Standard Revision Project Scheduling Problem Considering Coordination Degree of Standards Systems

Abstract

Standards undergo periodic review to ensure their alignment with technological advancements and market trends. However, this process can lead to incompatibilities between standards. A major challenge for standards development organizations (SDOs) is ensuring the coordination of standards systems through effective scheduling. Traditional project scheduling models focused on minimizing the duration or cost do not meet the unique management needs of standards. This study introduces the Standard Revision Project Scheduling Problem (SRPSP), which considers revision dependencies in a standard citation network. A new objective function, the Coordination Index of Standard Systems ($\mathit{CISS}$), is proposed to quantify the coordination degree among standards within a citation network. To solve this problem, a Particle Swarm Optimization (PSO) algorithm is employed. Computational experiments using real-world data from TC544 demonstrate the framework’s superiority, achieving a 12% higher $\mathit{CISS}$ than traditional makespan-centric models. Scenarios characterized by three key parameters of standard citation networks—network topology, scale, and average node degree—are analyzed. The results provide a benchmark for researchers to compare and improve upon. This research contributes to the development of a practical data-driven decision support system for SDOs to evaluate standards revision programs and enhance the systematic effects of standards systems during the revision process.

1. Introduction

Standards have become pervasive in modern industrial and digital landscapes, serving as critical enablers of technological advancement, organizational operations, and commercial competitiveness [1]. These specifications are developed and promulgated by Standards Development Organizations (SDOs)—institutions dedicated to establishing uniform requirements for specific sectors or technical domains to ensure compatibility, safety, quality, and consistency. Within SDOs, Technical Committees (TCs) act as specialized bodies responsible for creating and maintaining standards pertinent to designated fields. For instance, the International Organization for Standardization (ISO) oversees more than 300 TCs, collectively producing global standards spanning virtually all industry sectors. Thus, the standards managed by a TC constitute a normative system defining agreed-upon best practices. Standards have no predefined lifetime but undergo periodic review to ensure they incorporate the latest technological developments and market trends. Arguably, one of the SDO’s most important responsibilities is to establish a standards revision timeline, indicating forecast start and finish dates for standards within the system. Given the unique and temporary nature of each revision task, standards revision scheduling constitutes a distinct engineering project which is well suited for coordination through project scheduling methods.

Despite extensive research on project scheduling, the Standard Revision Project Scheduling Problem (SRPSP) remains significantly understudied. Optimizing revision scheduling is crucial, given the pivotal role of standards systems and the interoperability risks inherent in revision processes. The key challenge arises from the systemic nature of standards themselves [2]: they do not exist in isolation, but function as interdependent normative constraints establishing domain-specific order. This interdependence makes cross-standard coordination essential for overall system effectiveness. However, standards systems frequently suffer from interoperability failures, inconsistencies, and redundancies, often stemming from fragmented revision processes. While individual standards may be revised separately to meet emerging needs, systematic coordination between interdependent standards cannot be naturally guaranteed. Consequently, traditional project scheduling models—which primarily focus on minimizing delays and costs—are inadequate for addressing the complex coordination requirements essential for effective standards governance. To bridge this gap, this study proposes a systematic framework aimed at enhancing coordination within the standards system during revision scheduling.

Specifically, the revision of a standard transmits impacts to interdependent standards via their inherent dependencies within the network. One of the primary relationships among standards is normative reference dependency [3]. Normative reference refers to the practice whereby a newly developed standard incorporates pre-existing standards as integral components of its specifications or requirements. Normative references, systematically enumerated in Clause 2 of every standard, must be explicitly cited within operational clauses as binding requirements. By integrating the provisions of established standards, developers avoid redundant specification of technical minutiae while substantially mitigating inter-standard conflicts. Standards bound by normative references collectively form a standard citation network [4,5] whose elements maintain initial mutual coordination, adhering to the fundamental standardization principles. Once a standard in this network becomes outdated, its revision initiates networked propagation of provisions alignment through citation pathways. To preserve coordination across the citation network, provisions of a standard must align precisely with the specifications of its normative references.

While revision can ensure that standards are up to date, it may also introduce inter-standard incompatibilities. This study specifically investigates citation-induced revision projects scheduling within standard citation networks. A scheduling model is developed for standard revision projects overseen by a TC, explicitly incorporating the systemic interdependencies of standard systems to maximize the coordination degree of standards systems during revision cycles. Since the Resource-Constrained Project Scheduling Problem (RCPSP) has been proved to be an NP-hard problem [6], its extension—SRPSP—is also NP-hard. Exact algorithms typically struggle to solve large-scale problems within an acceptable time; therefore, an effective algorithm is needed to find an approximate optimal solution within a reasonable computation time. In this study, the Particle Swarm Optimization (PSO) algorithm is proposed to solve SRPSP. It is a metaheuristic known for its simplicity, strong global search capability, and widespread use in complex optimization, particularly project scheduling. Since there are no standard benchmark instances for comparison, this study uses real-world data as a case study. An instance and related basic parameters were taken from TC544, which is a technical committee within the Standardization Administration of China (SAC) that develops standards concerning BeiDou Satellite Navigation. The specific revision time for each standard is generated for a standard citation network size of 30 standards, representing the SRPSP scenarios. The model’s validity and robustness are confirmed through parameter sensitivity experiments. Comparative experiments against traditional duration-minimization models demonstrate the framework’s superior ability to balance coordination and efficiency, particularly in heterogeneous citation networks. Theoretically, this work extends RCPSP by considering systemic coordination objectives, bridging a critical gap in traditional project scheduling research. Practically, it equips TCs with actionable tools to improve revision planning, ensuring sustained alignment between evolving standards.

The main contributions of this study are threefold: (1) Project Scheduling Modeling for Standard Revision Scenarios: By analyzing the network topology and dynamic interdependencies of the standards system managed by TCs, we identify revision dependencies propagating through standard citation networks and formulate a scheduling model tailored to standard revision projects. The proposed SRPSP model addresses the operational challenges faced by TCs in managing such context-specific coordination tasks. (2) Proposing a Targeted Optimization Objective Incorporating Inter-Standard Coordination: To address the unique requirements of the standards system in project scheduling, we introduce the Coordination Index of Standard Systems ($CISS$)—a comprehensive metric designed to quantify the coordination relationships among standards within a citation network. This index not only facilitates the evaluation of revision plans, but also enables iterative refinement of standard optimization strategies. (3) For SRPSP, a Particle Swarm Optimization algorithm is used to solve this problem, which robustly generates high-quality solutions.

