Adaptability Analysis of Integrated Project Delivery Method in Large- and Medium-Sized Engineering Projects: A FAHP-Based Modeling Solution

Abstract

With the emerging large- and medium-sized engineering projects, prominent project delivery methods make sense in terms of cost, risk, management, and schedule. Among these, the Integrated Project Delivery (IPD) method stands out due to its adaptability for growing scale and complexity projects. This study compares the IPD method with other methods, emphasizing its benefits in large- and medium-sized projects and introducing the Fuzzy Analytic Hierarchy Process (FAHP) model to analyze IPD’s adaptability quantitatively. By conducting a matrix calculation of eighteen second-level indicators, this study derived weight values for four first-level indicators: Cost control, Risk control, Management control, and Schedule control. These first-level indicators were then used to formulate the total evaluation index calculation. Based on this foundation, we verified the calculations using a case study in Fujian. Implementing the IPD method led to a lower cost than the Owner’s Representative method and a one-year schedule acceleration. The FAHP model introduced in this study offers a novel and objective approach for adaptability analysis of the IPD method in large- and medium-sized engineering projects, coupling decision theory into project management.

1. Introduction

Project management has been discussed a lot since the 1950s and is widely used in multiple industries like petroleum, chemical, medicine, architecture, and other sectors [1,2,3,4]. Various project delivery methods are applied during the field implementation of engineering projects, some well executed and others not. An inappropriate project delivery method may result in a series of problems, including an unreasonable progress schedule, project cost overruns, and reduced execution efficiency [5,6], aggravating the risks taken by the owner and management company and complicating their responsibilities. Therefore, selecting appropriate project delivery methods in specific engineering projects is crucial to effective project implementation.

Accompanied by rapid urbanization and economic development, several project delivery methods are developed and applied in a wide range of engineering projects. Among them, several standard project delivery methods, like the Design–Bid–Build (DBB), Design–Build (DB), Construction Manager at Risk (CM at Risk), and Build–Operate–Transfer (BOT), are widely used in traditional projects [7,8,9,10]. With the increasing investment scale and project complexity in international engineering projects, typical delivery methods of Engineering Procurement Construction (EPC), Owner’s Representative (OR), Owner’s Construction Management (OCM), Public–Private Partnerships (PPP), and other delivery methods came into being [11,12,13,14]. Especially with the deepening cooperation between domestic and foreign enterprises and the continuous expansion of industrial scale, engineering projects also tend to become larger [15]. Especially in China, large- and medium-sized engineering projects have grown markedly over the past two decades.

Due to the characteristics of significant investment, long cycle, high complexity, and complex coordination in large- and medium-sized engineering projects, the Integrated Project Delivery (IPD) method has gradually been known and applied in recent years [16]. However, existing studies were more likely to use the IPD method mechanically, which lacked systematic discussion and comparison with other project delivery methods. As a newly integrated and emerging project delivery method, whether to select the IPD and how to apply the IPD in large- and medium-sized engineering projects are key subjective decision issues, especially under specific engineering project circumstances. The decision to select the IPD method usually depends on multiple factors, such as project scale, technical difficulty, project team membership, owner participation, etc. [17]. Therefore, the adaptability analysis of the IPD method in large- and medium-sized engineering projects deserves a deep inspection.

The relevant literature has focused on studying the performance and benefits of the IPD method in engineering projects [18]. However, an important aspect that has been overlooked is the adaptability analysis of the IPD method in these projects. Whether to utilize the IPD method becomes crucial, and the decision theory plays an important role in providing a quantitative index to account for the varying importance of factors influencing each project. However, there is a knowledge gap surrounding the limited use of decision theory in evaluating the adaptability of the IPD method in large- and medium-sized engineering projects. In this research, the Fuzzy Analytic Hierarchy Process (FAHP) [19] model is employed to comprehensively analyze and evaluate the adaptability of the IPD method by considering various aspects in large- and medium-sized engineering projects. The FAHP model could contribute to project policymakers’ evaluation of the suitability of adopting the IPD method in large- and medium-sized engineering projects. This study aims to introduce a modeling solution to guide the adaptability analysis of the IPD method.

The remainder of this paper is structured as follows: Section 2 describes a research review of the IPD method by consulting the existing literature to make clear the research status and its application fields, and a detailed comparison between IPD and other typical project delivery methods is conducted through characteristic analysis. Section 3 applies the FAHP model based on the factors affecting large- and medium-sized engineering projects as indicators, clarifying the interpretation of each indicator, its calculation process, and the significance of its weight scale. Section 4 establishes the weight matrix through the scoring results of experts in various fields in the industry and establishes a model for calculating the weights. By applying the FAHP model to an engineering project case, the adaptability of the IPD method was evaluated, resulting in notable advantages. Section 5 summarizes the conclusions of the article and describes the innovations and contributions of the article to the adaptability analysis of the IPD method.

2. Development of the IPD Method

2.1. Research Trends of Project Management

Before illustrating the research status of IPD, a bibliometric analysis of information on project management in the literature was conducted to display the related research trends. First, a general search on the project management category from the Elsevier ScienceDirect journal database was carried out, considering the twenty years from 2000 to the end of 2022. As shown in Figure 1, a total of 26,684 related articles were retrieved. Figure 1a shows the annual number of articles related to project management. There has been a significant increase in the number of annual published articles in the last two decades, which indicates accelerated growth in project management-related research, discussion, and application.

Figure 1b shows the classified statistics of different subject fields of this literature. Among these subject fields, themes on “environmental science” occupy the maximum quantity with more than 6500 articles, followed by “engineering”. There is also a substantial amount of literature covering several fields of “social sciences”, “medicine and dentistry”, and “agriculture and biological sciences”.

Second, considering the background of the dramatic development in engineering projects in China, a literature analysis on project management-related publications in China is conducted by searching the Chinese National Knowledge Infrastructure (CNKI) in the past two decades. As shown in Figure 2a, a total of 45,647 articles were retrieved, and the annual amount of literature about project management rose sharply from under 100 in 2000 to over 3000 in 2014. The yearly publication amount will maintain at about 3000 over the next five years. However, after 2020, the amount of literature declined significantly due to the COVID-19 pandemic [20]. Figure 2b also displays the number distribution of ten different main keywords related to project management. It can be seen that although several keywords covering “Risk management” and “Construction engineering” have more than 1000 publications, the keyword “project management” still occupies the majority, more than 70 percent. These search results reveal that topics on project management research stay relatively conservative in the particular project management field from these studies. Then, a further classification of these studies by subjects is displayed. As shown in Figure 2c, the subject of “architectural science and engineering” accounts for the highest proportion, followed by “industrial economics”, “macroeconomic management and sustainable development”, “business economics”, and “computer software and computer applications”. These subjects share more than 60 percent of the total project management-related studies.

