Fuzzy Assessment of Management Consulting Projects: Model Validation and Case Studies

Abstract

Management consulting (MC) has been heavily involved in emerging business opportunities in mainland China. However, there are no well-known local MC project management models to help evaluate whether an MC project can be successful or not. This paper reports a model for the self-assessment of management consulting projects, which has been validated by 15 experts and 13 cases. The new model, with seven factors that are critical to the success of MC projects, was developed from a literature review. The model was then verified by developing a questionnaire that was sent to 15 experts and using Dempster–Shafer theory to obtain the weight of each part of the model. The model was applied to 13 real cases to verify its effectiveness in evaluating an MC project. This new MC model can help consulting teams to conduct assessments in the early and middle stages, and evaluate in the late stage, of consulting projects, and also can help teams improve the probability of project success and client satisfaction. It can be used by consultants, client companies, or both.

1. Introduction

In recent decades, virtually every enterprise has been engaged in the process of project development or system reform. The enterprise normally invites outside consultants when their internal experience and ability are insufficient. This has made management consulting (MC) increasingly popular as a management practice applicable to many industries and has prompted the need to develop better standards, technologies, and practices for MC [1]. However, managing an MC project is a complex endeavor. Finding a comprehensive and applicable process model that can help MC projects succeed has been a critical and challenging task in the study of MC projects. Several MC project models have been proposed, but a truly comprehensive one remains elusive.

The above issue is even more challenging for Hong Kong MC teams in exploring the mainland market of China. Backed by the mainland market, the MC industry in Hong Kong has a huge potential market. The central government of China and Hong Kong signed the Closer Economic Partnership Arrangement (CEPA) for the first time in 2003. The purpose of the CEPA is to promote the industrial restructuring and upgrading of the two sides to achieve mutual benefit and complementarity. Since then, a supplement to the CEPA has been signed each year with the aim of continuously expanding market liberalization measures to further facilitate Hong Kong service providers. In 2014, the two sides signed a sub-agreement under the CEPA, namely the agreement on fundamentally liberalizing the mainland’s trade in services in Guangdong and Hong Kong (the Guangdong Agreement). In December 2015, the two sides signed the trade-in services agreement, delineating the liberalization measures that the mainland would undertake to open its doors to service providers and professionals from Hong Kong from June 2016. Furthermore, this agreement expanded the geographic scope of service trade liberalization to encompass the entirety of the mainland. The Chinese mainland has provided Hong Kong MC enterprises with a vast market place and unlimited growth potential. Hong Kong companies are the largest outside investors in mainland China, and mainland companies are significant investors in the Hong Kong economy.

MC is expected to provide a systematic approach to cover all phases of a management project and ensure that each phase is carefully planned, monitored, and measured [2]. While many researchers have solved the problems related to project management in large companies [3,4], more research should be conducted on project management in small and medium-sized enterprises (SMEs) [5].

At present, most of the international MC ideas have been widely accepted in the global scope. It is not difficult for entrepreneurs to accept advanced ideas, but helping them implement these theories in the local market remains a challenge. For the management consulting industry in mainland China, after 30 years of exploration, the dual transformation of the consulting subject and the consulting content is realized [6]. With the rapid development of local management consulting institutions in China, there is still a large-scale gap with international consulting companies, such as a lack of profitability and core competitiveness. Compared to mature international MC companies, Hong Kong’s local consultants fully understand the local market environment, but in the face of strong competitors, there is not a good selection of MC companies in Hong Kong, and the use of the MC method lacks many innovative and targeted MC models.

This paper aims to report a proposal and validation of a more suitable model for Hong Kong MC enterprises, enabling them to conduct management consulting effectively in Hong Kong and/or mainland China. From the literature review, we identified seven factors that are critical to the success of MC projects. The model was then evaluated by 15 experts, and the Dempster–Shafer theory was used to obtain the weight of each factor. Thirteen case studies are reported to verify the application. Section 2 provides the development of the new model from the literature review. The model is then evaluated using the Dempster–Shafer theory in Section 3 and Section 4 to obtain the weight of each part of the model, and in Section 5 is applied to 13 real cases to verify its effectiveness.

2. Literature Review and Model Development

2.1. Concepts and Terminologies

As a form of modern consulting, MC in contemporary society has rapidly developed and played a huge role. It is often referred to as a “brain industry” that helps managers identify and analyze problems, advise, and get out of trouble. However, there is still no unified definition of MC.

The Association of MC Engineers defines MC by stating: “a person with theoretical knowledge or experience in MC exposes problems in The Management of the enterprise and proposes practical solutions to help implement them”. As defined by The International Council of Management Consulting Institutes, “an MC consultant is an individual responsible for Management who provides independent Consulting advice and guidance to clients”. The International Labor Committee defines MC as “helping to solve management and business problems, to identify new opportunities, and to use it for the purpose of organizing administrative agencies to help continue and expand learning opportunities”.

According to [7], MC is “dynamically facing new challenges because the management tools, methods and methods that make up the field are applied in different fields, for different purposes and in different cultures”.

To sum up, MC refers to the management behavior in which natural persons or legal persons with professional knowledge and experience or training accept commissions, take operation and management as their primary business, and use management tools to provide knowledge, functions, planning, and other high-intelligence services in various fields for different purposes.

2.2. Previous Models for Consultation Management

While undeniably crucial, MC is fraught with challenges. Planning and implementing a successful MC project is not easy. It requires a criterion for success or a complete, comprehensive, and applicable process model. The ASQ team spent approximately 35 years and engaged numerous teams from over 30 countries, to create the International Team Excellence Award (ITEA) Criteria, and provide a framework for assessing team performance and project processes. On this basis, we searched the literature on MC and project management (PM) and reviewed the influencing factors and models related to MC.

From the literature, seven different MC models and seven associated factors were identified (see

Table 1. Factors in previous MC models.

Factors Affecting MC	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7
1. Project background and purpose	✓	✓	✓	✓	✓	✓	✓
2. Project framework	✓	✓	✓	✓	✓		✓
3. Project stakeholders and the project team	✓			✓		✓
4. Project overview	✓		✓	✓	✓	✓	✓
5. Project walkthrough	✓	✓	✓	✓	✓	✓
6. Project tracking and control		✓	✓	✓		✓	✓
7. Project presentation	✓				✓

✓: indicates one model includes the factor.

below).

In the following, the seven models will be elaborated from the following aspects: which factors will be included, to which fields and industries do they apply, whether to conduct quantitative analysis, whether there is empirical analysis or just a conceptual model, whether there is a flow chart, advantages and disadvantages, etc.

Model 1—The ASQ organization’s ITEA model [8] provides a six-section framework to help organizations improve the results of their projects, providing guidance and repeatable benchmarks for projects of different organization sizes, industry types, or project types. This model starts from the identification and selection of the project and ends with a project presentation, which relatively clearly and fully presents the process of all parts of the project. Every part is responsible for the detailed and rich further subdivided activities and description. For each sub-part, this model provides scoring criteria of differing maturity. The scores range from 0 to 4, with each layer having to perform better based on covering the previous layer. At the same time, the model emphasizes the relevance of each phase, its importance to the long-term planning of an MC project, and the relevant planning of the organization to support the project. However, the model does not provide a process or sequence, leaving the user with many considerations but no idea where to start or what to do at a certain point in time. This model is only suitable for evaluating completed projects, but it cannot be used as a starting point for a project.