The remainder of this article is structured as follows. In Section 2, a review of the standard- and RCPSP-related literature is provided. Section 3 describes the SRPSP model with the objective of maximizing $CISS$. Section 4 details the PSO technique for this specific problem. Section 5 presents the results of computational experiments and derives important insights from the analysis of the data. Section 6 concludes the study and outlines potential future research.

2. Literature Review

2.1. Research on Standard Revision and Standard Citation Network

This study focuses on the revision stage in the standard lifecycle. Although the term “life cycle” typically describes a product’s phases from “birth to death,” standard lifecycles—particularly their revision dynamics—have been seldom explored in academic discourse. Standard revision is a critical phase in the standard lifecycle. During the implementation phase, if discrepancies emerge between the standard and practical requirements, or conflicts arise with relevant regulations, policies, or other standards, its effectiveness diminishes, necessitating revision to restore alignment and utility. To investigate how phases of a standard sustain relevance over time, Botzem and Dobusch [7] analyzed transnational standards through a process perspective, focusing on their formation and diffusion. Their research revealed that benefits generated through the diffusion of standards feed back into the cycle of standard formation, diffusion, adoption, and reproduction. Moon and Lee [2] pioneered the study of standard dynamics in electronics manufacturing ecosystems, conceptualizing these dynamics as systemic changes driven by standard-setting and revision activities. Their work further dissected the influencing factors (e.g., technological shifts, regulatory pressures) and unique characteristics (e.g., cross-standard dependencies) inherent to revision processes. Different stages in the standard lifecycle have their respective important roles. Standard revision—a pivotal phase in this lifecycle—ensures the continued vitality and applicability of standards.

Similarly, research on standard citation networks also remains limited. At present, citation network analysis methods are mainly used in research on paper and patent citations. Given the structural similarities among these three citation network types (papers, patents, and standards), theoretical frameworks and analytical tools developed for patent and paper citation networks can be adapted to standard citation networks [4,5]. Standards, as codified bodies of interconnected knowledge and requirements, exhibit systemic dependencies that Wei et al. [4,5] have rigorously mapped using complex network theory. Their analysis of citation matrices in air quality and automotive standards revealed sparse connectivity and critical node deficiencies in air quality frameworks, undermining systemic resilience, while automotive standards exhibited temporal fragmentation with proliferated isolated nodes, indicative of ad hoc evolutionary trajectories. However, the rationale for citations differs fundamentally across these domains. In patent and paper citations, backward or forward citations reflect relationship and similarity with the applicable patent application or similarities to prior art or existing literature, signaling to examiners or reviewers that relevant precedents have been considered. In contrast, standard citations primarily serve to avoid redundant technical specifications and mitigate inter-standard conflicts. Cited clauses integrate with other provisions to form a cohesive standard. Unlike patents or papers—which lack formal revision mechanisms—standards undergo periodic revisions. Post-revision misalignments between cited and revised clauses may trigger conflicts, necessitating systematic revision scheduling to maintain system-wide coherence.

2.2. Research on RCPSP

The Standard Revised Project Scheduling Problem (SRPSP) is an extension of the Resource Constrained Project Scheduling Problem (RCPSP) [8]. As a typical scheduling problem in operations research, the RCPSP requires scheduling project activities under dual constraints: priority relationships and resource constraints [9]. Research on the RCPSP has evolved in new directions [10,11,12,13,14], but the SRPSP remains significantly understudied in the existing literature. Therefore, this section focuses on two streams of literature associated with SRPSP analysis: (1) interdependence analysis, which emphasizes risk propagation and cascading effects across standards, and (2) value-driven optimization frameworks, which integrate non-economic attributes beyond traditional time–cost tradeoffs.

From a relational property perspective, the cascade effect [15] denotes the phenomenon where unresolved quality issues of a single activity propagate to downstream activities, causing more serious quality problems and a wider range of rework [16]. The solution frameworks for this problem are divided into two main categories: proactive scheduling [17] and reactive scheduling [18]. The proactive scheduling problem aims to generate a baseline schedule that minimizes the expected cost of deviations caused by disruptions, while considering possible reactive adjustments [19]. Wang et al. [20] proposed an exact method based on a continuous time Markov decision process, aiming to minimize the expected project span, in order to solve the RCPSP with uncertain activity durations and rework. Zhu et al. [21] studied the buffer setting problem in project scheduling in order to fulfill the requirement of establishing an efficient scheduling for assembly processes with overall inspection and rework. Reactive project scheduling refers to modifying or re-optimizing the baseline schedule when it is no longer feasible or optimal after unanticipated disturbance events occur during project execution [22]. Akkan [23] studied the problem of inserting a new job on a single device during the execution of a scheduling plan and proposed three heuristic algorithms and a hybrid branch bounding algorithm. Rahmani [24] studied the case of process interruption due to the addition of new jobs in an open shop and proposed rescheduling methods.

From a value-driven perspective, value refers to the sum of actual and potential benefits created through project activities, including both economic and non-economic value. Researchers have proposed a variety of quantitative models and optimization methods to achieve a balance between project duration, cost, and value under resource constraints. Non-economic values, defined as those extending beyond traditional economic metrics, are increasingly critical in project management. These values typically encompass social, cultural, environmental, and utility considerations [25]. Although non-economic values are not easy to quantify, they are extremely important for assessing the overall impact and long-term sustainability of a program, policy, or decision. Szwarcfiter et al. [26] proposed a new project scheduling methodology to balance the time, cost, value, and risk of a project, in which the value not only includes the financial benefits but also covers the positive impacts of the project in terms of meeting customer needs, improving service quality, and enhancing operational efficiency. A new methodology to balance the value of a project with the net present value (NPV) has also been proposed for the uncertainty of activity duration [27]. Balouka et al. [28] proposed a quantitative model to measure the cost and value of the project and a multi-attribute technical performance function to define the project value in terms of radar range, quality, and radar reliability.