It can be seen from these project management-related studies that project management knowledge has been widely used worldwide in recent years, covering multiple research fields of environmental science, engineering, social sciences, et al. Especially in developing countries accompanied by rapid industrial development, project management research has been well applied in actual engineering projects covering a wide range of fields in urbanization and urban infrastructure forums. During the implementation process of an engineering project, a reasonable project delivery method is usually considered as the suppressed premise of high-quality project completion on time or ahead of schedule.

2.2. Development of the IPD Method

2.2.1. Introduction of the IPD Method

Emerging project delivery methods in engineering projects have attracted increasing attention in the international engineering fields [21]. With continuous progress in science, technology, social economy, and international financial service systems, more requirements of higher construction levels and the management ability of international contractors are put forward to deal with the larger investment scale of international engineering projects and greater complexity of international engineering projects [22,23]. The selection basis of one particular project delivery method is usually determined by several factors, including the project owner’s capacity and level of involvement, the degree of participation of the project management or construction engineering company, and the scope of their services. These factors collectively dictate the organizational and implementation approach for project management. This research aims to conduct a comparative analysis of several commonly used methods: Engineering Procurement Construction (EPC), Owner’s Construction Management (OCM), Owner’s Representative (OR), and the Integrated Project Delivery (IPD) method.

• The EPC method.

The Engineering Procurement Construction (EPC) method is a globally recognized management approach that integrates design, procurement, and construction [12]. In this method, the owner must complete the pre-project work by themselves or entrust experts to complete the project, then select the general contractor through public bidding. In the process of project construction, the general engineering contractor is entrusted by the owner to undertake all or most of the work of the project’s design, procurement, and construction within the scope of the contract. The owner’s representative oversees project budgeting and completion acceptance, among other responsibilities. The EPC general contractor must also manage various risks, including design uncertainties, environmental changes, unexpected circumstances, and challenges.

Generally, the owner’s contract is with the general contractor on only one side of the project, who then subcontracts the design, procurement, and construction. The three segments of engineering subcontracting can be composed in various combinations. The EPC method can be flexible depending on the project’s size and the owner’s requirements. And it is widely used worldwide [24], where all parties are familiar with the procedures involved. However, with this method, the owner lacks the project management personnel to serve it directly, and the investment in the early stage is high. When there is a significant change in the project, it is easy to cause more claims, and if there is a dispute between the design unit and the construction subcontractor, the owner’s interests are often jeopardized [25].

• The OCM method.

The Owner’s Construction Management (OCM) method refers to the owner-led approach to project management. In this method, the owner establishes a project management department within a matrix system that takes on the responsibility of project construction on behalf of the owner [26,27]. This department is solely accountable for organizing and implementing the construction project. In the OCM method, a temporary function is established under the owner, primarily staffed by permanent employees in key management positions. In contrast, secondary staff members are usually seconded or recruited temporarily. Presently, numerous small- to medium-sized projects adopt the OCM method, particularly those with relatively simple requirements and modest investments.

Under the OCM method, project management on the owner’s side becomes more involved, and tasks are decentralized. The owner must allocate significant human and material resources to ensure effective project control and meet quality, cost, and schedule requirements. On the other hand, the OCM method also imposes high demands on the owner’s professional and managerial capabilities. The owner’s ability to build upon and apply previous construction experience, the freedom to select supervisors for project oversight, control over design requirements, and complete decision-making power regarding project implementation. Nevertheless, suppose the owner lacks adequate management personnel or the necessary management experience to meet project management standards. In that case, the achievement of project goals cannot be assured, potentially resulting in project failure and investment loss.

• The OR method.

The Owner’s Representative (OR) method is a project delivery method in which the owner hires a professional project management company to manage and provide services on behalf of the owner for the whole process or several stages of the organization and implementation of the project [26]. Project management companies with OR qualifications have a strong technical force, complete professional configuration, rich experience in engineering management, mature project management systems and mechanisms, and integrated project management software platforms. As a result, they have increasingly become the primary providers of project management service outsourcing.

OR contractors typically begin with the owner’s investment planning, conducting project planning, organization, and interface coordination on behalf of the owner. They also effectively oversee the project’s schedule, quality, cost, and other critical elements throughout the construction process, including project design, construction, and acceptance, to achieve the desired objectives [28]. With the OR method, the owner needs to retain a smaller workforce to manage the project and make decisions on critical issues, thus allowing the owner to focus more on their core business. However, this approach also results in limited owner involvement, restricted change rights, and potential coordination challenges. The primary risk for the owner lies in selecting a reputable project management company [13].

• The IPD method.

Due to the characteristics of significant investment, long cycle, high complexity, and complex coordination in large- and medium-sized engineering projects, the Integrated Project Delivery (IPD) method has gradually become known and applied in recent years. It has been created to fit the requirements of the international engineering field in particular [29,30]. IPD is an integrated system that combines organizational personnel, project management processes, engineering and construction connections, and management objectives. This integration ensures a streamlined and consistent approach to project implementation [31]. The IPD method involves the implementation of multifaceted agreements encompassing a collaborative team comprising architects, engineers, and construction experts representing diverse organizations [32].

In recent years, large-scale engineering construction projects have come to the fore in the context of rapid urbanization. These projects have a large amount of investment and a long construction period with vital time nodes and many personnel and organizations, making their management very difficult. Other entities usually carry out the different phases of project implementation, often forming separate management processes. It is prone to problems such as fragmentation of functional relationships, lack of communication, and inconsistent objectives. According to the characteristics of these large construction projects, the IPD method has begun to be accepted with more prominent features in the application of engineering practice and has been widely adopted in these specific construction fields.

2.2.2. Benefits of the IPD Method Compared to Other Methods

To be precise, the IPD method is a fusion of several OCM and OR and EPC methods. It integrates the strengths of each method and complements the weaknesses and shortcomings of each delivery method [17]. Each participating unit combines the team strengths of each party to cooperate and manage together, avoiding the contradiction of traditional project delivery [33]. Integration management integrates the original independent project processes and elements together, which is conducive to the standardization and integrity of large-scale project design and construction [34].