Model 2—Reference [9] provided four main phases of a project decision analysis process (PDAP): decision framing, modelling the alternatives, quantitative analysis, and actual performance tracking. The four phases run in sequence, while part of the actual performance trace is continuously fed back to the remaining three. These four stages correspond to the project framework, project walkthrough, project background and purpose, and project tracking and control. The PDAP model provides process guidance that requires both qualitative and quantitative analysis, and in which the quantitative analysis method can be adjusted according to different requirements. This model takes more account of process quality and relationships with the system organization and is effective and practical: it is practical because it is easy to integrate with existing processes; its effectiveness is reflected in the scalability and flexibility of the model to provide effective feedback and adaptability. At the same time, this model also considers the correlation degree and strength between its effectiveness and organizational effectiveness under the framework of competitive value. However, the model is implemented on the premise that there must be high-quality useful information, sufficient and accurate information about competitors, that the project leader or decision maker needs to be trained, and that the appropriate, but not all, project processes can be integrated.

Model 3—Reference [3] discussed how to establish a project organization in a telecommunications environment and developed a standardized project management process, which was divided into four steps: project initiation, project definition, project implementation, and project completion. These four stages correspond to the project background and purpose, the project framework, project overview, and project walkthrough. At each stage, validation was repeated until all conditions were met. The main purpose of this model is to provide a common operational framework and major control mechanisms for all project managers. The advantage is that the framework is relatively flexible and can accommodate and monitor the situation of each part while maintaining necessary system control. Second, the model facilitates stakeholder participation in each phase of the project lifecycle. In addition, the model’s versatility makes it easy for new employees to start. However, this model is only a qualitative analysis and lacks a quantitative data analysis. In addition, the absence of risk anticipation and response procedures makes it difficult for project personnel or organizations to respond promptly to the changes in project requirements. At the same time, this model also lacks benchmarks as it is confined to individual project management and is not suitable for comparing or measuring different project management processes.

Model 4—Reference [5] identified six factors of successful project management with the greatest potential benefits for small and medium-sized businesses (SMEs). They are clear objectives, top management support, resource allocation, planning, monitoring and control, client consulting and risk management. The six success factors correspond to the project background and purpose, project framework, project stakeholders and project team, project overview, project walkthrough, project tracking and control. The six factors are based on a survey conducted asking managers of small and medium-sized enterprises their opinions on the six factors in their enterprises on a scale of 1 to 5. Each of the more than 200 small and medium-sized businesses in the survey had fewer than 250 employees, and they covered a wide range of sectors, including health care, telecommunications, electronics and engineering, and were mostly in high-tech industries. Although high-tech companies contribute a lot to society in terms of wealth creation and employment, these technical entrepreneurs have relatively poor business management skills, so this model is a good way to help these high-tech SMEs. The model analyzed the questionnaire results using SPSS 27 software and ranked the importance of six influencing factors. Among these factors, clear objectives and support from senior management were identified as the most important success factors. The significance of this model lies in the in-depth study of its project management model based on the characteristics of small and medium-sized enterprises, but the scope of use is also limited to small and medium-sized enterprises, therefore, there is no way of it being widely promoted.

Model 5—Reference [10] proposed a comprehensive project management model that elaborated several stages of systematic management of university processes: the general concept of processes, environmental characteristics and internal accuracy, and the ability to plan, organize, implement, evaluate, adjust and improve. These stages correspond to the project background and purpose, project framework, project overview, project walkthrough, and project presentation. This model is applicable to general university management and is an effective method of substantive process management. It helps optimize human, material, technical, financial and information resources to improve the quality and impact of management results. Notably, this model is characterized by high interactivity, meaning the completion of each stage affects the entire process and depends on at least one other stage. This feature facilitates the guidance of the process and allows for recalibration when necessary. The system model was successfully implemented during the 2012–2013 academic year at the tested universities, resulting in improvement in all its selected indicators. By observing the process and communicating with the actors involved in the process, Aguilera found that all stakeholders had a high degree of satisfaction with the management of the substantive process. The limitation of this comprehensive project management model is that it only extends to the organization and functions of the university, and only applies to the management of the university.

Model 6—In the Project Excellence Model^®, reference [11] proposed a series of critical key success factors, five project types and six organizational domains through a literature review. The critical factors for project success are organization, results, and feedback, respectively. These factors include (1) leadership and team, (2) policy and strategy, (3) stakeholder management, (4) resources, (5) contracting, (6) project management, (7) success criteria and (8) external factors, respectively. These factors are interrelated to form a coherent model.

Project types play a critical role in project management because the project objectives of different areas and types must match external factors. The five project types in the model include (1) product-oriented, (2) tool-oriented, (3) system-oriented, (4) process-oriented and (5) complete project management. The six result areas include (1) project results, (2) appreciation by the client, (3) appreciation by project personnel, (4) appreciation by users, (5) appreciation by contracting partners, and (6) appreciation by clients. This model includes the project background and purpose, project stakeholders and project team, project overview, project walkthrough, project tracking and control. At project startup, it is imperative to categorize the six resulting domain reads of the model and select the corresponding project type in each domain. This model has been successfully demonstrated in a medium-sized organization and is generally flexible in adapting to project objectives. Linking project outcome areas, organizational areas, and different project types can provide good insights into improving project organizational functions. However, the model has its limitations in terms of comprehensively covering all relevant success factors.

Model 7—Reference [12] proposed PRINCE2, a standard project management tool. PINS2 is a structured project management method that encompasses elements related to project organization, management, and control. It finds primary application with commercial, government and construction projects in the UK. The authors used it in clinical trial management and obtained good results. This model mainly has the following four characteristics: clear objectives, measurable conclusions, clearly defined resources and clearly defined organizational responsibilities. This model includes the project background and purpose, project framework, project overview, project tracking and control. This model can be used in different areas to improve management efficiency and reduce process costs. However, it should be noted that this approach comes with certain limitations. The tools and terminology employed may not be readily familiar to most participants, necessitating additional training to surmount the considerable learning curve.

Two gaps are identified from the above review of the seven MC models. First, these seven models identify seven factors that are important for MC. However, as shown in Table 1, they only cover some of the seven factors that are related to successful MC. All of them miss one or another factor. The following section will propose a new model that integrates all the seven factors identified from previous models.

Secondly, most of these models are qualitative, and only those involving maturity are quantitatively analyzed. The models rely more on managers’ experience and judgment of subjective consciousness. There is no complete and systematic model to conduct both qualitative and quantitative analysis of these factors step by step. Even these MC factors have differences in partitioning and qualification between different models, as shown in Table 1 above. This study solves this problem by proposing and applying a new model to the MC project.

2.3. The Proposal of a New Model

The success of the MC project firstly depends on the manager who leads the project. Therefore, this study proposes an MC project manager-oriented model, as shown in Figure 1. Managers can use this model to have clear control over the overall project framework and direction. In this model, the initial three parts (part A to part C) are mainly dedicated to understanding and mastering the basic information of the project, part D to part F place emphasis on methods, processes and results of the project, part G underscores the notion that, as a management consulting project, the presentation of project results and the project’s completion process should be conducted by consultants for the benefit of the client. This brings about the holistic process of management consultation. The subsequent section elaborates on the seven factors (categories) of this new model.

