range of the number of hidden neurons through continuous training. The initial range of the number of hidden layer neurons was determined empirically based on formula (1).

[0029] (1) in, , These are neurons in the input layer, output layer, and hidden layer, respectively, where 'a' is a constant. .

[0030] (2). Optimizing the BPNN model using IGA. After determining the network structure, IGA is used to establish the initial weights and thresholds of the BPNN for optimization. Subsequently, during training, the weights and thresholds of all enhanced BPNN models are continuously adjusted to learn the complex relationship between PPR and its influencing factors.

[0031] (3) Determine the optimal IGA-BPNN model. After training, to determine the optimal number of hidden neurons, the root mean square error (RMSE) is used as the evaluation index of learning performance, as shown in formula (2). Finally, the model with the best accuracy is selected for testing.

[0032] (2) in, and It is a sample The expected output and the predicted output.

[0033] 1.2.2 Model Training and Testing The effectiveness of the proposed model is validated through training and testing experiments, and a mature and usable PPR evaluation model is developed. Fuzzy logic should be used beforehand to obtain the necessary data, as follows: First, an assessment scale was designed based on the linguistic descriptions of risk probability and impact. Risk probability was divided into five levels: "extremely low", "low", "moderate", "high", and "extremely high", corresponding to trapezoidal fuzzy numbers (0.0, 0.1, 0.2, 0.3), (0.1, 0.2, 0.3, 0.4), (0.3, 0.4, 0.5, 0.6), (0.5, 0.6, 0.7, 0.8), and (0.7, 0.8, 0.9, 1.0), respectively. Risk impact was divided into five levels: "negligible", "minor", "moderate", "serious", and "critical", corresponding to trapezoidal fuzzy numbers (0.0, 0.1, 0.2, 0.3), (0.1, 0.2, 0.3, 0.4), (0.3, 0.4, 0.5, 0.6), (0.5, 0.6, 0.7, 0.8), and (0.7, 0.8, 0.9, 1.0), respectively.

[0034] Secondly, a questionnaire survey was conducted to collect their fuzzy language assessments of the probability and impact of each PPR factor. A total of 220 questionnaires were distributed, and 195 valid questionnaires were returned. After removing invalid questionnaires with missing information or logical contradictions, 180 valid questionnaires were finally obtained, corresponding to 180 sets of project portfolio risk PPR factor sample data. Finally, the fuzzy values ​​of each risk factor were calculated using formula (3), and fuzzification was performed using formula (4) to transform the fuzzy language information into quantitative PPR factor data.

[0035] (3) (4) in, express PPR factor, The PPR factor value is a fuzzy number, and the risk probability and risk impact are represented by trapezoidal fuzzy numbers respectively. and , for The values ​​of the PPR factors, where a, b, c, and d are constants in the trapezoidal fuzzy number.

[0036] It is particularly important to note that this invention randomly divides the data into 150 training samples and 30 test samples. The maximum number of iterations is set to 10,000, and the learning rate is (…). The target training error (RMSE) is 0.006, with a minimum training error (0.1). For activation functions, the hidden layers use the ReLU function, while the output layer uses a linear function. Regarding the model network structure, both the input and output contain 21 PPR factors and their corresponding PPR values. (The last sentence appears to be incomplete and requires further context.) =21 and Substituting 1 into formula (1), the initial range of the number of hidden neurons is calculated. Then, formula (2) is used to determine the optimal network structure. This model has 11 neurons in its hidden layer, resulting in the lowest RMSE value and thus the highest accuracy among all candidate schemes. Therefore, the network structure of this model is determined to be 21-11-1. Specific parameters are detailed in Table 1.

[0037] Table 1: Initial parameters of the model

[0038] During the training of the IGA-BPNN model, the root mean square error (RMSE) continuously decreases by dynamically adjusting the weights and thresholds. The system records the RMSE value every ten iterations. Figure 3 As shown, when the maximum number of iterations is reached, the model's RMSE approaches the target error value, indicating that the model exhibits good learning performance. This means that the model can effectively learn and fit the nonlinear relationship between risk factors and risk, thereby accurately evaluating the PPR index.