The IPD method involves the establishment of a collaborative project management department by the owner, engineering project management company, and other involved parties, according to a cooperation agreement. This collaborative entity jointly manages the entire project process. This integration encompasses the integration of organizational structure and staffing. In addition, this method facilitates the integration of various project management process systems and the targeted interests of all parties involved in the project [35]. Owners can leverage the expertise of project management contractors and benefit from their skilled professional knowledge and project management experience. This allows for a rational redistribution of integration within the project organization, enabling the utilization of the contractor’s expertise while maintaining owner control.

Compared to other delivery methods, IPD excels in mobilizing and complementing the technical expertise and project delivery experience of team members, maximizing the use of project resources [36]. Owners can focus on their core competencies by delegating project management responsibilities to contractors and transferring most project management tasks. This approach addresses owner workforce constraints and maximizes resource utilization, resulting in significant value adds to the project. Additionally, the owner’s management system, experience, and tools are enhanced through this process, establishing a stronger foundation for future projects.

By adopting the IPD method, integrated teams are formed to create a new type of “partnership” in which participants work together based on mutual respect and resource sharing. It enables unified decision-making and the hierarchical management of projects, which dramatically improves the efficiency and management level of project management during the construction period. The operational mechanism of IPD is characterized by integrated management. The method particularly highlights the synergy between individual members of the organization and organizational goals in the management concept so that the members can better achieve cooperation. The IPD method enhances the owner’s participation and decision-making power in project management, resulting in project outputs that align with the owner’s expectations and requirements. In collaborative cooperation, the owner’s participants can also acquire advanced project management systematic knowledge, and their management capabilities can improve.

2.2.3. Integration of IPD and Other Methods

In complex and challenging large-scale petrochemical projects, such as those involving large oil fields and long-distance pipelines, the owner’s management and technical capabilities alone may not be sufficient to handle all aspects of the project [37], from the initial definition phase to the management of EPC contractors during implementation [38]. To address this issue, many oil companies have successfully adopted the OR and EPC method, which involves introducing an OR management company to compensate for the owner’s lack of expertise. However, this method has its limitations. Firstly, the widely used “Cost and Fee” billing method of OR can lead to high contracting costs because OR management companies sometimes prioritize their interests at the expense of project schedules and costs. Secondly, the owner may lack effective control over the construction process when using this method, resulting in inefficiency.

To overcome these drawbacks, the IPD and EPC project delivery method has been proposed [39]. This method inherits the advantages of the OR method’s management specialization while addressing its shortcomings. It is a new method that expands and extends the “Owner and OR and EPC” method, fundamentally different from the newer IPD method. The IPD and EPC method aims to balance practical management specialization and maintaining control over the construction process, offering a more efficient and cost-effective approach to project management in complex petrochemical projects.

2.2.4. Research Necessity of the IPD Method in Engineering Projects

According to existing research, the organization structure of the IPD method has reached a stable state. The strengths and weaknesses of this method have been identified, and an academic consensus has been reached [40]. The IPD method leverages the abilities of both the owner and the consultant to enhance project efficiency [41]. It also enables the owner to control and supervise the project effectively throughout the process [42]. Additionally, it facilitates the owner’s development of competent management personnel. Several characteristic analyses prove that integrating IPD and EPC and other methods usually exhibits remarkable advantages in actual projects.

However, emphasis on the scientific selection of project delivery methods through advanced, precise, and rational assessment methods is insufficient. The lack of a clear delineation of rights and responsibilities among parties involved in the IPD method may result in project inefficiencies [43]. Currently, it is still difficult to quantitatively judge the applicability and adaptability of these management methods. Advanced solutions addressing the adaptability analysis of the IPD method in large- and medium-sized engineering projects are rarely discussed in detail. Therefore, a reasonable advanced decision-making method should be conducted to illustrate the adaptability analysis of the IPD method in specific engineering.

3. Modeling Methods

Given the distinctive features of the IPD method and the specific requirements of medium and large-sized engineering projects, a systematic and objective evaluation model is essential for assessing the adaptability of the IPD method for such projects. In this research, the widely recognized decision theory model, the Fuzzy Analytic Hierarchy Process (FAHP) [19], is employed to comprehensively analyze and assess the IPD adaptability by considering various aspects of considerations in these medium and large-sized projects. The study outlines a set of computational equations to quantitatively measure the IPD method’s adaptability, as discussed below.

3.1. FAHP-Based Evaluation Indicators

3.1.1. A Brief Description of FAHP Theory

Among the various decision-making methods, the Analytic Hierarchy Process (AHP) [44,45] is preferred by many contractors for its ability to effectively blend qualitative and quantitative aspects in addressing diverse evaluation factors and its system flexibility. The AHP method conducts quantitative analysis based on qualitative analysis, facilitating a more cohesive integration of the two. Additionally, it offers a systematic approach to problem analysis, aiding in scientific management and rational decision-making. The AHP method initiates qualitative and quantitative analysis by breaking down the decision problem elements into distinct levels of objectives, criteria, and scenarios, thereby mathematizing and systematizing the analyst’s thought process. The AHP method identifies key decision factors through decomposition and synthesis, assigns weights based on their interrelationships, and establishes an analytical structural model to determine the optimal solution.

However, the AHP method has limitations. It can only select the best option from the original choices and may not generate entirely new and improved alternatives [46]. Furthermore, it may prioritize a suboptimal option over others, and inconsistencies in judgment matrices may complicate the decision-making process, requiring multiple adjustments to achieve consistency.

To overcome these limitations, the FAHP model emerges as a practical solution for multi-objective evaluation and decision-making problems with optimal ranking [47]. Differing from the AHP method, FAHP categorizes indicators, uses fuzzy mathematical tools [48] to determine indicator weights, and employs the fuzzy comprehensive judgment method for thorough evaluation. By establishing relationships between factors, creating a judgment matrix, and calculating relative indicator weights, FAHP effectively addresses bias in systematic scoring, enhancing the realism and accuracy of evaluation processes and outcomes [49].

3.1.2. FAHP-Based Indicators

Indicators affecting the decision-making for choosing the IPD method are first focused on during the quantitative adaptability evaluation. Four dimensions of cost, risk, management, and schedule are usually recognized as critical indicators that could significantly influence successful project implementation and management [50,51]. The IPD method is designed to ensure effective control of infrastructure projects in terms of these four aspects to achieve project objectives. These interconnected indicators require integrated consideration and balance to ensure comprehensive project control. Thorough evaluation of these indicators when selecting an IPD method can assist the project management team in achieving project objectives and ensure smooth project implementation and management. Therefore, drawing from a review of the pertinent literature and insights gained from large- and medium-sized engineering projects, “Cost control”, “Risk control”, “Management control”, and “Schedule control” are identified and utilized as four first-level indicators. These indicators are considered crucial aspects that influence project construction.