In summary, standards inherently require periodic revisions triggered by technological advancements, market fluctuations, or regulatory shifts, with such revisions propagating systemic perturbations through citation networks. While TC managers often prioritize standards via experience-driven approaches based on urgency and importance, these methods inadequately address the systemic interdependencies within standards systems. Although recent research on the RCPSP has advanced project relationship and value attributes, the SRPSP remains virtually nonexistent. To address this gap, this study proposes a proactive scheduling framework for standard revision planning, emphasizing holistic governance of standards systems. Building on classical RCPSP foundations, we propose a general model for solving the SRPSP, aiming to maximize coordination between interdependent standards. This model serves dual objectives: (1) mitigating the negative impacts of revisions on standard-system-wide coherence, and (2) ensuring the sustained real-world applicability of both individual standards and the integrated system throughout revision cycles. By formalizing $\mathit{CISS}$ as a quantifiable optimization target, the framework shifts prioritization from isolated efficiency metrics to systemic effect, offering actionable strategies for TC governance in a complex standard citation network.

3. Problem Description and Mathematical Model

3.1. Problem Description

SRPSP is a typical combinatorial optimization problem that can be described as follows: a standard citation network can be represented as a directed acyclic graph $G=(S,C)$ where $S=\{\mathrm{0,1},\dots ,N,N+1\}$ the set of nodes (standards), and nodes $0$ and $N+1$ represent dummy standards marking the start and end of the standard citation network. $C$ is the citation matrix, which represents the set of precedence relationships between standards. Normative references represent the incorporation of established standards’ provisions into new standards, explicitly listed in Clause 2 (“Normative References”) of every standard and publicly accessible. In our model, the standard citation network $G=(S,C)$ is constructed based on the normative references enumerated in Clause 2 of all standards administered by a TC, where standard identifiers (numbers and names) can be directly obtained without natural language processing or manual identification. If $(i,j)\in C$, denoting that standard $j$ cites standard $i$ per its Clause 2 listing, the revision of standard $i$ may create technical misalignment between standards $i$ and $j$. In this citation network $G$, the revision task of a standard $j$ must start after the completion of standard $\mathrm{i}\mathrm{’}\mathrm{s}$ revision.

From a lifecycle perspective, the standardization process goes through several stages, from the introduction of an idea to the publication of the standard. These stages are listed as follows: proposal stage, preparatory stage, committee stage, draft stage (enquiry stage), approval stage, and publication stage. Throughout the standard implementation process, a “review stage” is carried out to check whether the standard is being implemented effectively and, if necessary, to revise it. Then, a new version of the standard is created and submitted to a new approval and publication stage. SDO controls versions with the publication year and after the transition stage, the standard with the “latest version” at time t, $v_{it}$, as shown in Figure 1.

To define clear and unambiguous provisions, the document should be consistent, clear, and accurate according to standardization principles. In this study, we assume that the standard citation network initially exists in a state of mutual coordination among all standards. When a standard in the citation network undergoes revision, its latest version $v_{it}$ is generated at time $\mathrm{t}$. The necessity for revision of standard $j$ is determined by the condition status ${\theta }_{ij}=1$, indicating incompatibility with the latest version of its normative reference standard $i\in {NR}_j$. This lack of coordination consequently initiates revision requirements for other standards referencing the revised standard. Under the worst-case scenario, any standard revision would trigger subsequent revisions of all dependent standards in the citation network. The standard system administered by the TC will regain its state of mutual coordination only after all standards in the citation network have completed their respective revisions.

Specifically, formulating the revision plan for the entire standard system involves deciding the revision start time $s_i$ for each standard. The standard revision process is constrained by two factors: one is the standard revision capability of the TC, i.e., the upper limit number of standards that the TC can handle simultaneously, denoted as $\mathrm{A}\mathrm{T}\mathrm{C}$; the other is the standard citation relationship. For any two standards $i,j\in C$, if there is a citation relationship, the revision start time $s_j$ of standard $\mathrm{j}$ must not be earlier than the revision completion time $s_i$ of standard $i$, $i\in {NR}_j$, where ${NR}_j$ denotes standards cited by standard j.

The assumptions involved in formulating the SRPSP are as follows:

(1) In the initial state, the standards in the standard citation network are mutually coordinated.

(2) Once the standard revision project starts, it cannot be interrupted (non-preemptive).

(3) The model exclusively addresses coordination failures between standards triggered by revision activities, excluding external factors.

(4) Each standard’s state is defined by its version number $v_{it}$ at time $t$. Coordination between standards is assumed when their version numbers align. Secondary revisions of the same standard are excluded from consideration.

3.2. Parameters and Variables

Table 1. Symbols and definitions.

Index and sets	$i,j$	Index of standards, $i,j\in 𝒮=\{1,\dots ,N\}$;
	$t$	Index of time, $t\in \{1,\dots ,T\}$;
	${NR}_i$	The set of normative references of standard $i$;
Parameters	$N$	Number of standards constituting the citation network;
	$C$	Standards citation relationship Matrix;
	$T$	The upper bound on the duration of the entire revision process, spanning from the revision of the first standard to the implementation of the last revised standard;
	${dr}_i$	Revision duration of standard $i$;
	${dp}_i$	Implementation transition period of standard $i$, which starts from the revision completion time point to the suggested implementation time point;
	$ATC$	Upper capacity limit of TCs for concurrent standard revision;
Decision variables	$s_i$	Start time of standard $i’s$ revision;
Other variables	$f_i$	Completion time of standard $i\mathrm{’}\mathrm{s}$ revision;
	$h_i$	Implementation time of the new version of standard $i$;
	$v_{it}$	Version number of standard $i$ at time $t$;
	${\alpha }_{it}$	0/1 variable that equals 1 if standard $i$ is in a revision state at time $t$, 0 otherwise;
	${\beta }_{ijt}$	0/1 variable that equals 1 if standard $i$ and $j$ have identical version numbers at time t, 0 otherwise;
	${\delta }_{ij}$	0/1 variable that equals 1 if standard $i$ references standard $j$, 0 otherwise;
	${\theta }_{ij}$	0/1 variable that equals 1 if standard $j$ requires revision after its normative reference standard $i\in {NR}_j$ is revised, 0 otherwise;
	$CISS$	average Coordination Index of Standards System.

below lists the parameter symbols used in the model constructed in this paper and their definitions.