[0039] To assess the model's accuracy, the mean absolute percentage error (MAPE), defined by formula (5), is used for measurement. Figure 4 As shown, the actual output of this model is in good agreement with the expected value. It is noteworthy that the MAPE value of this model is only 0.034. The calculated average assessment accuracy is 96.6% ((1-MAPE)%), indicating that the model can effectively capture the complex relationship between PPR and its influencing factors. Therefore, this model can be used as a risk response effectiveness assessment tool to measure the change in PPR before and after the implementation of risk response measures.

[0040] (5) in, and It is a test sample The actual output and the expected output.

[0041] Figure 5The prediction results of the basic GA-BPNN model are presented. Data shows that the actual output of the IGA-BPNN model has a higher degree of agreement with the expected values, with MAE, MAPE, RMSE, and MSE values ​​of 0.0064, 0.034, 0.0098, and 0.00009557, respectively. In comparison, the corresponding values ​​for the GA-BPNN model are 0.0174, 0.1079, 0.0287, and 0.0008209. Compared to the GA-BPNN model, the IGA-BPNN model achieves significant improvements of 63.08%, 68.49%, 65.88%, and 88.36% in MAE, MAPE, RMSE, and MSE, respectively. This fully demonstrates the advantage of the IGA-BPNN model in prediction accuracy and highlights its efficiency and superiority in practical applications.

[0042] 1.3 Selection of Risk Response Strategies Effectively assessing the efficiency of Risk Reduction and Profitability (PPR) response measures provides crucial information for managers to formulate reasonable and optimized risk response plans. Risk response efficiency can be understood as the ratio of the effectiveness of a risk response to its cost. However, risk response typically involves multiple measures with varying cost units, making direct efficiency calculation difficult. Data Envelopment Analysis (DEA) provides a robust solution. This method assesses the relative efficiency of multiple decision units (DMUs) by converting multiple inputs and outputs into efficiency ratios, without requiring a unified currency unit conversion. Based on this, this invention uses DEA to assess the efficiency of PPR response strategies. Specifically, given that the input of PPR response measures is not necessarily proportional to the risk mitigation effect, the Variable Returns to Scale (VRS) assumption is more appropriate because it can flexibly handle the impact of scale on efficiency. Therefore, the DEA-BCC model is chosen because it introduces convexity constraints to relax the constant returns to scale assumption of the DEA-CCR model, making the efficiency assessment more consistent with the realistic assumptions of VRS, acknowledging that response strategies may not necessarily lead to a proportional increase in risk mitigation effect.

[0043] Besides estimating the overall efficiency score, the main advantage of the DEA-BCC model lies in its ability to decompose overall efficiency (OE) into pure technical efficiency (TE) and scale efficiency (SE), thus facilitating the precise identification of the root causes of inefficiency. Specifically, OE is derived from the DEA-CCR model assuming constant returns to scale (CRS), while TE is derived from the DEA-BCC model assuming constant returns to scale (VRS). SE is calculated as the ratio of OE to TE, reflecting the impact of scale on efficiency. In this decomposition, TE represents management and operational capabilities, while SE reflects the scale effect. To maintain consistency with the software output, the term "TE" will be used consistently throughout the paper to represent pure technical efficiency. To concretize these concepts, an input-oriented body-centered cubic model is constructed as shown in Equations 6-10.

[0044] (6) (7) (8) (9) (10) in, It is overall efficiency. It is a decision-making unit The One input, It is a decision-making unit Input. It is the decision-making unit Output, Indicates the decision-making unit. It is the coefficient of the decision-making unit.

[0045] This invention uses different combinations of risk response measures as decision units (DMUs) in a DEA model. The cost of each specific risk response measure in each decision unit is used as an input parameter of the DEA model. By calculating the reduction in the PPR (Profitability Per Target) before and after the implementation of the risk response measures, this risk response effect is used as the output result of the DEA model. The specific calculation steps are as follows: Step 1: Input the risk factor data into the developed PPR assessment model to obtain the PPR value ( ).