In the FAHP model, the bottom level is the sub-criteria level, which contains all the elements to be sorted; the middle level is the criterion level, which governs the lower elements and is also governed by the upper elements to determine the criterion for the sorting of the elements; and the highest level, which has only one element, is called the target level [52]. The highest level is the score for IPD method selection, denoted as $P_{IPD}$, which is a quantitative indicator of whether to select the IPD method in an engineering project during the decision process.

• Cost control.

Cost control is a crucial process in project management, encompassing budgeting, monitoring, and adjusting project costs throughout the project lifecycle. This involves comparing actual costs to estimated costs, identifying discrepancies, and preparing forecasts to ensure the rational allocation of project resources and maintain cost control. Development cost (DC), purchase cost (PCC), production cost (PDC), and selling cost (SC) are key factors influencing the overall project cost control.

DC encompasses expenses related to real estate sales, including the fees for ancillary facilities, environmental landscaping, and external pipeline networks. PCC comprises materials and procurement-related other expenditures. PDC refers to the expenses incurred by the production unit for manufacturing products or providing labor services, serving as a crucial indicator of the enterprise’s technical and management capabilities. SC includes the production expenses of sold products, labor costs for services provided, and other business-related sales expenses.

By effectively managing development, purchase, production, and selling costs, project teams can optimize cost control measures and enhance project performance.

• Risk control.

Risk control encompasses the measures and strategies employed by managers and risk controllers to mitigate potential risks and minimize associated losses, aiming to reduce the likelihood of risk events and prevent unmanageable losses. It involves identifying existing or potential risks during the risk identification process and analyzing their impact on project construction based on their likelihood of occurrence and severity of loss. In the project construction process, the occurrence of a risk event can impact various project attributes, including schedule, quality, cost, and personnel, leading to Schedule Risk (SR), Quality Risk (QR), People Risk (PR), and Cost Risk (CR).

SR pertains to potential schedule disruptions in the project, which can result in project delays. SR involves the possibility of quality issues such as requirement changes, design flaws, or inadequate testing. PR arises from uncertainties and potential risks within an enterprise or organization stemming from human behavior and quality. CR encompasses the probability and severity of foreseeable hazardous situations, comprehensively assessing the risks and consequences associated with cost-increasing scenarios.

• Management control.

Management control involves effectively organizing, planning, and coordinating resources to achieve specific objectives in practical work and establishing routine working procedures and management systems. Its purpose is to enable the strategy to be implemented to achieve the organization’s goals. This encompasses Quality Management (QM), Investment Management (IM), Human Resources Management (HRM), Health, Safety, and Environment Management (HSEM), and Communication Management (CM).

QM encompasses all management activities to define quality programs and implement them through quality system processes. IM involves the comprehensive management of tasks throughout the investment project development cycle to achieve investment objectives using project management principles. HRM consists of formulating human resource policies and corresponding management activities within an enterprise. HSEM is a comprehensive system focusing on health, safety, and environmental considerations [53]. CM is vital for organizational success, as effective communication is integral to management. By understanding customer needs, integrating resources, and delivering quality products and services, organizations can create value for customers and generate wealth for the enterprise and society.

• Schedule control.

Schedule control in engineering refers to the process of monitoring and adjusting the progress of a project to ensure that it can be completed on time according to plan. It is combined with the process of time and the need for deadlines. It is mainly used to control whether the production or engineering progress is completed on schedule and whether the operations can relate to each other in time. According to the project development and construction process, it is divided into five progress nodes: Initiation Phase (IP), Exploration Phase (EP), Construction Phase (CP), Acceptance Phase (AP), and Operation and Maintenance Phase (OMP).

IP puts a predetermined project into the formal implementation stage, which contains the basic information of the project’s goal, plan, time and cost, etc., and is an indispensable step in the realization process of the project. EP includes engineering surveys, engineering geology, and hydrogeology investigations, which are a series of comprehensive evaluations conducted to find out the natural conditions of the project’s construction site. CP is a critical stage of capital construction. It is essential that construction activities adhere to the engineering design, construction organization design, and acceptance specifications to guarantee timely completion and high-quality outcomes. AP refers to the acceptance of quality assurance information, quality control information, and physical appearance of the unit work, as well as the acceptance phase of physical safety function sampling. OMP is the process by which the deliverables of a project are put into production or operation to produce benefits on an ongoing basis. Figure 3 illustrates the correlation between the eighteen sub-criteria levels and the four criterion levels, as well as their association with the target level.

3.2. FAHP-Based Modeling Process

The FAHP method converts the qualitative assessment of the system into a quantitative evaluation based on an Intuitionistic Fuzzy Set (IFS) [48], which represents the degree of agreement or disagreement of decision-makers towards the indicator. As shown in Figure 4, $S_1$ represents the indicator of Cost control; $S_2$ displays the indicator expressing Risk control; $S_3$ is the indicator describing Management control; $S_4$ is the indicator reflecting Schedule control. Each S has its corresponding secondary indicator, and the number of these basic characteristic parameters of its S varies with different considerations. For $S_1$ and $S_2$, there are four basic characteristic parameters with the j value of 4, while $S_3$ and $S_4$ cover five characteristic parameters and the j takes the value of 5.

Some basic calculation steps applied in this manuscript are shown as follows.

Step 1 (Definitions): We consider that $S_k\left(k=1,2,3,4\right)$ represents the integrated spatial factors. Let $X=\{x_1$, $x_2$, $x_3$, …, $x_n\}$ be a finite set of alternatives, in which $x_i$ (i = 1, 2, …, n) means the sub-factors of the corresponding $S_k$. Then, $\omega$ means the underlying subjective priority weight, which belongs to a vector $\omega$ = (${\omega }_1$, ${\omega }_2$, ${\omega }_n$) with ${\omega }_i>0\left(i=1,2,\dots ,n\right)$, and ${\sum }_{i=1}^n{\omega }_i=1$. Then, let a matrix $A={\left(a_{ij}\right)}_{n\times n}$, where $a_{ij}$ is the intensity of preference of $x_i$ over $x_j$ measured using the 0.1 to 0.9 scales and satisfies the reciprocal conditions $0<a_{ij}<1$ and $a_{ij}+a_{ji}=1$. $a_{ij}$ indicates the degree that the alternative $x_i$ is preferred to $x_j$, and the case $a_{ij}=0.5$ indicates that there is indifference regarding the alternatives $x_i$ and $x_j$.