3.3. Objective Function

In this study, we construct an SRPSP model that explicitly incorporates the coordination degree of the standard system. $\mathit{CISS}$ is a comprehensive index designed to quantify the level of coordination of the standard system and its advancement over time. The optimization objective is to maximize the $\mathit{CISS}$.

$$f=\mathit{Max}CISS=\mathit{Max}{\displaystyle \frac{{\sum }_{i=1}^N{\sum }_{j=1}^N{\sum }_{t=0}^T{\beta }_{ijt}{\delta }_{ij}{\theta }_{ij}}{T{\sum }_{i=1}^N{\sum }_{j=1}^N{\delta }_{ij}}}$$

(1)

Equation (1) formalizes the objective function of the proposed model. This study postulates that at any given time, the relationship between two referentially related standards is considered mutually coordinated if their version numbers are identical at that moment. Suppose two standards$i$and $j$ with a referential relationship $({\delta }_{ij}=1$) share the same version number at time $t$; then, their coordination status is denoted as${\beta }_{ijt}=1$. The numerator is the cumulative sum of coordination levels between all standards during the revision period $T$. The denominator normalizes the numerator, where ${\sum }_{i=1}^N{\sum }_{j=1}^N{\delta }_{ij}$ is the total number of referential relationships between standards. The objective function aims to maximize the Coordination Index of Standard Systems ($\mathit{CISS}$) by orchestrating orderly revisions across standards. This optimization seeks a revision plan ${\{s}_1,s_2,...,s_N\}$ that balances three critical dimensions: interdependencies among standards, revision sequencing, and resource allocation. The goal is to achieve maximal coordination, thereby ensuring that the $\mathit{CISS}$ attains its optimal state throughout the revision process.

Figure 2 provides an illustrative example of the standard revision coordination optimization process proposed in this study. The figure displays a citation network comprising three standards, where Standard 2 cites Standard 1 and Standard 3 cites Standard 1, with no citation link between Standards 2 and 3; then,${\delta }_{\mathrm{2,1}}=1$, ${\delta }_{\mathrm{3,1}}=1$, ${\delta }_{\mathrm{2,3}}=0$, ${\delta }_{\mathrm{3,2}}=0$. All three standards are initially assigned version numbers $v_{\mathrm{1,0}}=1$, $v_{\mathrm{2,0}}=1$, and $v_{\mathrm{3,0}}=1$. After revision and official implementation at $t=15$, its version number is updated to $v_{\mathrm{1,15}}=2$, indicating the second version of standard 1. When the second version of standard 1 is implemented, the revision status variables representing whether Standard 2 and Standard 3 require revision after Standard 1 is revised are ${\theta }_{21}$ and ${\theta }_{31}$. In the proactive scheduling model, we adopt a conservative approach by setting ${\theta }_{ij}=1$ for all standards with normative references to simulate the worst-case inconsistency scenario. ${\beta }_{ijt}$ is used to denote the relationship between the version number of standard $i$ and standard $j$ at time $t$; if the version number of the two standards is the same, ${\beta }_{ijt}=1$, otherwise it is 0. In the figure, when $t=15$, ${\beta }_{\mathrm{1,2},15}=0$, ${\beta }_{\mathrm{1,3},15}=0$, and ${\beta }_{\mathrm{2,3},15}=1$. By $t=24$ (i.e., after the official implementation of the new version of Standard 2), the value of the coordination parameter transitions to 1, namely ${\beta }_{\mathrm{1,2},24}=1$, which signifies that Standard 2 resolves its inconsistency with Standard 1. Standard 3 undergoes an identical revision process. Therefore, the entire revision process concludes at $t=32$. Consequently, the model parameter, the duration of the entire revision process, T, is set to 32, after which the standards system enters a state of full mutual coordination.

For this revision scheduling, the $\mathit{CISS}$ is then calculated by first determining version consistency between any two standards at each time point, summing the results, and subsequently applying normalization. With the denominator being $32\times 2=64$ (where $T=32$ and there are two reference relationships), the numerator is $23+15=38$. This value derives from the following: Standard 2 and Standard 1 are coordinated from period $\left[0,15\right]$ to $\left[24,32\right]$, totaling 23 time units; Standard 3 and Standard 1 are coordinated over period $\left[0,15\right]$, totaling 15 time units. Thus, $\mathit{CISS}=38/64=0.59375$, indicating an average coordination index of the standard system is 59.375% for the current revision scheduling.

In our model, $\theta ij$ is fixed at 1 to reflect the worst-case scenario, i.e., each reference standard must be aligned after the referenced standard is revised. This deterministic setting avoids underestimating the future coordination workload. In practical scenarios, if ${\theta }_{12}=0$ and ${\theta }_{13}=0$, means that the revised Standard 1 does not cause coordination issues with Standards 2 or 3. The revision scheme may be terminated at any time without further action.

3.4. Constraints

$$\sum _i^N{\alpha }_{it}\le ATC,t=1,\dots ,T$$

(2)

$${\alpha }_{it}=\left\{\begin{array}{c}1,s_i\le t\le f_i\\ 0,otherwise\end{array}\right.,\mathrm{i}\in \mathrm{S}$$

(3)

$${\beta }_{ijt}=\left\{\begin{array}{c}1,v_{it}=v_{jt},{\delta }_{ij}=1\\ 0,otherwise\end{array}\right.,i,j\in S,t=1,\dots ,\mathrm{T}$$

(4)

$$f_i\ge s_i+d{r}_i,i\in S$$

(5)

$$h_i\ge f_i+{dp}_i,i\in S$$

(6)

$$0\le f_i\le s_j,i\in {NF}_j$$

(7)

$${\theta }_{jk}\le {\theta }_{ij},iϵ{NR}_j,jϵ{NR}_k$$

(8)

$$T=\mathit{max}\{h_i|i\in S\}$$

(9)

$${\delta }_{ij}=\left\{\mathrm{0,1}\right\},\mathrm{i},\mathrm{j}\in S$$

(10)

$$v_{it}=\left\{\mathrm{1,2}\right\},i\in S,t=1,\dots ,T$$

(11)

$${\theta }_{ij}=\left\{\mathrm{0,1}\right\},j\in S,iϵ{NR}_j$$

(12)