[0046] Step 2: Implement risk response measures for risk factors.

[0047] Step 3: Update the values ​​of the risk factors.

[0048] Step 4: Input the updated risk factor values ​​into the assessment model to obtain the PPR value. ).

[0049] Step 5: Calculate the risk response effect (E= ).

[0050] The DEA-BCC model settings in this invention are shown in Table 2.

[0051] Table 2: DEA-BCC Model Settings

[0052] in, Indicates the first A combination of risk response measures, It is the first Risk response measures represent The cost, and That is Risk response effectiveness (PPR reduction).

[0053] Example 2: refer to Figures 6-8 Based on the above embodiment one, an example is disclosed to verify the effectiveness of the risk response planning method proposed in this invention, including two parts: problem description and result analysis.

[0054] 1. Problem Description First, 180 sets of PPR factors and their corresponding PPR values ​​were selected as raw data. It is worth noting that these risk factors are completely consistent with the PPR factors identified in this study. Each PPR factor value was calculated by multiplying the risk probability by the degree of impact. To verify the effectiveness of the proposed method, one set was randomly selected from all 180 sets of PPR factor data for verification; the specific data is shown in Table 3. Second, through systematic analysis of literature related to PPR and risk response, and combined with the characteristics of the identified PPR factors, the corresponding response measures for each risk factor were determined (see Table 4 for details). , , Based on this, the mitigation effect and cost-effectiveness of each risk response measure need to be evaluated. Considering that the intensity of some risk response measures can be adjusted with the increase of investment, this invention divides risk response measures into two categories: non-adjustable intensity and adjustable intensity (see Tables 5 and 6, respectively). Subsequently, by randomly combining these two types of measures, 27 risk response measure combination schemes are constructed as the decision-making units of the DEA model. The model uses the cost of each risk response measure as the input variable and the PPR reduction calculated by the method in Example 1 as the corresponding output variable, and the specific results are shown in Table 7. Subsequently, the efficiency of each possible risk response measure combination is evaluated according to the procedure proposed in Example 1.

[0055] Table 3: Risk Factor Data

[0056] Table 4: Risk Response Measures

[0057] Table 5: Costs and Mitigation Effects of Response Measures to Risks of Unadjustable Intensity

[0058] Table 6: Costs and Mitigation Effects of Adjustable-Intensity Risk Response Measures

[0059] Table 7: Inputs and Outputs of the DEA Model

[0060] 1.2 Results and Analysis In this phase, SPSSPRO software was used for DEA analysis, and the efficiency scores for different risk response action combinations were discussed. To clarify the methodology of efficiency decomposition presented in Table 8, this invention provides a brief explanation. The decomposition of OE into TE and SE is not accomplished step-by-step using the body-centered cubic model, but rather through a comparison between the body-centered cubic model and the CCR model.

[0061] The DEA-BCC model, based on the Virtual Returns to Scale (VRS) assumption, calculates the total efficiency (TE) of each decision unit (DMU). This model effectively distinguishes between managerial efficiency and operational efficiency by eliminating the effects of scale effects. Meanwhile, the DEA-CCR model, based on the Actual Returns to Scale (CRS) assumption, calculates the total efficiency (OE) of the same DMU. Total efficiency integrates managerial efficiency and scale effects, while scale efficiency (SE) is determined by... The ratio is used to derive the result. This decomposition method can accurately pinpoint the root cause of inefficiency: if... <1 indicates that inefficiency stems from poor management or outdated technology; if but This is entirely due to inappropriate scale selection. When total efficiency reaches 1, it indicates that the input-output structure of the decision-making unit is reasonable, and its relative efficiency is optimal. If total efficiency is below 1, it means that the input-output structure is flawed, the relative efficiency is not optimal, and it may be accompanied by varying degrees of input redundancy and output insufficiency. Therefore, the decision-making unit... , , , , , , , , , , and The optimal effect value (OE) of all the units was 1, indicating that the corresponding risk control strategies were effective and worth prioritizing. The OE values ​​of other decision units were all less than 1, indicating that their strategies were relatively weak. SPSSPRO software automatically performed dual-model comparison and calculation, and finally generated the decomposition results shown in Table 8.