Step 2 (Weight calculation): We consider the matrix $A={\left(a_{ij}\right)}_{n\times n}$ as a fuzzy complementary judgment matrix. Then, summing the data according to matrix row, we obtain $r_i={\sum }_{k=1}^n{a}_{ik}$, $i=1,2,\dots ,n$. Then, after mathematical transformation we obtain $r_{ij}=\left(r_i-r_j\right)/a+0.5$. Let $a=2\left(n-1\right)$; then, we obtain $r_{ij}=\frac{\left(r_i-r_j\right)}{2\left(n-1\right)}+0.5$. Thus, $R={\left(r_{ij}\right)}_{n\times n}$ is a fuzzy complementary judgment matrix. Then, with the normalizing rank aggregation, we apply the matrix R to the n-dimensional vector $\omega =\left({\omega }_1,{\omega }_2,\dots ,{\omega }_n\right)$ and obtain the calculation formula ${\omega }_i=\frac{{\sum }_{i=1}^n{a}_{ij}+\frac{n}{2}-1}{n\left(n-1\right)}$.

Step 3 (Consistency check): If $A={\left(a_{ij}\right)}_{n\times n}$ and $B={\left(b_{ij}\right)}_{n\times n}$ are both fuzzy complementary judgement matrixes, then $CI\left(A,B\right)\frac{1}{n^2}{\sum }_{i=1}^n{\sum }_{j=1}^n\left|a_{ij}-b_{ij}\right|$ is the compatibility indicator of A and B. Then, if we consider $W={\left(W_1,W_2,\dots ,W_n\right)}^{\Gamma }$ as the weight vector of $A={\left(a_{ij}\right)}_{n\times n}$, then ${\omega }_{ij}={\omega }_i-{\omega }_j+0.5$ and then, $CI\left(A,W\right)\frac{1}{n^2}{\sum }_{i=1}^n{\sum }_{j=1}^n\left|a_{ij}-{\omega }_{ij}\right|$ is the compatibility indicator of $A={\left(a_{ij}\right)}_{n\times n}$. If $CI\left(A,W\right)<\partial$ (where ∂ represents the attitude of the decision-maker and is usually set as 0.1), we consider the matrix $A={\left(a_{ij}\right)}_{n\times n}$ to be consistently acceptable and then calculate the weight values.

Step 4 (Hierarchy sort): We singly sort the $W={\left(W_1,W_2,\dots ,W_n\right)}^{\Gamma }$, and obtain the relative weight of an element on a given layer compared to a related element on the previous layer. Then, we perform hierarchical total ordering and calculate the ranking weights of the relative importance of all elements with respect to the target layer, a process that starts at the highest layer and proceeds layer by layer to the lowest layer. For example, $S_1$ includes n risky determinates $X=\{x_1$, $x_2$, $x_3$, …, $x_n\}$, and its weight proportional to $S_1$ separately is $a=\left\{a_1,a_2,a_3,\dots ,a_n\right\}$. And the next level of the $A_1$, which includes m parameters, designed to $B=${$B_1,B_2,B_3,\dots ,B_m\}$. The weight proportional of the B to $A_1$ is b = $\{b_{j1},b{j}_2,b{j}_3,\dots ,b_{jm}\}$. Then, we consider the $b_j={\displaystyle \sum _{k=1}^m}{a}_k{b}_{kj},\left(j=1,2,\dots ,m\right)$. The weights of the remaining layers are also calculated layer by layer in this way, until the bottom layer, we can obtain the weight order of all factors relative to the top layer, which is the target layer, and we can realize the importance order of all factors.

Following the steps outlined in the FAHP model, we derive the mathematical equations necessary to compute the final decision evaluation value. The detailed calculation steps are shown in Figure 4.

3.3. Decision-Making Score Evaluation Method

The selection of comprehensive evaluation indexes for deciding the IPD method is established based on a thorough consideration of engineering projects. This process involves an extensive selection of indexes related to Cost control, Risk control, Management control, and Schedule control. The comprehensive evaluation of the IPD method includes many qualitative indexes, making it challenging to define the boundaries of relative opposites. The FAHP provides a powerful aid in transforming qualitative indicators into quantitative indicators; relative concepts such as high and low project costs and fast and slow project schedules can be accurately quantified.

In the FAHP model, $a_{ij}$ represents the importance of one criterion relative to another. The value of $a_{ij}$, ranging from 0.1 to 0.9 in increments of 0.1, is determined based on experts’ judgments using the Saaty 1–9 scale [54]. A lower $a_{ij}$ value indicates less importance attached to the indicator than others at the same level. By comparing each indicator with others at the same level, an evaluation matrix is constructed to calculate the weight value of each indicator. This process helps determine the significance of different indicators in the evaluation of the IPD method.

As shown in

Table 1. Expert scoring table.

Target Level	Criterion Level
$P_{IPD}$		Cost control	Process control	Management control	Schedule control
	Cost control	0.5
	Risk control		0.5
	Management control			0.5
	Schedule control				0.5
Criterion Level	Sub-Criteria Level
Cost control		DC	PCC	PDC	SC
	DC	0.5
	PCC		0.5
	PDC			0.5
	SC				0.5
Risk control		SR	QR	PR	CR
	SR	0.5
	QR		0.5
	PR			0.5
	CR				0.5
Management control		QM	IM	HRM	HSEM	CM
	QM	0.5
	IM		0.5
	HRM			0.5
	HSEM				0.5
	CM					0.5
Schedule control		IP	EP	CP	AP	OMP
	IP	0.5
	EP		0.5
	CP			0.5
	AP				0.5
	OMP					0.5

, the expert scoring table is utilized to create the evaluation matrix, encompassing the assessment of four first-level indicators and eighteen second-level indicators. Experts can methodically compare element weights using this table, drawing on their engineering expertise to establish a comprehensive weight matrix. A value of 0.5 serves as the threshold: values above 0.5 signify the column elements’ higher significance compared to the row elements. The greater the deviation from 0.5, the greater the importance, and conversely.

Determining the rating levels in the sub-indicators using expert scoring allows further calculation of the scores for each $S_i$, resulting in a rating score for the IPD method. The method’s indicator level evaluation, which must meet the basic level requirements for most indicators to qualify, uses a value greater than or equal to 3 as the basis for selection. As shown in Figure 5, four $S_i$ scales are illustrated, where a position further to the right on the scale indicates better adaptation of the IPD method to the metric. In comparison, a position towards the left suggests poorer adaptation.