2.3.1. Project Background and Purpose

The project background and purpose include these parts: organizational approach to project planning, project identification process, project selection process, project goals and benefits, and success measures/criteria identified [8]. Before the start of an MC project, the manager should select and prioritize. Total resources resemble a pie, and they are limited. Each project cannot share the same amount of manpower, funds, equipment and other resources. It is the first step of the model, which is how to identify the scope of the project and allocate resources according to the project’s revenue and requirements. In this step, the project needs to be evaluated and predicted in terms of cost, potential benefits, development risks, time to market and so on. Methods commonly used in project selection are the checklist model, scoring model and analytic hierarchy process (AHP) [13].

Secondly, success criteria are the criteria to measure the success or failure of a project, and an MC project manager should clearly distinguish between critical success factors and critical success criteria before starting.

2.3.2. Project Framework

This project framework section builds upon the project selection, goals, and success measures discussed in Factor 1. For maximum effectiveness, it is crucial that all team members have a clear understanding of both the “what” and the “why” (the significance) of their projects. Whether an organization follows a formal project charter process or not, team members should possess the ability to succinctly summarize their project, comprehend the type of project they are undertaking, grasp the scope of their work, and be aware of the project’s timeline. The team should explicitly define the project type, which can include problem-solving, process/continuous improvement, design, or transformational, among other examples. Documenting basic assumptions and anticipated risks is important to prevent unexpected challenges during the project. Furthermore, the team should have a thorough understanding of the resources available to them. A project framework template is provided to ensure consistency in capturing and sharing the necessary information.

The project framework includes these parts: concise project statement, type of project, scope statement, assumptions/expectations, project schedule/high-level plan, budget (financial or resource) and risk management. The combination of project type and team is crucial, in particular because the personality and personal style of the project manager have a certain influence on the success of the project [14].

The project scope needs to state everything about the project, including all activities to perform, resources to consume, end products and quality standards. A scoping statement usually uses a work breakdown structure (WBS), an organization breakdown structure (OBS), and a linear responsibility chart. Gantt charts are a popular way of time scheduling which is crucial. Reference [5] proved that the completion schedule can make the project more likely to succeed.

2.3.3. Project Stakeholders and the Project Team

Project stakeholders include these elements: stakeholders and how they are identified, project champions, project team selection, team preparation, and team routines. Project stakeholders are significant. A successful operation of the MC project requires the support and cooperation of banks, governments, environmental groups, customers, employers, employees, the public, shareholders, suppliers, distributors and other groups. In a successful MC project, stakeholders can be involved throughout the whole process. Reference [11] also considered appreciation and other feedback from both the direct and indirect parties involved in the project.

In addition, as far as team development is concerned, there are generally four stages: forming, storming, cooperation, and performing [15]. Managers need to keep an eye on the development of the team and resolve internal and external conflicts.

Team preparation requires training in tools, techniques, and knowledge of the project. Consulting training has not been given sufficient concern [16]. The lack of training practice may be related to the lack of research on consulting training [17]. In the past, a project would provide consultation courses focused on the theoretical knowledge of consulting, the development of the intervention, the process, and the maintenance of the intervention through consultation [18]. After determining the background, purpose, framework and team members of the MC project, the manager needs to organize training and preparation for the members of the team in terms of content, culture, methodology, and development. This is a critical step. Sufficient training can improve the efficiency of project members and project completion. In terms of content, each member should be made aware of all information about the project. Regarding culture, members need to understand each other’s cultural differences and the cultural backgrounds of other stakeholders. There are clear cultural elements in the consulting literature, such as “multicultural consulting” [19] and “cross-cultural consulting” [20], which can be regarded as the theoretical framework of consulting. Project participants usually spend much less time in the field of multiculturalism or diversity [18]. Skills and methods can be taught to engineers without many difficulties [21]. Only with simple and rapid training can project members continuously learn in action [22].

2.3.4. Project Overview

The project overview serves as a bridge between the background/preparation work and project execution/results. The project overview includes these parts: project approach, tools used throughout project, tool output at different stages of a project, how a team was prepared to use the tools, dealing with project risk, encountering and handling resistance as a risk and stakeholder involvement in a project. The project needs to be subdivided into more detailed work steps at each stage, and one or more project management tools must be used at each stage [10]. Project tools are many, such as project management maturity models (PMMMs) [23], critical path method (CPM), process evaluation and review techniques(PERT) [24], critical chain project management (CCPM) [25] and increasingly popular hybrid methods [26].

2.3.5. Project Walkthrough

The project walkthrough is the core of the project to demonstrate how they moved from decision to decision to complete their project. The project walkthrough includes these parts: data-driven project flow, solution validation, solution justification, results, maintaining the gains and project communication. Process improvement has been a top priority for the past decade [27]. Teams should validate and improve their solutions and always communicate with project stakeholders before implementing project solutions.

2.3.6. Project Tracking and Control

Project tracking and control is further discussions and implementation of the risks in the project overview. This must be a continuous process overseen by a designated individual.

Project tracking includes the implementation, monitoring and review of project [9]. Specifically, the team is implementing the best alternative, monitoring project execution, and reviewing the project experience. Project tracking and monitoring is a very important phase for the execution and management of an MC project. A previous study by [28] pointed out that proper tracking and monitoring practices are critical to successfully delivering a project.

Project control includes the control of time, process progress, capital use, risk and uncertainty factors, etc. Risk management is the most important part of project control. Uncertainty and risk are at the heart of all projects. Effective risk management is essential of successful project management [1]. Appropriate risk management can help project managers mitigate known and unexpected risks for various of projects [29].

2.3.7. Project Presentation

Although the project presentation is not a separate phase of a project, it is a collection of key points for the project team to share with stakeholders.

Project presentation includes slide readability, logical flow of information, use of graphics and illustrations, and narrative and visual text. In addition, the speaker’s body language and eye contact with the audience are important.

Project presentation is the integration of everything, such as project purpose, team, stakeholders, method of use, process, end results and gap with expectations. The speaker needs to concisely explain these key points and key information to the internal and external groups. It is the final stage of completion of the project.

3. Model Evaluation Methodology

3.1. Data Collection Method

To verify the model shown in Figure 1, a questionnaire (assessment tool) was designed based on the seven factors in Figure 1 and supported by relevant literature. For each factor, about 6–12 questions were asked to measure the importance of the factor. Scores ranged from 1 to 10, from unimportant to very important. This questionnaire is supposed to be used for two purposes. The first is that the questionnaire will be used for the expert assessment of the seven factors and the questions under each factor, and the data analysis of the assessment results will be carried out. The weight of each factor will be determined based on the results of the expert assessment. The second is that the questionnaire will be used for the next phase of the case project evaluation.

The questionnaire (assessment tool) is attached in Appendix A.

3.2. Data Analysis Method

To quantitatively assess the model, integrate expert ratings, and enhance its applicability in real-world scenarios, the following seven factors should be evaluated to obtain their respective weights. The MC model proposed in this paper contains seven factors and dozens of problems, so we did not use methods like AHP (analytical hierarchical process), but adopted the combination method of Dempster–Shafer, based on upper and lower bound probability [30].

The D-S theory was proposed by Dempster in 1967. It belongs to artificial intelligence and the expert system. The method has the ability to cope with uncertain information by the expert scoring and represented in the data structure [31]. D-S evidence theory is a tool for decision making on multi-source data with uncertain information [32]. D-S theory has been widely used in many fields including sensor data, biometric recognition, and decision support systems [33,34,35].