[0062] More importantly, the decomposition analysis of inefficient decision-making units (OE<1) provides key insights for precise improvement. However, this decomposition process reveals a truly remarkable pattern: all inefficient decision-making units (OE<1)

[0063] The total effect value is always 1. The inefficiency of all suboptimal decision-making modules stems entirely from scale, not management style. Specifically, although each combination of risk response measures is executed skillfully ( However, the operating scale of each combination is slightly below the optimal level. This ultimately leads to an overall efficiency (OE) below 1. Therefore, the optimization strategy for these scenarios is not to change the implementation of the countermeasures, but to achieve this by fine-tuning the scale of operations—because the technical management level is already perfect. The minimum deviation of system efficiency (SE) from 1 is between 0.998 and 0.999, indicating that only fine-tuning the scale of inputs is needed to achieve full efficiency. For example, a mere 0.1%–0.2% adjustment in resource allocation can propel these decision-making units to the forefront of efficiency. This finding has significant implications for project risk managers: overall, the combination of countermeasures is well-managed, and the focus of optimization should be on precisely calibrating the scale and scope of the measures, rather than completely overhauling the execution process.

[0064] Table 8: Efficiency Analysis

[0065] This invention evaluates the efficiency of each risk response scenario (DMU) using the DEA-BCC model, focusing on the process of decomposing the overall efficiency (OE) into pure technical efficiency (TE) and scale efficiency (SE). Figure 6 This decomposition result is visually illustrated. As shown in Table 8 and the accompanying graph, the TE value for all 27 DMUs remained consistently at its maximum value of 1.000. This general trend reveals a key conclusion: all risk response measures were implemented in a technically proficient manner, and there was no waste of resources due to mismanagement or process defects. In contrast, the SE metric showed significant fluctuations across the DMUs. Figure 6 The perfect alignment of the OE and SE curves indicates that this fluctuation is the sole factor determining the OE score. A suboptimal SE score suggests that inefficiency stems solely from inappropriate scale selection—some DMUs are too large, leading to diseconomies of scale (e.g., resource redundancy or bureaucratic inefficiency), while others are too small to effectively leverage economies of scale. When PTE remains constant, the convergence of the OE and SE curves strongly demonstrates that the challenge of integrating technical and scale efficiency lies not in synergies, but in parameter calibration. The "fluctuation" in the OE curve does not originate from management differences, but is directly and uniquely caused by the misalignment between the scale chosen for the response and its optimal production scale.

[0066] To supplement the analytical perspective of relative efficiency scoring and to intuitively present the absolute input-output levels of each strategy, the following approach was adopted. Figure 7The diagram illustrates the input-output quadrant analysis method. This figure spatially locates all decision units (DMUs) using a two-dimensional coordinate system, clearly demonstrating their scale operation characteristics. Data shows that decision units are mainly concentrated in the first quadrant (high input, high output) and the second quadrant (low input, high output). This spatial distribution characteristic intuitively echoes the DEA analysis results: the prevalent TE value of 1.000 can be visually verified through the blank areas in the inefficient quadrants (third and fourth quadrants); and the differences in scale efficiency (SE) values ​​are explained by their position relative to the optimal scale frontier. Specifically, decision units closer to the coordinate axis (e.g., ) embody optimal scale operation (SE=1). Large-scale decision-making units located in the first quadrant may be facing diseconomies of scale (SE<1).