Among these indicators, Cost control utilizes cost as a control measure. A score exceeding 3 in engineering signifies that employing the IPD method can effectively reduce project costs, leading to cost savings. Similarly, a score above 3 in Risk control indicates that the IPD method can mitigate or minimize the likelihood of risk events and their associated losses. Manage control involves the managerial influence on organizational members to align with the organization’s strategy. A score exceeding 3 indicates the effective utilization of the IPD method in this aspect. Schedule control involves employing systematic methods to meet scheduling objectives in harmony with quality, cost, and safety goals. A score above 3 of Schedule control suggests that the IPD method can expedite project scheduling, thereby reducing duration and enhancing efficiency while aligning with quality, cost, and safety objectives.

In general, using the FAHP model to evaluate each index of the IPD method, the evaluation function model of IPD method selection is established through weight assignment and calculation, which provides a calculation basis and practical tool for the optimal delivery method scheme of engineering projects.

4. Results and Case Application

4.1. Mathematical Expressions for IPD Adaptability

Based on the fuzzy hierarchical analysis, the final model expression of the IPD is as follows.

$$\begin{array}{c}{P}_{IPD}={\omega }_c\times S_1+{\omega }_r\times S_2+{\omega }_m\times S_3+{\omega }_s\times S_4\end{array}$$

(1)

where, $P_{IPD}$ represents the evaluation values of the IPD method. ${\omega }_c$ denotes the weight assigned to Cost control, with $S_1$ representing the corresponding indicators. Similarly, ${\omega }_r$ indicates the weight for Risk control, with $S_2$ as the associated indicators. The weight for Management controls is denoted by ${\omega }_m$, with $S_3$ representing the Management control indicators. Additionally, ${\omega }_s$ signifies the weight allocated to Schedule control, with $S_4$ representing the Schedule control indicators. The S also contains subsidiary evaluation indicators S $=\left\{S_1,S_2,S_3,S_4\right\},$ which expression is as follows for example.

$$\begin{array}{c}{S}_{\mathrm{i}}={\omega }_1\times V_1+{\omega }_2\times V_2+{\omega }_3\times V_3+{\omega }_4\times V_4\end{array}$$

(2)

According to the FAHP model described above, screening of appropriate experts is necessary. This study used the F-test to calculate the number of experts with an effect size of 0.25 ($\alpha$ = 0.05, 1 −$\beta$ = 0.8), quantifying a significant difference between groups [55]. G*Power 3.0.10 software was used to calculate the sample size. During the calculation, the number of measurements was five, denoting the maximum limit of secondary indicators, and with the number of measurements was four, each consisting of four measures. After calculation, the required sample size was determined as 30, as shown in Appendix A. Therefore, more than thirty experts participated in the questionnaire, covering a wide professional range, including engineers, managers, and academics in related fields across the whole of China. In this way, the calculation results can be applied to relevant large- and medium-sized engineering projects in different regions. Each expert provided ratings for the weight matrix based on Table 1 in the questionnaire, and the average scores from all experts were computed to determine the weight assigned to each indicator in the evaluation process.

The first level indicator of Cost control according to the questionnaire can be obtained as a judgment matrix:

$$\left[\begin{array}{cccc}0.50& 0.15& 0.30& 0.25\\ 0.85& 0.50& 0.15& 0.30\\ 0.70& 0.85& 0.50& 0.15\\ 0.75& 0.70& 0.85& 0.50\end{array}\right]$$

(3)

It can be calculated according to the weighting formula:

$$\begin{array}{c}{\omega }_1=\frac{{\sum }_{i=1}^n{a}_{1_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.267\end{array}$$

(4)

$$\begin{array}{c}{\omega }_2=\frac{{\sum }_{i=1}^n{a}_{2_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.233\end{array}$$

(5)

$$\begin{array}{c}{\omega }_3=\frac{{\sum }_{i=1}^n{a}_{3_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.317\end{array}$$

(6)

$$\begin{array}{c}{\omega }_4=\frac{{\sum }_{i=1}^n{a}_{4_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.183\end{array}$$

(7)

The first-level indicator of the Cost control calculation equation is

$$\begin{array}{c}{S}_1=0.267\times v_{dc}+0.233\times v_{pcc}+0.317\times v_{pdc}+0.183\times v_{sc}\end{array}$$

(8)

The first-level indicator of the Risk control calculation equation is

$$\left[\begin{array}{cccc}0.50& 0.15& 0.25& 0.35\\ 0.85& 0.50& 0.15& 0.25\\ 0.75& 0.85& 0.50& 0.15\\ 0.65& 0.75& 0.85& 0.50\end{array}\right]$$

(9)

$$\begin{array}{c}{\omega }_1=\frac{{\sum }_{i=1}^n{a}_{1_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.271\end{array}$$

(10)

$$\begin{array}{c}{\omega }_2=\frac{{\sum }_{i=1}^n{a}_{2_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.229\end{array}$$

(11)

$$\begin{array}{c}{\omega }_3=\frac{{\sum }_{i=1}^n{a}_{3_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.188\end{array}$$

(12)

$$\begin{array}{c}{\omega }_4=\frac{{\sum }_{i=1}^n{a}_{4_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.312\end{array}$$

(13)

The first-level indicator of the Risk control calculation equation is

$$\begin{array}{c}{S}_2=0.271\times v_{sr}+0.229\times v_{qr}+0.188\times v_{pr}+0.312\times v_{cr}\end{array}$$

(14)

The first-level indicator of the Management control calculation equation is

$$\left[\begin{array}{ccccc}0.50& 0.10& 0.15& 0.20& 0.35\\ 0.90& 0.50& 0.10& 0.15& 0.20\\ 0.85& 0.90& 0.50& 0.10& 0.15\\ 0.80& 0.85& 0.90& 0.50& 0.10\\ 0.65& 0.80& 0.85& 0.90& 0.50\end{array}\right]$$

(15)

$$\begin{array}{c}{\omega }_1=\frac{{\sum }_{i=1}^n{a}_{1_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.260\end{array}$$

(16)

$$\begin{array}{c}{\omega }_2=\frac{{\sum }_{i=1}^n{a}_{2_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.233\end{array}$$

(17)

$$\begin{array}{c}{\omega }_3=\frac{{\sum }_{i=1}^n{a}_{3_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.167\end{array}$$

(18)

$$\begin{array}{c}{\omega }_4=\frac{{\sum }_{i=1}^n{a}_{4_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.200\end{array}$$

(19)

$$\begin{array}{c}{\omega }_5=\frac{{\sum }_{i=1}^n{a}_{5_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.140\end{array}$$

(20)

The first-level indicator of the Management control calculation equation is

$$\begin{array}{c}{S}_3=0.260\times v_{qm}+0.233\times v_{im}+0.167\times v_{hrm}+0.200\times v_{HSEm}+0.140\times v_{cm}\end{array}$$