Dempster–Shafer theory provides many combination rules for framework construction. This paper uses the combined Dempster–Shafer method, which is widely used, easy to implement, and emphasizes the consistency between multiple sources.

The process of determining the weight for each category is shown as follows. First, for each expert, we calculate the score of each category as the mean value of the questions in that category. Then, the category scores were normalized using the following formula:

m_i(X) = m_ix/sum_i

where m_ix is the score of categories X(X = A to H) from expert i, and sum_i is the sum of all category score by expert i.

Then, according to the Dempster–Shafer combination rule, to combines 2 experts’ score.

$$[m_1\oplus m_2](y)=\left\{\begin{array}{cc}0& y=\phi \\ \frac{{\sum }_{A\cap B=y}{m}_1\left(A\right)m_2\left(B\right)}{1-{\sum }_{A\cap B=\phi }{m}_1\left(A\right)m_2\left(B\right)}& y\ne \phi \end{array}\right.$$

4. Model Evaluation Process

4.1. Experts Evaluation

We invited 15 experts who agreed to support this project, as listed in

Table 2. The background of the 15 experts.

	Gender	Age Range	Work Area	Years of Experiences in MC	Industry of MC Projects Involved
1	Male	26~30	East China	10	IT, Engineering and Construction
2	Male	Over 60	Hong Kong	30	Manufacturing
3	Female	31~40	East China	8	Quality Management
4	Male	51~60	East China	22	Utilities, Enterprises, Hospitals
5	Female	31~40	Southwest of China	5	Communication, Transportation Industries
6	Male	31~40	South China	5	Finance, State-owned Enterprises
7	Female	26~30	South China	5	Finance Industry
8	Male	26~30	Greater Bay Area	5	Finance Industry
9	Male	51~60	North China	15	Aviation Industry
10	Male	41~50	Greater Bay Area	20	Technology, Mergers and Acquisitions, Marketing, Production
11	Male	51~60	Hong Kong	20	Information Technology
12	Male	Over 60	Greater Bay Area	24	Manufacturing Industry
13	Male	51~60	East China	25	Manufacturing Industry
14	Female	26~30	South China	5	Strategy Management, Human Resources
15	Male	26~30	East China	5	Internet, Medical Industry

. They all have experience in management consultation for years in China. During the separate correspondence process with each expert, the information gathered reveals that the new MC model is comprehensive and can be used to evaluate an MC project relatively fully. The 15 experts were finally invited for the evaluation of the model according to the questionnaire (assessment tool) in Appendix A. The backgrounds of the 15 experts are listed in Table 2.

4.2. Expert Evaluation Analysis via the Dempster–Shafer Combination Method

According to the expert scoring, we obtained 15 pieces of data with different weights. In order to obtain a more accurate and comprehensive weight, the data need to be normalized according to the principles and guidelines of the Delphi method to obtain a comprehensive evaluation of the model [36]. Through the D-S data processing method described above, 15 expert scores were combined one by one to obtain the D-S value.

The weight of each category is determined as follows. First, for each expert, we calculate the average of their response to the questions with each category. Subsequently, we calculate the sum of these averages across all specialists.

Average score (A) = (A₁ + A₂ + … + A_i)/i;

Average score (B) = (B₁ + B₂ + … + B_j)/j;

……

Average score (G) = (G₁ + G₂ + … + G_m)/m;

SUM of Average score = Average score (A) + Average score (B) + …… + Average score (G)

As shown in

Table 3. The average and sum scores from the 15 experts.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
A	8.167	8.000	8.000	8.500	8.000	8.500	8.167	9.667	8.000	9.167	8.833	6.667	7.667	8.333	8.500
B	9.429	7.714	9.143	9.000	8.429	8.429	9.000	8.714	8.571	9.571	8.857	7.000	7.857	6.429	8.429
C	7.286	6.857	8.857	8.429	8.571	7.714	8.429	7.571	7.571	9.429	8.857	6.714	8.571	3.571	7.714
D	8.000	7.000	8.000	8.429	8.143	9.571	8.571	8.000	8.429	8.714	8.714	5.286	8.000	3.000	7.000
E	8.167	7.000	9.000	8.667	9.000	8.667	7.667	7.667	7.667	9.000	9.167	6.167	7.000	3.833	9.000
F	8.167	7.333	8.333	8.500	9.167	9.167	7.500	8.167	8.000	10.00	8.000	4.167	9.000	3.000	9.000
G	6.250	6.917	8.083	8.167	9.667	7.083	8.000	8.083	7.500	8.083	8.667	5.833	7.833	4.333	8.333
SUM	55.464	50.821	59.417	59.690	60.976	59.131	57.333	57.869	55.738	63.964	61.095	41.833	55.929	32.500	57.976

, the scores of 15 experts on seven factors are processed.

Second, the following formula is used to standardize category scores:

m_i(X) = m_ix/sum_i

where m_ix is the score of categories X (X = A to G) from expert i, and sum_i is the sum of all category score by expert i.

As shown in

Table 4. The standard scores.

	m1	m2	m3	m4	m5	m6	m7	m8	m9	m10	m11	m12	m13	m14	m15
A	0.147	0.157	0.135	0.142	0.131	0.144	0.142	0.167	0.144	0.143	0.145	0.159	0.137	0.256	0.147
B	0.170	0.152	0.154	0.151	0.138	0.143	0.157	0.151	0.154	0.150	0.145	0.167	0.140	0.198	0.145
C	0.131	0.135	0.149	0.141	0.141	0.130	0.147	0.131	0.136	0.147	0.145	0.161	0.153	0.110	0.133
D	0.144	0.138	0.135	0.141	0.134	0.162	0.150	0.138	0.151	0.136	0.143	0.126	0.143	0.092	0.121
E	0.147	0.138	0.151	0.145	0.148	0.147	0.134	0.132	0.138	0.141	0.150	0.147	0.125	0.118	0.155
F	0.147	0.144	0.140	0.142	0.150	0.155	0.131	0.141	0.144	0.156	0.131	0.100	0.161	0.092	0.155
G	0.113	0.136	0.136	0.137	0.159	0.120	0.140	0.140	0.135	0.126	0.142	0.139	0.140	0.133	0.144
SUM	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000

, scores are standardized.

Then, using the Dempster–Shafer combination rule to combine two experts’ score.