[0067] To date, while this invention has identified various risk response strategies, it has not yet provided managers with precise decision support. Determining the optimal combination of PPR response strategies hinges on in-depth analysis of effective decision units (DMUs) to identify the best combination of risk response measures. Therefore, this invention extracts the risk response effectiveness (PPR reduction) of effective DMUs from Table 7, as shown in Table 9. The calculated risk response effectiveness values ​​based on these data range from 0.427 to 0.435, with risk reduction fluctuating between 71.2% and 72.5%. This visualization demonstrates that these indicators provide important reference for evaluating the risk management performance of various DMUs. Data shows that the most efficient units often exhibit the most effective risk response strategies, representing exemplary risk management solutions. Real-world case studies validate the effectiveness of the proposed method, proving its ability to achieve a balance between efficiency and effectiveness. This provides strong support for managers to formulate scientific risk response decisions and optimize PPR management and response mechanisms.

[0068] Table 9: Response effects of different DMUs

[0069] 2. Summary Inspired by current risk response research and the application of DEA and BPNN, this invention proposes an innovative PPR response planning method. First, PPR elements are identified, and a PPR evaluation model is established using IGA-BPNN, followed by training and testing. Then, a DEA model is used to evaluate the efficiency of the risk response strategy, ultimately validating the effectiveness of the proposed method.

[0070] Unlike previous studies that focused solely on the effectiveness of risk response strategies, this invention takes a Portfolio (PP) perspective, simultaneously considering the efficiency and effectiveness of Portfolio Risk Management (PPR) strategies in developing risk response plans. This innovative research not only enriches the research findings on PPR response mechanisms but also provides practical references for other PP-related decision-making and planning issues. For example, simultaneously evaluating the effectiveness and efficiency of PPRM (Portfolio Risk Management) strategies may provide managers with more practical guidance for improving the quality of risk management. Furthermore, this research expands the knowledge boundaries of the risk management field, injecting new research momentum into subsequent PPRM research.

[0071] Secondly, this invention provides a new extension to existing PPR response planning methods. The PPR assessment model constructed using IGA-BPNN incorporates risk reduction as the output of the DEA model, achieving an effective integration of BPNN and DEA. This innovative combination not only promotes the interdisciplinary integration of operations research and artificial intelligence but also provides new ideas for integrating machine learning and operations research methods. Furthermore, the model proposed in this study demonstrates the potential for deep integration of risk assessment and response strategies, helping managers to effectively assess and manage PPR from a holistic perspective.

[0072] Furthermore, the methodology proposed in this invention helps managers make informed decisions and better address risk retaliatory reactions (PPRs). Through this methodology, managers can formulate and implement appropriate PPR response strategies based on their own risk appetite. This methodology considers both the efficiency and effectiveness of risk response strategies. This dual focus enhances the overall level of organizational risk management, enabling it to effectively respond to changes in the external environment, seize potential opportunities, and ultimately ensure the achievement of strategic goals.

[0073] Finally, the method proposed in this invention can significantly improve the flexibility and efficiency of organizations in developing risk response plans. For a specific project portfolio (PP), managers can add or remove any project parameter response factors and corresponding measures based on project parameter characteristics (discord), and implement a "dynamic adjustment" process for the developed methods. By using a risk assessment model based on IGA-BPNN, managers can monitor the project parameter response level in real time, thereby flexibly selecting appropriate response strategies. This mechanism provides greater flexibility in solution design.

[0074] 3. Conclusion This invention integrates the IGA-BPNN and DEA models and validates their effectiveness through numerical case studies. By overcoming the limitations of theoretical risk assessment, this invention provides a data-driven framework for PPR planning, filling a gap in existing research. The core findings of this invention demonstrate that all response strategies are executed with perfect technical proficiency (TE=1), and effectiveness optimization (OE) is entirely dominated by scale effects (SE), marking a paradigm shift. Research shows that the key to optimization lies not in radical reforms of the management structure, but in precise scale calibration—this innovative insight lays a new foundation for PPR academic research. For practitioners, this means a powerful and practical decision-making tool: managers can not only select effective response strategies but also precisely optimize response scale, significantly improving decision quality in uncertain environments while optimizing the monitoring and control of PPR actions. Furthermore, by integrating the methodology of DEA efficiency assessment with IGA-BPNN predictive modeling, a robust DEA-IGA-BPNN model is constructed. The model achieved a test accuracy of 98.6%, surpassing the traditional GA-BPNN in both error reduction and convergence speed, providing a superior, empirically validated method for planning and predicting risk response strategies.