Equation (2) imposes resource constraints, specifying that at any time $t$, the number of standards the TC can revise simultaneously must not exceed its $ATC$. Equation (3) is the resource utilization determination equation. If time $t$ is between $s_i$ and $f_i$, it means that standard $i$ is using the resource, and the value of ${\alpha }_{it}$ equals 1; otherwise, it equals 10. Equation (4) specifies that if standards $i$ and $j$ have a citation relationship and share the same version number at time $t$, the coordination indicator ${\beta }_{ijt}$ equals 1. Equation (5) specifies that the revision completion time of a standard must be greater than or equal to its revision start time plus the revision duration. Equation (6) requires that the implementation time of a standard must be no earlier than its revision completion time plus the transition time for implementation. Equation (7) specifies that if standard $j$ cites standard $i$, the revision start time of standard $j$ must be later than the revision completion time of standard $i$. Equation (8) indicates that if the new version of standard $i$ after revision is still compatible with standard $j$, then standard $k$, which references standard $j$, is still compatible with standard $i$. Conversely, if the new version of standard i after revision is incompatible with standard $j$, then standard $k$, which references standard $j$, is incompatible with standard $i$. Equation (9) defines that the total revision cycle duration equals the implementation start time of the last revised standard. Equation (10) represents the range of values for the relationship between standard $i$ and $j$. Equation (11) represents the version number of standards. Equation (12) represents the range of values for the status whether standard $j$ requires revision after its normative reference standard $i\in {NR}_j$ is revised.

4. Solution Algorithm

4.1. Particle Swarm Algorithm Workflow

Evolutionary algorithms, as a class of optimization search methods, are widely used in various NP-hard problems (e.g., the traveler’s problem [29], the scheduling problem [30]). Classical evolutionary algorithms, including the Genetic Algorithm (GA) [31], the Particle Swarm Algorithm (PSO) [32], and other algorithms, can be effectively applied to function optimization problems. Compared with the GA and the ant colony algorithm, the PSO algorithm has the advantages of fewer parameters, a simple structure, real number coding, and a faster search speed. Therefore, the PSO algorithm is suitable for the optimization of standard revision scheduling. PSO is a meta-heuristic algorithm developed by Kennedy [33] based on the social behavior of animals or human beings to cluster towards certain goals. However, it also has problems such as poor local search ability, low search accuracy, a tendency to fall easily into local minimal solutions, and being sensitive to parameters [34]. Thus, it is necessary to adjust the inertia weights of the PSO algorithm to improve the algorithm’s search efficiency and search ability.

When addressing the Standard Revision Project Scheduling Problem (SRPSP), the core reason for selecting the PSO algorithm over GA or Ant Colony Optimization (ACO) lies in its unique computational characteristics and problem adaptability. As an extension of the resource-constrained project scheduling problem (RCPSP), SRPSP must balance the dynamic dependencies of the standard reference network (e.g., the specification reference matrix $G$) with the global optimization objective of the coordination index ($\mathit{CISS}$). PSO, with its parameter simplicity (requiring only the inertia weight $\omega$ and acceleration factors $c_1$ and $c_2$) and real number encoding mechanism, naturally adapts to continuous scheduling variables (such as revision start time $s_i$), avoiding the binary encoding conversion overhead of GA or the discrete path mapping limitations of ACO. In contrast, GA’s genetic operations (selection, crossover, mutation) involve multi-parameter tuning, which is prone to premature convergence in complex citation networks (e.g., unscaled topologies); while ACO relies on pheromone update rules, which are less efficient at modeling the “revision-citation” dynamic propagation in SRPSP (e.g., revision completion triggering subsequent standard adjustments). PSO algorithms have also been widely applied to research in the field of project scheduling. Yousefzadeh [35] proposed a dominance metric framework combining genetic algorithms and particle swarm optimization, which provides a robust solution for multi-project scheduling under uncertainty.

The PSO first initializes a population of random particles, each of which is a feasible solution to the optimization problem, and then iteratively finds the optimal solution to the problem. A particle is a point in n-dimensional space, representing a solution, with a position $x$ and a velocity attribute $v$, which determines the direction and distance of the optimization, and a fitness value, determined by the optimization problem, which is used as a measure of the particle’s performance. At the $t_{die}$ iteration, the n-dimensional position vector of particle $i$ is denoted as $X_i\left(t\right)=\left\{x_{i1}\right(t_{die}),x_{i2}(t_{die}),...,x_{in}(t_{die}\left)\right\}$. The n-dimensional velocity vector is denoted as $V_i\left(t\right)=\left\{v_{i1}\right(t_{die}),v_{i2}(t_{die}),...,v_{in}(t_{die}\left)\right\}$. The globally optimal particle is denoted as $X^G=\{x_1^G,x_1^G,...,x_n^G\}$. During the iterative process, the particles update themselves by keeping track of the optimal solutions found by the particles themselves (individual poles$P_{\mathrm{best}}$) and the optimal solutions found by the population as a whole (global poles $g_{best}$). The particle accomplishes the updating of its own velocity and position according to the following equations:

$$V_i^{t_{die}+1}=\omega V_i^{t_{die}}+c_1{r}_1(p_{best}^{t_{die}}-x_i^{t_{die}}){+c}_2{r}_2(p_{best}^{t_{die}}-x_i^{t_{die}})$$

(13)

$$x_i^{t_{die}+1}=x_i^{t_{die}}+v_i^{t_{die}+1}$$

(14)

where $\omega$ is the inertia weight, which determines the particle’s ability to inherit the previous velocity; $c_1$,$c_2$is the learning factor, which determines the particle’s ability to learn its own best position and the group’s optimal position; and $t_{die}$ is the number of current iterations; rand() is a random number between (0, 1).

In the PSO algorithm, the inertia weight factor $\omega$ represents the effect of the current particle velocity on the velocity update, which can regulate the global and local search ability of the particle population. A smaller $\omega$ facilitates the local search and better searches for the optimal value, while a larger $\omega$ can search the solution space faster and improve the convergence speed of the algorithm. The study [36] used exponentially decreasing inertia weights to enhance convergence speed, combined with a randomized segmental variation strategy to enhance population diversity, effectively avoiding early convergence and late oscillation. Another study [37] proposes an adaptation-based nonlinear dynamic inertial weight particle swarm optimization algorithm (NIWPSO), which improves the convergence performance of traditional PSO by introducing adaptation information.