(21)

The first-level indicator of the Schedule control calculation equation is

$$\left[\begin{array}{ccccc}0.50& 0.05& 0.15& 0.30& 0.35\\ 0.95& 0.50& 0.05& 0.15& 0.30\\ 0.85& 0.95& 0.50& 0.05& 0.15\\ 0.70& 0.85& 0.95& 0.50& 0.05\\ 0.65& 0.70& 0.85& 0.95& 0.50\end{array}\right]$$

(22)

$$\begin{array}{c}{\omega }_1=\frac{{\sum }_{i=1}^n{a}_{1_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.173\end{array}$$

(23)

$$\begin{array}{c}{\omega }_2=\frac{{\sum }_{i=1}^n{a}_{2_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.227\end{array}$$

(24)

$$\begin{array}{c}{\omega }_3=\frac{{\sum }_{i=1}^n{a}_{3_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.257\end{array}$$

(25)

$$\begin{array}{c}{\omega }_4=\frac{{\sum }_{i=1}^n{a}_{4_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.143\end{array}$$

(26)

$$\begin{array}{c}{\omega }_5=\frac{{\sum }_{i=1}^n{a}_{5_{ij}}+\frac{n}{2}-1}{n\left(n-1\right)}=0.200\end{array}$$

(27)

The first-level indicator of the Schedule control calculation equation is

$$\begin{array}{c}{S}_4=0.173\times v_{\mathrm{ip}}+0.227\times v_{\mathrm{ep}}+0.257\times v_{cp}+0.143\times v_{ap}+0.200\times v_{omp}\end{array}$$

(28)

where, $v_{\mathbf{dc}}$ is development cost, $v_{\mathbf{pcc}}$ is purchase cost, $v_{\mathbf{pdc}}$ is production cost, $v_{\mathbf{sc}}$ is selling cost; $v_{\mathbf{sr}}$ is schedule risk, $v_{\mathbf{qr}}$ is quality risk, $v_{\mathbf{psr}}$ is people risk, $v_{\mathbf{cr}}$ is cost risk; $v_{\mathbf{qm}}$ is quality management, $v_{\mathbf{im}}$ is investment management, $v_{\mathbf{hrm}}$ is human resources management, $v_{\mathbf{HSEm}}$ is HSE management, $v_{\mathbf{cm}}$ is communication management; $v_{\mathbf{ip}}$ is initiation phase, $v_{\mathbf{ep}}$ is exploration phase, $v_{\mathbf{cp}}$ is construction phase, $v_{\mathbf{ap}}$ is the acceptance phase, $v_{\mathbf{omp}}$ is the operation and maintenance phase.

The final evaluation model expression is

$$\begin{array}{c}{P}_{IPD}=0.273\times S_1+0.228\times S_2+0.189\times S_3+0.310\times S_4\end{array}$$

(29)

Based on the evaluation ratings, sub-indicators can be used to calculate the IPD values under multiple sampling $S_1$, $S_2$, $S_3$, and $S_4$ combinations. The $P_{\mathbf{IPD}}$ magnitude can be calculated based on the final evaluation model expression. The model’s indicator level evaluation, which needs to meet the requirements of the base plane for most indicators to be qualified, takes a value greater than or equal to 3 as the basis for selection. The IPD method is applicable to a specific project when the calculated P score for that project is greater than or equal to 3. As shown in Figure 6, it illustrates the calculation of the coefficient matrix for the IPD method using the FAHP model.

The results indicate a clear hierarchy of the importance of various indicators within the IPD method. In Cost control, PDC occupies the majority proportion, followed by DC, PCC, and SC. This prioritization underscores the emphasis on investing in production costs, particularly construction materials, over selling costs. In Risk control, CR takes up a more excellent reweighting ratio, reflecting a focus on mitigating financial risks to ensure project cash flow remains unimpeded. While risks related to personnel, such as construction-related injuries, bear a lower weight, they are not to be disregarded.

Management control sees QM as the most critical indicator, followed by IM, HSEM, HRM, and finally CM. It may demonstrate a commitment to ensuring high-quality project outcomes. Progress control highlights the importance of CP in managing construction phase timelines, with AP carrying less weight due to its position at the project’s conclusion. In the final evaluation model expression, Schedule control reigns supreme, followed by Cost control, Risk control, and finally Management control. It aligns with the IPD method’s emphasis on optimizing economic benefits through efficient project cycles and cost reductions.

4.2. Case Application

4.2.1. Description of the Case Project

A case project in Fujian, China, has been selected to express the IPD application. The case project is a significant collaboration between the multiple cooperative institutions [56]. This project aims to establish an oil refining capacity of 8 million tons per year, along with an ethylene production capacity of 800,000 tons per year, encompassing 18 process units and associated infrastructure. Initially, the project adopted the OR method, engaging a consortium of two international oil companies through a public tender. The International Engineering Company was also involved in the EPC contracting for the ethylene and Integrated Gasification Combined Cycle (IGCC) plants.

As the project progressed, various issues and discrepancies within the management model became apparent. Divergent corporate cultures and interests among the OR parties led to conceptual differences, resulting in sluggish project advancement. Moreover, discrepancies between the construction standards of foreign companies and those in Chinese projects significantly impeded project development. Financially, the project experienced substantial cost overruns, with the OR construction exceeding the budget by RMB 4.5 billion. The management fees and implementation costs associated with the OR method were exorbitant, with project management expenses reaching RMB 400 million. One of the oil companies quoted RMB 1.8 billion for the ethylene plant, while another RMB 200 million was paid for the IGCC plant. In terms of scheduling, the project faced significant delays. Under the OR method, completion was estimated to take fifty months, with an additional ten months required for operational readiness.

4.2.2. Application of the IPD Method

To address the OR method’s deficiencies, the project requires a dynamic and efficient management approach to enhance performance in management, cost, and scheduling aspects. Based on the research, the IPD method may effectively address these shortcomings. This study used the FAHP model to evaluate the adaptability of the IPD method to the primary conditions. First, the weighting calculation, determining the coefficient matrix V and S using the FAHP model, was determined through a ranking assessment conducted by the expert group. As shown in

Table 2. Weighting calculation using the FAHP model.