[0075] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A risk assessment method for project portfolios based on an improved integration of BPNN and DEA, characterized in that, The steps are as follows: Step S1: Identify project portfolio risk factors and construct a PPR factor set based on inter-project dependencies from six dimensions: organizational operations, time management, cost management, quality management, human resource management, and stakeholder management. Step S2: Construct an improved genetic algorithm-optimized backpropagation neural network model, namely the IGA-BPNN model, to evaluate the portfolio risk value; Step S3: Train and test the IGA-BPNN model; Step S4: Based on the trained IGA-BPNN model, calculate the change in PPR value before and after the implementation of risk response measures, as the risk response effect; Step S5: Construct the DEA-BCC model to evaluate the efficiency of each risk response strategy.

2. The risk assessment method for project portfolios based on the improved BPNN and DEA integration as described in claim 1, characterized in that, In step S2, the steps are as follows: S2.1: Construct a three-layer BPNN structure with an input layer, a hidden layer, and an output layer. The number of nodes in the input layer is the same as the number of PPR factors, and the output layer is the PPR value. S2.2: According to Determine the initial range for the number of neurons in the hidden layer, where, For neurons in the input layer, For neurons in the output layer, For neurons in the hidden layer, 'a' is a constant. ; S2.3: An improved genetic algorithm is used to optimize the initial weights and thresholds of the BPNN; S2.4: Using root mean square error as the training performance indicator, determine the optimal number of hidden layer neurons through trial and error to complete the construction of the IGA-BPNN model.

3. The risk assessment method for project portfolios based on the improved BPNN and DEA integration as described in claim 2, characterized in that, In step S2.3, the improved genetic algorithm adopts a specific crossover and mutation operation strategy to enhance the global search capability and convergence speed of BPNN.

4. The risk assessment method for project portfolios based on the improved BPNN and DEA integration as described in claim 1, characterized in that, The network structure of the IGA-BPNN model is 21-11-1, corresponding to 21 input PPR factors, 11 hidden layer neurons, and 1 PPR output value.

5. The risk assessment method for project portfolios based on the improved BPNN and DEA integration as described in claim 1, characterized in that, In step S3, the steps are as follows: S3.1: Use fuzzy logic to obtain training data, including designing a language assessment scale for risk probability and impact, and converting it into trapezoidal fuzzy numbers; S3.2: Collect PPR factor assessment data through questionnaires. Calculate the fuzzy values ​​of each risk factor and convert them into numerical data using a defuzzification formula; S3.3: Divide the data into training and testing sets, and set the training parameters, including the maximum number of iterations, learning rate, target error, and activation function; S3.4: After completing model training, use the test set to verify the model accuracy, calculate MAPE and RMSE metrics, and evaluate the model's predictive ability.

6. The risk assessment method for project portfolios based on the improved BPNN and DEA integration as described in claim 5, characterized in that, In step S3.1, the linguistic variables representing risk probability and impact are mapped to trapezoidal fuzzy numbers, and then... Defuzzification is performed, where a, b, c, and d are constants in the trapezoidal fuzzy number.

7. The risk assessment method for project portfolios based on the improved BPNN and DEA integration as described in claim 1, characterized in that, In step S5, the steps are as follows: S5.1: Use different combinations of risk response measures as the decision-making unit, with the cost of each measure as the input variable and the reduction in PPR as the output variable; S5.2: Establish an input-oriented DEA-BCC model to calculate the overall efficiency, pure technical efficiency, and scale efficiency of each decision-making unit; S5.3: Select the optimal combination of risk response strategies based on efficiency scores.

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