To illustrate the combination rule, see the following example. If the normalized score from expert 1 is [m₁(A), m₁(B), m₁(C)…, m₁(F), m₁(G)] for category A to G, and the normalized score from expert 2 is [m₂(A), m₂(B), m₂(C)…, m₂(F), m₂(G)] for category A to G it would be optimized to calculate the Dempster–Shafer value for the expert 1 and expert 2 for category A as follows:

$$\begin{gathered} {DS}_2(A)=\frac{m_1\left(A\right)m_2\left(A\right)}{1-\left(\sum m_1\left(A\right)m_1\left(B\right)m_1\left(C\right)\dots m_1\left(H\right)m_2\left(A\right)m_2\left(B\right)m_2\left(C\right)\dots m_2\left(G\right)\right)} \\ =\frac{m_1\left(A\right)m_2\left(A\right)}{1-(\left(1-m_1\left(A\right)\right)\times m_2\left(A\right)+\left(1-m_1\left(B\right)\right)\times m_2\left(B\right)+\dots +\left(1-m_1\left(G\right)\right)\times m_2\left(G\right))} \end{gathered}$$

For category B:

$$\begin{gathered} {DS}_2(B)=\frac{m_1\left(B\right)m_2\left(B\right)}{1-\left(\sum m_1\left(A\right)m_1\left(B\right)m_1\left(C\right)\dots m_1\left(H\right)m_2\left(A\right)m_2\left(B\right)m_2\left(C\right)\dots m_2\left(G\right)\right)} \\ =\frac{m_1\left(B\right)m_2\left(B\right)}{1-(\left(1-m_1\left(A\right)\right)\times m_2\left(A\right)+\left(1-m_1\left(B\right)\right)\times m_2\left(B\right)+\dots +\left(1-m_1\left(G\right)\right)\times m_2\left(G\right))} \end{gathered}$$

For category C:

$$\begin{gathered} {DS}_2(C)=\frac{m_1\left(C\right)m_2\left(C\right)}{1-\left(\sum m_1\left(A\right)m_1\left(B\right)m_1\left(C\right)\dots m_1\left(H\right)m_2\left(A\right)m_2\left(B\right)m_2\left(C\right)\dots m_2\left(G\right)\right)} \\ =\frac{m_1\left(C\right)m_2\left(C\right)}{1-(\left(1-m_1\left(A\right)\right)\times m_2\left(A\right)+\left(1-m_1\left(B\right)\right)\times m_2\left(B\right)+\dots +\left(1-m_1\left(G\right)\right)\times m_2\left(G\right))} \\ \dots \dots \end{gathered}$$

For category G:

$$\begin{gathered} {DS}_2(G)=\frac{m_1\left(G\right)m_2\left(G\right)}{1-\left(\sum m_1\left(A\right)m_1\left(B\right)m_1\left(C\right)\dots m_1\left(H\right)m_2\left(A\right)m_2\left(B\right)m_2\left(C\right)\dots m_2\left(G\right)\right)} \\ =\frac{m_1\left(G\right)m_2\left(G\right)}{1-(\left(1-m_1\left(A\right)\right)\times m_2\left(A\right)+\left(1-m_1\left(B\right)\right)\times m_2\left(B\right)+\dots +\left(1-m_1\left(G\right)\right)\times m_2\left(G\right))} \end{gathered}$$

where DS₂ means 2 experts’ score are combined.

After the scores from expert 1 and expert 2 are combined, the result would be combined with score from expert 3, as follows:

For category A:

$$\begin{gathered} {DS}_3(A)=\frac{{DS}_2\left(A\right)m_3\left(A\right)}{1-\left(\sum {DS}_2\left(A\right){DS}_2\left(B\right){DS}_2\left(C\right)\dots {DS}_2\left(H\right)m_3\left(A\right)m_3\left(B\right)m_3\left(C\right)\dots m_3\left(G\right)\right)} \\ =\frac{{DS}_2(A)m_3\left(A\right)}{1-(\left(1-{DS}_2\left(A\right)\right)\times m_3\left(A\right)+\left(1-{DS}_2\left(B\right)\right)\times m_3\left(B\right)+\dots +\left(1-{DS}_2\left(G\right)\right)\times m_3\left(G\right))} \end{gathered}$$

For category B:

$$\begin{gathered} {DS}_3(B)=\frac{{DS}_2\left(B\right)m_3\left(B\right)}{1-\left(\sum {DS}_2\left(A\right){DS}_2\left(B\right){DS}_2\left(C\right)\dots {DS}_2\left(H\right)m_3\left(A\right)m_3\left(B\right)m_3\left(C\right)\dots m_3\left(G\right)\right)} \\ =\frac{{DS}_2\left(B\right)m_3\left(B\right)}{1-(\left(1-{DS}_2\left(A\right)\right)\times m_3\left(A\right)+\left(1-{DS}_2\left(B\right)\right)\times m_3\left(B\right)+\dots +\left(1-{DS}_2\left(G\right)\right)\times m_3\left(G\right))} \\ \dots \dots \end{gathered}$$

For category G:

$$\begin{gathered} {DS}_3(G)=\frac{{DS}_2\left(G\right)m_3\left(G\right)}{1-\left(\sum {DS}_2\left(A\right){DS}_2\left(B\right){DS}_2\left(C\right)\dots {DS}_2\left(H\right)m_3\left(A\right)m_3\left(B\right)m_3\left(C\right)\dots m_3\left(G\right)\right)} \\ =\frac{{DS}_2\left(G\right)m_3\left(G\right)}{1-(\left(1-{DS}_2\left(A\right)\right)\times m_3\left(A\right)+\left(1-{DS}_2\left(B\right)\right)\times m_3\left(B\right)+\dots +\left(1-{DS}_2\left(G\right)\right)\times m_3\left(G\right))} \end{gathered}$$

where DS₃ means 3 experts’ score are combined.

And then the result would be combined with expert 4. It would be repeated until all of the experts’ score are combined.

As shown in

Table 5. The D-S value of 7 sections from expert 1 to expert 15 (weight of section).

	DS2	DS3	DS4	DS5	DS6	DS7	DS8	DS9	DS10	DS11	DS12	DS13	DS14	DS15
A	0.162	0.152	0.151	0.139	0.139	0.139	0.161	0.160	0.159	0.161	0.176	0.171	0.276	0.280
B	0.180	0.193	0.203	0.198	0.196	0.215	0.225	0.240	0.248	0.252	0.290	0.288	0.359	0.362
C	0.124	0.129	0.126	0.125	0.114	0.117	0.106	0.100	0.102	0.104	0.114	0.124	0.086	0.079
D	0.139	0.130	0.128	0.120	0.136	0.142	0.136	0.143	0.135	0.134	0.117	0.118	0.069	0.057
E	0.141	0.150	0.151	0.157	0.160	0.150	0.138	0.131	0.128	0.135	0.136	0.121	0.090	0.096
F	0.148	0.145	0.144	0.152	0.164	0.150	0.147	0.147	0.159	0.145	0.100	0.113	0.066	0.071
G	0.107	0.102	0.097	0.108	0.090	0.088	0.085	0.080	0.070	0.069	0.066	0.066	0.055	0.055

, the D-S scores of 15 experts for seven factors are shown.

The scores of DS 15 are the composite weight scores of 15 experts for 7 factors, also called weight of section.

After the weighting factor of each issue at organization readiness has been calculated, it is time to generate the weighting factor for each KPI in each section, which is the result of the multiplication of the MC factors’ weight and the KPI weight of that related issue.

First, the same method is used to standardize the data. Subsequently, according to the Dempster–Shafer combination rule, the DS value of KPI in each section can be calculated in

Table 6. The DS value of KPI in each section by 15 experts.