Therefore, this study modifies the calculation method of inertial weights such that the weights can be adjusted during the algorithm iteration process. In the early stages of iteration, the weights remain large to maintain the diversity of the initial solution and prevent the model from falling into a local optimum too early. In the later stages, the search range is narrowed to avoid excessive invalid searches.

$$\omega ={\omega }_{max}-({\omega }_{max}-{\omega }_{min})({{\displaystyle \frac{t_{die}}{T_{die}}})}^2$$

(15)

Equation (15) is the iterative expression for the inertia weight factor, where ${\omega }_{max}$ is the maximum value of $\omega$, ${\omega }_{min}$ is the minimum value of $\omega$, $t_{die}$is the current number of iterations, and $T_{die}$ is the total number of iterations.

4.2. Algorithm Design

Based on the analysis of the characteristics of standard revision and formal implementation, the specific process of standard revision coordination optimization model is given by combining the characteristics of PSO.

1.

Firstly, according to the reference relationship between standards, input the standard relationship matrix $G$ (e.g., $G=\left\{\left[234\right]\left[4\right]\left[\right]\left[\right]\right\}$), in this standard system, composed of four standards. According to the standard relationship matrix, there are four reference relationships in the system: standards 2, 3, and 4 refer to standard 1, and at the same time, standard 4 refers to standard 2. Input the number of standards $N$, the maximum number of standards to be revised in a single TC revision $ATC$, the revision duration ${dr}_i$, the standard implementation transition period ${dp}_i$, and a series of initial parameters for PSO.

2.

Establish standard 1 as the first standard to be revised (a series of standard revision tasks caused by the revision of standard 1), i.e., $s_1=0$. According to the revision period ${dr}_1$ of standard 1, determine the next decision point as ${t=s}_1$+${dr}_1$ = ${dr}_1$. $E_t$ is set to represent the set of standards eligible for revision at time $t$. At time $t$, the set $E_t$ of standards eligible for revision is determined, and the number of standards not exceeding the $ATC$ is randomly selected for revision.

3.

According to the revision period of the standard being revised, select the earliest end of the revision of the standard for the next decision point time $t$, and determine a new set of standards to be revised $E_t$; then, randomly select a number of standards to be revised and ensure that the standard revised at decision point time $t$ is not higher than the $ATC$.

4.

The decision-making process continues until the last standard revision is completed, resulting in a feasible standard revision program.

5.

Calculate the fitness value of the scheme (i.e., the position of each particle) and record it, and iterate $T_{die}$ times to get the revised scheme with the highest fitness value.

The overall operational framework of the PSO algorithm for the standard revision scheduling problem is shown in Figure 3.

5. Computational Experiments

5.1. Experimental Design

Given the absence of existing example databases for SRPSP, this study conducts experimental validation using publicly accessible standards data. Standards managed by TC544 (National Technical Committee for Standardization of BeiDou Satellite Navigation) are used as the actual case; all standard information can be obtained from the National Standard Information Public Service Platform (NSIPSP). TC544 is in charge of managing 34 active standards, 30 of which contain normative references. We directly obtained the citation relationships from Clause 2 (“Normative References”) of each standard, where standard identifiers (numbers and names) are clearly listed, and these references have been systematically sorted out in

Table 2. Table of standard citation relationship for TC544.

Standard Number	Number	Referenced Standard	Revised Duration	Implementation Transition Period
GB/T39267-2020	1	None	2	3
GB/T39268-2020	2	1	8	5
GB/T39396.1-2020	3	1	4	2
GB/T39396.2-2020	4	1	6	4
GB/T39397.1-2020	5	1	3	3
GB/T39397.2-2020	6	1, 5	8	2
GB/T39398-2020	7	1	5	6
GB/T39399-2020	8	1	9	8
GB/T39409-2020	9	1	2	6
GB/T39410-2020	10	1, 2	7	2
GB/T39411-2020	11	1	9	2
GB/T39414.1-2020	12	1	2	3
GB/T39414.2-2020	13	1	6	4
GB/T39414.3-2020	14	1	10	3
GB/T39414.4-2020	15	1	6	1
GB/T39413-2020	16	1, 12, 13, 14, 15	5	2
GB/T39472-2020	17	1	3	3
GB/T39473-2020	18	1, 7, 12, 13, 14, 15	7	4
GB/T39723-2020	19	1	2	3
GB/T39772.1-2021	20	1, 19	7	2
GB/T39772.2-2021	21	1, 19, 20	2	2
GB/T39721-2021	22	1, 20, 21	3	3
GB/T39783-2021	23	1	3	2
GB/T39787-2021	24	1	7	3
GB/T42575-2023	25	1	8	3
GB/T42576-2023	26	1	3	3
GB/T42577-2023	27	1, 6	7	2
GB/T42579-2023	28	1, 12, 13, 14, 15	2	3
GB/T42832.1-2023	29	1	7	4
GB/T42833-2023	30	1, 29	7	2

(Data source: https://openstd.samr.gov.cn/bzgk/gb/, accessed on 5 July 2025).

. To facilitate understanding, the original standard number has been replaced by a numerical code.

The time parameters associated with the revision of standards are variable and unknown. Based on the Administrative Rules for National Standards, the development and revision processes for Chinese national standards typically require a timeframe of 1–2 years. We have also time-verified some of the revised standards, and they are in compliance with the rules. Therefore, the parameters of this model are initialized based on the real situation: a revision cycle of 1–2 years and an implementation transition period of approximately 6 months. These parameters are randomly generated as follows: the revision duration ${dr}_i$ uniformly distributed in the interval $[1,10]$ with a mean${\mu }_{{\mathrm{dr}}_i}=5$; the implementation transition period ${dp}_i$ uniformly distributed in the interval $\left[1,8\right]$, with a mean ${\mu }_{{dp}_i}=3$.

Through multiple experiments, the optimized parameter configurations identified in this section demonstrate superior performance compared with alternative setups: the population size $P_{size}=50$, the number of iterations $T_{die}$ = 500, the inertia weight parameters are $W_{max}=0.8$ and $W_{min}=0.4$, the acceleration factor parameters are set to $c_1=4$ and $c_2=4$, the maximum value of particle velocity is $V_{max}=10$, and the minimum value of particle velocity is $V_{min}=-10$. The experiments were performed on a computer with an AMD Ryzen 7 5800H with a Radeon Graphics CPU (3.20 GHz), 16 GB of RAM, and a 64-bit Windows 11 operating system. The programming platform was MATLAB 2021b.