Indicators	Weighting Calculation	Scale
$S_1$	$S_1=0.267\times 3+0.233\times 5+0.317\times 4+0.183\times 2$	3.60
$S_2$	$S_2=0.271\times 4+0.229\times 3+0.188\times 2+0.312\times 5$	3.71
$S_3$	$S_3=0.260\times 3+0.229\times 4+0.167\times 3+0.200\times 1+0.140\times 5$	3.10
$S_4$	$S_4=0.173\times 1+0.227\times 5+0.257\times 4+0.143\times 3+0.200\times 3$	3.37
$P_{IPD}$	$P_{IPD}=0.273\times 3.60+0.228\times 3.71+0.189\times 3.10+0.310\times 3.37$	3.46

, the scores for $S_1$, $S_2$, $S_3$, $S_4$ are 3.60, 3.71, 3.10, and 3.37, respectively. The final value of $P_{IPD}$ is 3.46, exceeding the threshold of 3, with each Si also assigning over 3. According to the evaluation threshold definition, the IPD method is well-suited for the project.

4.2.3. Comprehensive Benefit Analysis between the IPD Method and OR Method

The project staff actually applied the IPD method. After establishing infrastructure management expertise and on-site realities, a comprehensive management strategy for each project phase and process was considered based on the IPD method. This approach standardized management protocols and systems, streamlined workflows, and boosted functional department efficiency. In terms of personnel management, the IPD method differs from the OR method by aligning managers with shared cultural philosophies and objectives, fostering collaborative efforts towards common goals through contractual obligations and administrative cooperation. Notably, the owner’s oversight in the IPD method is more robust, enabling proactive leadership and decisive involvement in critical project milestones. Implementing the IPD method resulted in significant project advancements, reducing project duration by twelve months compared to the OR method and enhancing project operational efficiency. In terms of cost, the IPD method achieved substantial savings, including RMB 400 million in management expenses, RMB 1.3 billion in imported material procurement costs, and a total project investment reduction of RMB 4.5 billion compared to the OR method, yielding considerable cost efficiencies.

The successful application of this project management approach has not only expedited project delivery but also equipped the engineering construction management team with valuable experience, laying a solid foundation for cultivating skilled and proficient project management. The whole set of methods can be appropriately extended to evaluate other large- and medium-sized engineering projects, facilitating effective control of the four aspects of cost, risk, management, and schedule.

4.3. Limitations and Future Directions

4.3.1. Contributions

This study addresses the needs of large- and medium-sized engineering projects both domestically and internationally in project management, with a specific focus on the adaptability of integrated project delivery methods. Decision-making suggestions for large- and medium-sized project delivery methods are provided based on decision-theoretic parsing schemes. The results of this study are highly relevant to the project reality, offering valuable insights for management teams to effectively select delivery methods that align with project requirements such as cost, risk, management, and schedule. From a scientific research perspective, the FAHP model is innovatively applied in the decision-making process for delivery methods of large- and medium-sized projects. By establishing a weight calculation equation to construct the FAHP model, this study addresses the common challenges faced by various large- and medium-sized projects in selecting delivery methods.

4.3.2. Limitations

This paper derives the weighting formula for evaluating the applicability of IPD using the FAHP model. This study only focused on the classical FAHP model to conduct the adaptability analysis of the specific IPD method. However, in the decision theory field, numerous brilliant evaluation methods may better evaluate the adaptability analysis of different engineering management methods. When applied to managing different projects, there is a lack of detailed discussion of the advantages and disadvantages of varying decision theory models. Furthermore, in this study, the FAHP scoring results were mainly applied to one single petrochemical case project without exploring its potential in other domains, lacking a broader application across multiple cases.

4.3.3. Future Directions

Based on the current research findings, several future works can be immediately undertaken. First, while the IPD method was initially tailored for construction projects, we seek to explore its applicability across a broader spectrum of project types, including logistics management. Second, to tackle the issue of inadequate communication with engineers, we plan to develop an evaluation tool incorporating the FAHP model for automated assessment of the IPD method’s efficacy, streamlining the evaluation process for engineering projects. Last but not least, we aspire to gather additional real-world engineering cases to enhance our utilization of the FAHP model, thereby refining model precision and accuracy.

It is important to mention that the choice of experts can be customized based on different factors, such as the specific characteristics and needs of the project, as well as its unique environmental features. Professionals working across various regions and projects can create evaluation models that take into account local nuances, thereby improving the precision of the model. In addition, by increasing the number of experts and expanding into more areas in the near future, the reliability of the associated weight coefficients can be enhanced.

5. Conclusions

In large- and medium-sized engineering projects, the IPD method is favored for its excellent coordination and control characteristics. Currently, studies place more emphasis on the economic benefits brought by the IPD method, remaining in the absence of comprehensive research on the adaptability analysis of IPD. This study applies an evaluation model for analyzing IPD adaptability; weighting equations are obtained and applied in engineering projects with positive results.

Compared to the EPC, OCM, and OR methods, the IPD method combines organizational personnel, project management processes, engineering and construction connections, and management objectives. This integration ensures a streamlined and consistent approach to project implementation. Each participating unit combines the team strengths of each party to cooperate and manage together, avoiding the contradiction of traditional project management. Integration management integrates the original independent project processes and elements, which is conducive to the standardization and integrity of large-scale project design and construction.

This study conducted a matrix calculation using eighteen second-level indicators to derive weight values for four first-level indicators: Cost control, Risk control, Management control, and Schedule control. These first-level indicators were then used to formulate the total evaluation index calculation. By assigning quantitative values based on the importance of each index, the FAHP model calculated the first-level index $S_i$ and the total index $P_{IPD}$. Values exceeding 3 indicate the utilization of the IPD method in the project. The model can provide a basis for decision analysis in the case of large- and medium-sized engineering projects considering multiple aspects of the situation.

More than thirty large- and medium-sized project experts, including engineers, managers, and academics, participated in the questionnaire that resulted in the weighting matrix formula. In a practical case study of oil engineering in Fujian, the FAHP model was employed to assess the applicability of IPD. The calculated values for the four first-level indexes $S_1$, $S_2$, $S_3$, $S_4$ were 3.60, 3.71, 3.10, and 3.37, resulting in a final $P_{IPD}$ value of 3.46, all exceeding 3, indicating a high suitability for the IPD method. By implementing IPD, the project achieved significant cost savings of RMB 4.5 billion and accelerated the schedule by 12 months.

It should be noted that the evaluation results of this study are mainly applied to a petrochemical case project, and there is a lack of practical application in other large- and medium-sized engineering case studies. In the future, the research will expand the application scope of the FAHP model, increase the number of experts, and broaden their areas of expertise to enhance the model’s accuracy. As a whole, this paper contributes a novel and objective approach to the adaptability analysis of the IPD method in large- and medium-sized engineering projects by coupling decision theory into project management.