		DS2	DS3	DS4	DS5	DS6	DS7	DS8	DS9	DS10	DS11	DS12	DS13	DS14	DS15
A	A1	0.229	0.229	0.242	0.185	0.210	0.225	0.227	0.250	0.253	0.235	0.239	0.307	0.286	0.261
	A2	0.142	0.142	0.134	0.154	0.174	0.166	0.167	0.144	0.145	0.118	0.171	0.176	0.205	0.210
	A3	0.183	0.183	0.172	0.198	0.224	0.213	0.215	0.237	0.240	0.251	0.109	0.112	0.131	0.134
	A4	0.142	0.142	0.134	0.120	0.041	0.034	0.027	0.023	0.012	0.014	0.006	0.005	0.004	0.003
	A5	0.160	0.160	0.151	0.173	0.157	0.131	0.132	0.145	0.147	0.171	0.198	0.153	0.143	0.130
	A6	0.142	0.142	0.167	0.171	0.194	0.231	0.232	0.200	0.202	0.211	0.276	0.247	0.231	0.263
B	B1	0.156	0.137	0.135	0.128	0.147	0.113	0.114	0.117	0.085	0.094	0.089	0.083	0.096	0.096
	B2	0.082	0.081	0.071	0.067	0.054	0.060	0.060	0.061	0.063	0.056	0.053	0.044	0.025	0.020
	B3	0.137	0.149	0.131	0.155	0.125	0.138	0.154	0.158	0.163	0.181	0.221	0.258	0.374	0.372
	B4	0.117	0.115	0.114	0.108	0.087	0.077	0.060	0.048	0.049	0.044	0.047	0.028	0.024	0.019
	B5	0.156	0.154	0.168	0.180	0.207	0.228	0.229	0.234	0.243	0.242	0.230	0.215	0.156	0.172
	B6	0.176	0.192	0.211	0.200	0.230	0.253	0.282	0.289	0.300	0.299	0.324	0.341	0.296	0.296
	B7	0.176	0.173	0.171	0.162	0.149	0.131	0.102	0.093	0.097	0.086	0.035	0.033	0.028	0.025
C	C1	0.225	0.205	0.217	0.247	0.264	0.249	0.169	0.154	0.165	0.152	0.138	0.111	0.088	0.089
	C2	0.197	0.201	0.213	0.244	0.162	0.191	0.182	0.166	0.107	0.110	0.117	0.094	0.074	0.084
	C3	0.138	0.141	0.100	0.114	0.121	0.129	0.175	0.160	0.171	0.157	0.190	0.218	0.231	0.203
	C4	0.099	0.089	0.084	0.077	0.062	0.058	0.063	0.058	0.062	0.071	0.075	0.069	0.036	0.028
	C5	0.085	0.086	0.091	0.084	0.078	0.073	0.080	0.083	0.089	0.102	0.109	0.125	0.165	0.145
	C6	0.118	0.121	0.128	0.102	0.136	0.112	0.076	0.080	0.085	0.078	0.071	0.074	0.078	0.078
	C7	0.138	0.157	0.166	0.133	0.177	0.187	0.255	0.299	0.320	0.330	0.301	0.310	0.328	0.372
D	D1	0.075	0.074	0.079	0.076	0.078	0.094	0.098	0.103	0.123	0.115	0.115	0.152	0.157	0.197
	D2	0.105	0.091	0.097	0.081	0.084	0.091	0.095	0.089	0.084	0.089	0.107	0.113	0.155	0.130
	D3	0.140	0.121	0.100	0.096	0.099	0.095	0.112	0.092	0.109	0.115	0.162	0.149	0.103	0.086
	D4	0.123	0.121	0.114	0.110	0.079	0.086	0.112	0.105	0.100	0.117	0.094	0.099	0.068	0.057
	D5	0.175	0.173	0.163	0.157	0.162	0.156	0.143	0.150	0.179	0.167	0.101	0.133	0.182	0.178
	D6	0.201	0.198	0.210	0.227	0.234	0.225	0.207	0.217	0.259	0.242	0.145	0.134	0.185	0.206
	D7	0.180	0.222	0.236	0.255	0.264	0.253	0.232	0.244	0.145	0.153	0.276	0.219	0.150	0.147
E	E1	0.122	0.108	0.099	0.086	0.058	0.070	0.072	0.079	0.089	0.077	0.066	0.088	0.044	0.044
	E2	0.187	0.185	0.211	0.231	0.209	0.193	0.201	0.192	0.216	0.211	0.179	0.213	0.213	0.237
	E3	0.157	0.156	0.160	0.175	0.158	0.147	0.153	0.187	0.210	0.206	0.210	0.218	0.219	0.170
	E4	0.143	0.142	0.129	0.127	0.144	0.152	0.119	0.113	0.089	0.097	0.165	0.171	0.172	0.190
	E5	0.187	0.185	0.169	0.129	0.146	0.135	0.141	0.172	0.194	0.190	0.194	0.144	0.144	0.128
	E6	0.204	0.225	0.231	0.252	0.285	0.302	0.314	0.257	0.202	0.220	0.187	0.166	0.208	0.231
F	F1	0.218	0.207	0.215	0.237	0.258	0.263	0.285	0.308	0.308	0.274	0.379	0.407	0.471	0.510
	F2	0.218	0.233	0.242	0.214	0.232	0.267	0.289	0.311	0.311	0.357	0.197	0.212	0.245	0.212
	F3	0.218	0.233	0.242	0.240	0.209	0.213	0.180	0.151	0.151	0.134	0.074	0.072	0.062	0.061
	F4	0.098	0.093	0.097	0.096	0.104	0.080	0.077	0.083	0.083	0.085	0.094	0.090	0.052	0.057
	F5	0.134	0.127	0.103	0.102	0.077	0.069	0.067	0.048	0.048	0.061	0.084	0.072	0.042	0.036
	F6	0.114	0.109	0.101	0.111	0.120	0.108	0.103	0.099	0.099	0.089	0.171	0.147	0.128	0.124
G	G1	0.070	0.079	0.078	0.081	0.089	0.087	0.085	0.101	0.070	0.065	0.063	0.051	0.043	0.044
	G2	0.070	0.061	0.061	0.056	0.047	0.040	0.039	0.046	0.032	0.034	0.016	0.009	0.008	0.006
	G3	0.082	0.072	0.071	0.073	0.071	0.087	0.074	0.088	0.061	0.057	0.055	0.050	0.042	0.048
	G4	0.068	0.077	0.085	0.088	0.110	0.134	0.115	0.121	0.140	0.114	0.146	0.135	0.141	0.161
	G5	0.094	0.094	0.104	0.107	0.149	0.146	0.142	0.131	0.152	0.177	0.113	0.130	0.137	0.141
	G6	0.078	0.088	0.098	0.101	0.098	0.108	0.131	0.138	0.160	0.149	0.191	0.220	0.231	0.211
	G7	0.082	0.092	0.091	0.094	0.104	0.127	0.156	0.163	0.190	0.199	0.223	0.256	0.269	0.277
	G8	0.123	0.108	0.093	0.077	0.064	0.062	0.053	0.049	0.057	0.060	0.076	0.044	0.046	0.037
	G9	0.110	0.109	0.095	0.097	0.081	0.069	0.068	0.053	0.043	0.040	0.032	0.026	0.022	0.017
	G10	0.068	0.068	0.068	0.070	0.058	0.050	0.048	0.038	0.031	0.032	0.016	0.013	0.011	0.008
	G11	0.047	0.047	0.052	0.048	0.040	0.034	0.034	0.031	0.025	0.026	0.025	0.026	0.016	0.015
	G12	0.106	0.105	0.104	0.107	0.089	0.055	0.053	0.042	0.039	0.045	0.044	0.040	0.034	0.035

.

And the weight of each KPI is the result of the multiplication of the weight of the section and DS15 of KPI, the combined weight value of 15 experts in

Table 7. The weight of KPI by 15 experts.