To validate the proposed model and algorithm, this study performed computational experiments simulating the scheduling of national standard revision projects. The experiments assessed the framework’s strengths and limitations by evaluating the average $\mathit{CISS}$ across three distinct scenarios. Scenario 1: Model efficacy is verified by comparing schedules optimized for maximum $\mathit{CISS}$ against traditional duration-minimization approaches. Scenario 2: The impact of revision capacity constraints on $\mathit{CISS}$ is quantified, identifying critical thresholds where resource allocation balances coordination and effectiveness. Scenario 3: The influence of network characteristics—including topology, scale, and average node degree—on $\mathit{CISS}$ is systematically analyzed. Finally, parameter sensitivity analyses are conducted to test the robustness of coordination outcomes under perturbations to key variables (revision durations ${dr}_i$ and implementation transition periods ${dp}_i$).

5.2. Analysis of Experimental Results

5.2.1. Comparative Experimental Analysis of Objective Functions

To verify the effectiveness of the model designed in this study for the standard revision problem, a comparison was conducted between this study’s model with the optimal $\mathit{CISS}$ as the objective function and the traditional model with the shortest makespan as the objective function. The TC standard revision capacity was set as $ATC=3$, 10 runs were conducted, and the optimal solution was chosen, as shown in

Table 3. Table of experimental results for different models.

Model	Makespan	$\mathit{C}\mathit{I}\mathit{S}\mathit{S}$
Modeling with the goal of the shortest makespan	55	0.5841
Modeling with the goal of maximum $\mathit{CISS}$	64	0.6556

below.

The evolutionary curve of $\mathit{CISS}$ for this model is shown in Figure 4.

The Gantt chart of the revised plan for the model with the shortest makespan objective is shown in Figure 5 below.

The Gantt chart illustrating the revised plan aimed at achieving maximum $\mathit{CISS}$ is presented in Figure 6.

Based on the experimental results, the model proposed in this study achieved a significant improvement in the $\mathit{CISS}$, which was 12% higher than that of the traditional makespan-centric model. This improvement implies that during standard revision processes, the model can more effectively realize the coordination among the standards and enhance the overall $\mathit{CISS}$ of the whole standards system. While the $\mathit{CISS}$ was improved, the makespan increased by 16% compared with the traditional makespan-centric model due to the fact that more time is needed to prioritize the $\mathit{CISS}$ of the standards system in the pursuit of coordination among standards. Given that coordination degree and timeline efficiency in standardization governance are both important, TCs may adopt flexible revision strategies based on specific operational contexts: when long-term systemic stability and coordination among standards are prioritized, TCs may prefer the model proposed in this study, despite accepting longer revision makespan; on the contrary, if the TC is more concerned about the rapid completion of the project, the traditional makespan-centric model will be chosen. By strategically balancing these factors, TCs can optimize standard revision plans to address diverse governance requirements.

5.2.2. Impact of Citation-Triggered Revision Ratio on $\mathit{CISS}$

In actual standard systems, not all citation relationships lead to revisions of the cited standards (${\theta }_{ij}$ is not always equal to 1). In other words, there are differences in the ‘trigger strength’ of citation relationships between standards, meaning that revisions to subsequent standards are only triggered when the citing standard has a high degree of dependency on a particular clause or when the revision content has a substantial impact on the citing standard. To simulate this phenomenon, we constructed three experimental scenarios, setting the proportion of citation relationships required to trigger subsequent revisions at 33%, 67%, and 100%. In the 33% scenario, only the most critical 1/3 of the reference relationships are retained as trigger conditions, while the remaining reference relationships are considered ‘weak dependencies’ and will not trigger revisions to the referenced standards even if they are revised. In the 67% scenario, the trigger ratio is expanded to 2/3, while the 100% scenario corresponds to the conservative assumption in the model, where all reference relationships constitute revision trigger conditions. The system evaluated their impact on the $\mathit{CISS}$. The experimental results are shown in

Table 4. Comparison of $\mathit{CISS}$ under different citation trigger ratios.

Number of Reference Relationships That Need to Be Revised	Makespan	$$\mathit{CISS}$$
33% of citations	50	0.8401
67% of citations	42	0.7390
100% of citations	64	0.6556

.

Two significant trends can be observed from the results:

(1) Coordination decreases monotonically as the trigger ratio increases: when the ratio increases from 33% to 100%, $\mathit{CISS}$ decreases from 0.8401 to 0.6556, a decrease of 22%. This indicates that as more citation relationships are incorporated into the revision trigger conditions, the overall coordination of the system significantly decreases. This trend reflects the ‘fragility’ of the standard system; that is, the widespread triggering of citation relationships may trigger a chain reaction of frequent revisions, thereby disrupting the original stable coordination state.

(2) Total project duration exhibits non-linear characteristics: Notably, total project duration does not increase monotonically with the increase in trigger ratio. At a 67% trigger ratio, the makespan is shortest (42 units of time) while, at a 100% ratio, it extends to 64 units. This phenomenon may stem from the following mechanism: in the 67% scenario, the ‘exemption’ of some reference relationships allows standard revisions to proceed in parallel, reducing resource conflicts and waiting times; in the 100% scenario, all reference relationships must respond to revisions, leading to highly coupled revision tasks, increased resource scheduling complexity, and ultimately a longer total duration.

Although we have explored the impact of different citation trigger ratios on system coordination, this study has consistently adhered to a design criterion of ‘100% citation trigger’ (i.e., all ${\theta }_{ij}=1$) when formulating standard revision scheduling schemes. This assumption means that as long as a standard is cited by its citing standards, regardless of the strength of the citation relationship or the criticality of the provisions, it is considered necessary to trigger subsequent revisions. This conservative setting aims to maximize the avoidance of systemic mismatch risks caused by omitting potential dependencies, ensuring that the scheduling scheme maintains global consistency and governance robustness even when faced with complex citation networks.