		DS15	Weight of Section	Weight of KPI
A	A1	0.261	0.280	0.07295
	A2	0.210		0.05884
	A3	0.134		0.03752
	A4	0.003		0.00084
	A5	0.130		0.03631
	A6	0.263		0.07355
B	B1	0.096	0.362	0.03475
	B2	0.020		0.00709
	B3	0.372		0.13466
	B4	0.019		0.00676
	B5	0.172		0.06233
	B6	0.296		0.10685
	B7	0.025		0.00908
C	C1	0.089	0.079	0.00699
	C2	0.084		0.00667
	C3	0.203		0.01607
	C4	0.028		0.00218
	C5	0.145		0.01148
	C6	0.078		0.00620
	C7	0.372		0.02941
D	D1	0.197	0.057	0.01131
	D2	0.130		0.00745
	D3	0.086		0.00493
	D4	0.057		0.00327
	D5	0.178		0.01022
	D6	0.206		0.01182
	D7	0.147		0.00842
E	E1	0.044	0.096	0.00423
	E2	0.237		0.02283
	E3	0.170		0.01638
	E4	0.190		0.01835
	E5	0.128		0.01233
	E6	0.231		0.02229
F	F1	0.510	0.071	0.03610
	F2	0.212		0.01504
	F3	0.061		0.00430
	F4	0.057		0.00401
	F5	0.036		0.00257
	F6	0.124		0.00881
G	G1	0.044	0.055	0.00240
	G2	0.006		0.00034
	G3	0.048		0.00264
	G4	0.161		0.00885
	G5	0.141		0.00771
	G6	0.211		0.01156
	G7	0.277		0.01517
	G8	0.037		0.00202
	G9	0.017		0.00096
	G10	0.008		0.00046
	G11	0.015		0.00083
	G12	0.035		0.00190

.

5. Case Studies

5.1. Background of 13 Cases

With the help of several consulting firms, we found some real cases of MC projects. These companies are located in China’s Hong Kong, Greater Bay Area, southwest, east and south, and they are all typical companies that meet the application conditions of the MC model (in China’s market background and corresponding demand). As shown in

Table 8. Background of the 13 cases.

	Industry	Type	Location/Area	The Number of Team	Estimated Project Duration	Actual Project Duration	The Rate of Time Overruns	Customer Satisfaction (0–10)
Case 1	Energy	Strategy management	Southwest	3	3 months	3.5 months	16.67%	5
Case 2	Agriculture	Human resources	South	3	5 months	18 months	260%	3
Case 3	Finance	Strategy management	Southeast	4	3 months	3 months	0	7
Case 4	Grid	Technology management	Northwest	6	3 months	2 months	−33.33%	8
Case 5	Manufacture	Technology training management	North	10	4 weeks	4.5 weeks	12.5%	7
Case 6	Finance	Post-investment management	Southeast	6	18 weeks	18 months	300%	4
Case 7	Finance	Strategy management	Southeast	11	14 weeks	12 months	242.86%	7
Case 8	Food Manufacturing	ERP	Hong Kong	6	14 months	20 months	42.86%	8
Case 9	Wholesales	ERP	Hong Kong	8	16 months	18 months	12.5%	9
Case 10	Properties Management	Corporate Performance Management (CPM)	Hong Kong	4	8 months	9 months	12.5%	9
Case 11	Medicine	Performance Excellence Coaching	East	3	3 weeks	3 weeks	0	9
Case 12	Grid	Performance Excellence Coaching	Northwest	3	6 months	5.5 months	−8.33%	10
Case 13	Grid	Science and technology innovation	East	4	5 months	4 months	−20%	10

, these projects cover different industries, have different application scopes and project sizes, which can verify that the MC model can effectively evaluate a management consulting project, regardless of organizational size, industry type or project type.

5.2. The Process of Case Studies

The process is divided into the following four steps: project study (basic information acquisition and statement), project evaluation, weighted score calculation (combined with project evaluation scores and MC model weight scores), score comparison and conclusion. Project research mainly introduces the project background, including project type, industry involved, number of team members, expected completion time, actual completion time, client satisfaction, etc. Project scoring is to invite the consultant or the person in charge of the consultant to fill in the project measurement and evaluation questionnaire. Weighted score calculation is based on the score of the project and the weight of the experts.

5.3. Case Study One as an Example

Case 1 is from Team A, which is a management consulting team from a consulting firm in the Greater Bay Area. The total number in the team is 10. It has been established for eight years and has completed nearly 100 management consulting projects.

The project was carried out by Team A in Sichuan Province in March 2018. The project enterprise is a newly established provincial state-owned enterprise with more than 20 employees at its headquarters and six subordinate companies, each with about 30 employees. The purpose of this project is to establish an organizational structure and develop a performance appraisal plan for the enterprise. It was planned to be completed in three months, but it was actually delayed by two weeks. In this project, the participation of the senior management is high, but the cooperation between the middle management and the grassroots is not high, which leads to some resistance and affects the project schedule.

We obtained the project evaluation data according to the team leader’s score of the project through the project measure and assessment tool (Appendix A).

In order to evaluate the project through the model, we combined the evaluation data provided by the team leader with KPI weight.

KPI Score = Evaluation from Case × Weight of KPI

Weight% = ∑ of weight of each KPI, which shows the importance of that section, which also is weight of section (see Table 7).

Score of Section = ∑ of KPI score/∑ of weight of each KPI

The project weight data processing of case 1 is shown in

Table 9. Project weight data of case 1.

Section	KPI	Weight of KPI	Evaluation from Case 1	KPI Score 1	Score 1 of Section	Weight %
A	A1	0.07295	3	0.219	1.787	28.00%
	A2	0.05884	1	0.059
	A3	0.03752	1	0.038
	A4	0.00084	2	0.002
	A5	0.03631	1	0.036
	A6	0.07355	2	0.147
	sub-sum		10	0.500
B	B1	0.03475	3	0.104	2.476	36.15%
	B2	0.00709	2	0.014
	B3	0.13466	2	0.269
	B4	0.00676	0	0.000
	B5	0.06233	3	0.187
	B6	0.10685	3	0.321
	B7	0.00908	0	0.000
	sub-sum		13	0.895
C	C1	0.00699	2	0.014	0.816	7.90%
	C2	0.00667	0	0.000
	C3	0.01607	1	0.016
	C4	0.00218	2	0.004
	C5	0.01148	1	0.011
	C6	0.00620	3	0.019
	C7	0.02941	0	0.000
	sub-sum		9	0.064
D	D1	0.01131	3	0.034	2.090	5.74%
	D2	0.00745	3	0.022
	D3	0.00493	3	0.015
	D4	0.00327	1	0.003
	D5	0.01022	1	0.010
	D6	0.01182	3	0.035
	D7	0.00842	0	0.000
	sub-sum		14	0.120
E	E1	0.00423	1	0.004	1.601	9.64%
	E2	0.02283	3	0.068
	E3	0.01638	1	0.016
	E4	0.01835	1	0.018
	E5	0.01233	2	0.025
	E6	0.02229	1	0.022
	sub-sum		9	0.154
F	F1	0.03610	2	0.072	1.634	7.08%
	F2	0.01504	2	0.030
	F3	0.00430	1	0.004
	F4	0.00401	1	0.004
	F5	0.00257	2	0.005
	F6	0.00881	0	0.000
	sub-sum		8	0.116
G	G1	0.00240	1	0.002	1.470	5.48%
	G2	0.00034	1	0.000
	G3	0.00264	2	0.005
	G4	0.00885	1	0.009
	G5	0.00771	1	0.008
	G6	0.01156	3	0.035
	G7	0.01517	1	0.015
	G8	0.00202	1	0.002
	G9	0.00096	1	0.001
	G10	0.00046	1	0.000
	G11	0.00083	1	0.001
	G12	0.00190	1	0.002
	sub-sum	0.07295	15	0.081
SUM					11.875	1.000

.

5.4. Comparison of the 13 Cases

Due to page limitations, we will not report the application of the other 12 cases. Through the project evaluation of 13 management consulting cases of 6 consulting companies by the new MC model, we can obtain the weight score of these 13 cases as shown in

Table 10. Comparison of weight scores and client satisfaction of 13 cases.

Case	A	B	C	D	E	F	G	SUM	Client Satisfaction (0–10)
1	1.787	2.478	0.816	2.090	1.601	1.634	1.470	11.876	5
2	1.997	1.778	1.189	2.090	1.601	1.124	1.470	11.249	3
3	2.526	2.975	1.737	2.090	1.601	2.004	1.470	14.403	7
4	2.729	2.141	1.710	0.551	1.342	2.722	1.470	12.665	8
5	2.605	2.249	1.129	1.092	1.549	2.846	1.048	12.519	7
6	2.081	1.755	1.680	1.315	1.829	1.742	0.815	11.219	4
7	2.003	2.313	2.651	2.558	2.956	1.062	1.455	14.998	7
8	0.263	0.879	0.346	0.635	0.872	0.305	0.863	4.153	8
9	1.736	2.706	2.478	2.372	2.555	2.305	1.161	15.315	9
10	3.000	3.000	3.000	2.943	3.000	2.876	1.209	19.028	9
11	2.870	3.000	2.855	3.000	3.000	3.000	1.470	19.195	9
12	3.000	3.000	3.000	3.000	3.000	3.000	1.470	19.470	10
13	3.000	2.980	2.743	3.000	3.000	3.000	1.470	19.193	10

.

As can be seen from Table 10, it is evident that projects with evaluation scores above 12 are generally more recognized and satisfied by clients, while projects with evaluation scores below 12 are generally less successful and less satisfactory.

We can divide the project into the following fractional sections. From the perspective of different sections, the individual scores of the first six sections also impact the success of the project, as shown in

Table 11. The benchmarks for assessing MC projects.

SUM Score Range	The Number of Section Points > 2 (Section A–F)	Project Degree of Success
<12	<2	Failure projects
12–15	3–4	Projects with fair performance and client satisfaction
>15	5–6	Projects with outstanding performance

.

According to the classification in Table 11, among the 13 cases found in this paper, there are 4 failure cases, namely, cases 1, 2, 6 and 8; there are 4 common cases (with general performance), namely, cases 3, 4, 5 and 7; and there are 5 success cases, namely, cases 9, 10, 11, 12 and 13. This is shown in

Table 12. The assessment results for 13 cases under 3 categories.

Degrees of Success	Case	A	B	C	D	E	F	G	SUM	Customer Satisfaction (0–10)
Unsatisfied cases	1	1.787	2.478	0.816	2.090	1.601	1.634	1.470	11.876	5
	2	1.997	1.778	1.189	2.090	1.601	1.124	1.470	11.249	3
	6	2.081	1.755	1.680	1.315	1.829	1.742	0.815	11.219	4
	8	0.263	0.879	0.346	0.635	0.872	0.305	0.863	4.153	8
Fair cases	3	2.526	2.975	1.737	2.090	1.601	2.004	1.470	14.403	7
	4	2.729	2.141	1.710	0.551	1.342	2.722	1.470	12.665	8
	5	2.605	2.249	1.129	1.092	1.549	2.846	1.048	12.519	7
	7	2.003	2.313	2.651	2.558	2.956	1.062	1.455	14.998	7
Satisfactory cases	9	1.736	2.706	2.478	2.372	2.555	2.305	1.161	15.315	9
	10	3.000	3.000	3.000	2.943	3.000	2.876	1.209	19.028	9
	11	2.870	3.000	2.855	3.000	3.000	3.000	1.470	19.195	9
	12	3.000	3.000	3.000	3.000	3.000	3.000	1.470	19.470	10
	13	3.000	2.980	2.743	3.000	3.000	3.000	1.470	19.193	10

. Feedback was provided to the case projects and mostly matched the client satisfaction measure except for case 8.

6. Discussions and Implications

6.1. Theoretical Implications

Using models to help manage consulting projects is not a novel approach. There are many such models, but some parts of these models need to be improved. The ITEA model of the ASQ organization only carries out post-project evaluations and lacks the weight analysis and process analysis of each part, so it cannot be used as a reference model in the early stages of the project. Reference [9] provided the project decision analysis process (PDAP), and reference [3] presented the project organization model, providing only a process guide. Reference [5] only proposed six management factors for successful projects. References [10,11,12] proposed a qualitative conceptual model without quantifying the model.

Compared with previous models, this new management consulting model explains the relationship between the factors and processes. It covers the tracking and control part of the project. It is convenient for the consulting team to follow the D-S theory, and it can help the consulting team to predict, track and evaluate the consulting project in the early, middle and late stages, thereby helping the team to improve the success of a project and client satisfaction.

The new management consulting model was validated through the professional evaluation by 15 experts with 5–30 years of experience and Dempster–Shafer theory. This allows the new model to perform both qualitative and quantitative analysis of management consulting projects. This was not possible in all the previous models.

6.2. Practical Implications

The new model can help the project team to conduct guidance, self-tests and correction in the early and middle stages of the project. The process-based model and the maturity scale with clear levels can help the project team to conduct self-assessment and improvement in the early stage of a project, and improve the success probability and client satisfaction of the project through clear standards. In the middle of the project, it can be based on the model to fill in the missing pieces of the successful factors.

A good management consulting model can be applied to different stages and situations in a project [12]. This model can be used for project establishment, management and evaluation, providing a transparent and powerful tool for managing the risk, budget and more aspects of consulting projects [11].

7. Conclusions

Based on the review of the previous management consulting models, this paper discovered the existing deficiencies and proposed a new MC model. A total of 15 experts with 5–30 years of experience were invited to assess the importance of the seven factors of the new model. The Dempster–Shafer algorithm was used to summarize the 15 expert scores and obtain the weight of each part of the model. Then, the MC model was proved to be effective in the evaluation of management consulting projects in Hong Kong and mainland China through 13 cases. This new MC model can help the consulting team to conduct an assessment in early stage, track in the middle stage and evaluate in the late stage of the consulting project, and also can help the team improve the probability of project success, and client satisfaction.

The contribution of the new model can be summarized as follows. (1) the model covers all seven important factors identified from the literature review, providing a more integrated and systematic model to evaluate an MC project; (2) the model is evaluated by D-S theory and verified by case study, providing a complete and systematic model to conduct qualitative and quantitative analysis for an MC project; (3) the model can be applied to different stages of an MC project, allow flexibility in real-world applications and improve both project success and client satisfaction.

The research is not without limitations. First, the study was conducted in the Chinese context. As the success of an MC project may be related to cultural factors, the effectiveness of the proposed model beyond the boundary of China is questionable. Second, this model was only applied in a relatively small sample size of 13 cases. In the future, the model should be verified in an international context to see its validation across cultures and verified by more real cases.