5.2.3. Analysis of TC Revision Capability

The TC standard revision capacity ($ATC$) is an important parameter in standardization governance. In practice, TC secretariats are often attached to specialized institutions. For instance, the secretariat of TC544 is jointly hosted by the China Satellite Navigation Engineering Center and the China Aerospace Standardization Institute. The number of standard revision projects a secretariat can undertake concurrently varies based on its project management capacity. In the traditional RCPSP, an increase in the number of resources is often effective in improving the makespan. As TC staff are mostly part-time, insufficient standards revision capacity influences the systematic effect of the standards in this field, while excessive standards revision capacity leads to resource inefficiencies. The following experiments analyze the $\mathit{CISS}$ and the makespan of the standard revision project under different $ATC$ levels. Using the example in 5.1, the following experiment analyzed the standard revision project and total completion time at different levels. Taking the example in Section 5.1, the $ATC$ is set at 1, 3, 5, 7, 9, 11, 13, 15, and the optimal $\mathit{CISS}$ value obtained through iteration of the standard revision plan and its corresponding construction period is calculated for each $ATC$ condition. The results are shown in Figure 7.

As indicated in Figure 7, with a continuous increase in the $ATC$ level, the $\mathit{CISS}$ initially rises rapidly, then stabilizes, and eventually declines. This suggests that increasing $ATC$ generally improves $\mathit{CISS}$, and there exists a value ($ATC=13$) that can ensure the optimal $\mathit{CISS}$. Therefore, for the 30 standards managed by TC544, if the optimal $\mathit{CISS}$ is the goal, under the condition of sufficient staff and material resources, setting the $ATC$ upper limit to 13 achieves peak coordination; exceeding this threshold ($ATC>13$) not only wastes resources, but also diminishes $\mathit{CISS}$.

5.2.4. Analysis of Standard Citation Network Types

For TC, its standard citation network is not constructed according to its subjective design, but is gradually formed based on the actual citation needs during the standard development process. Its key features can be defined by three parameters: network type, network scale, and network average degree. The key features can be defined by three parameters: network type, network size, and average node degree. This section focuses on investigating the common rules for TC in revising standards with different features; specifically, we analyze how these parameters influence revision strategies and systemic coordination outcomes.

Network type: The standard citation networks are mostly scale-free networks, with a minority structured as stochastic networks. The scale-free network is dominated by a small number of scattered nodes [38], where a majority of edges are linked to a small number of nodes. However, the citation networks of some TCs lack distinct scale-free or other identifiable features; therefore, this study selects a random network structure for comparative analysis. In the random network, all nodes are connected with the same probability [39].

Network size: The number of standards in a standard citation network is also an important parameter affecting the standard revision strategies. This study defines the small-scale standard citation network as containing 10 standards, and the large-scale networks as 30 standards.

Average degree: In practice, the number of edges of a standard citation network is much less than its theoretical maximum, so network density cannot be used to distinguish different standard citation networks. Therefore, Average Degree is used to quantify the closeness of the standards within the citation network. It is the arithmetic average of the degree of all nodes, and is calculated differently in the undirected network and the directed network. In the undirected network, the average degree $d=2m/n$, where $\mathrm{m}$ is the number of edges in the network and $\mathrm{n}$ is the number of nodes in the network. In the directed network, the average degree $d=m/n$. The standard citation network is directed, thus $d=m/n$. For experimental purposes, connectivity is classified into two levels—low and high—based on the ratio of citation relationships to standards. The citation network parameters are shown in

Table 5. Citation network parameters.

Parameter	Parameter Value Setting
Network scale	10-Low scale	30-Large scale
Network type	Scale-free network structure	Random network structure
Network average degree	1.5-Low average degree	1.5-High average degree

, and

Table 6. Scenario setting sheet.

Scenario Setting
Scenario 1	Scale-free network-small—Low scale—Low average degree
Scenario 2	Scale-free network-small—Large scale—Low average degree
Scenario 3	Scale-free network-small—Low scale—High average degree
Scenario 4	Scale-free network-small—Large scale—High average degree
Scenario 5	Random network structure—Low scale—Low average degree
Scenario 6	Random network structure—Large scale—Low average degree
Scenario 7	Random network structure—Low scale—High average degree
Scenario 8	Random network structure—Large scale—High average degree

outlines eight experimental scenarios derived from these parameters.

To investigate the trend of the $\mathit{CISS}$ with the TC standard revision capability in different scenarios, the $ATC$ is set to 1, 3, 5, 7, 9, 11, 13, and 15 in this section.

We first examine the trends of $\mathit{CISS}$ and revision makespan under small-scale network scenarios (Scenarios 1, 3, 5, and 7), as illustrated in Figure 8. All four scenarios exhibit a decreasing revision makespan until a stabilization threshold is reached. For the $\mathit{CISS}$, low average degree networks (Scenario 1 and Scenario 5) exhibit similar trends where $\mathit{CISS}$ reaches the peak value at $ATC=3$and then decline to a steady state, and the high average degree networks (Scenario 3 and Scenario 7) exhibit similar trends, where $\mathit{CISS}$ reaches the peak value and then remains constant. In small-scale networks, whether scale-free or stochastic, and regardless of network average degree (both low and high), there exists a specific threshold for $ATC$ that maximizes $\mathit{CISS}$ during the revision cycle. When this threshold is exceeded, the $\mathit{CISS}$ will either decline or remain stable without improvement during the revision cycle, indicating a waste of standards revision resources. For TCs governing such standard citation networks, maintaining the revision capacity at $ATC=3$ is recommended to achieve optimal coordination while preventing resource inefficiency.

We then examine the trends of $\mathrm{C}\mathrm{I}\mathrm{S}\mathrm{S}$ and revision makespan under large-scale network scenarios (Scenarios 2, 4, 6, and 8), as illustrated in Figure 9. All four scenarios exhibit a decreasing revision makespan until a stabilization threshold is reached. For the $\mathit{CISS}$, the scale-free large-scale networks (Scenario 2 and Scenario 4) exhibit similar trends, where $\mathrm{C}\mathrm{I}\mathrm{S}\mathrm{S}$ first increases and then declines, and the random networks (Scenario 6 and Scenario 8) exhibit similar trends, where $\mathrm{C}\mathrm{I}\mathrm{S}\mathrm{S}$ reaches the peak value at a very low level of $ATC$ and then show a slight decline. This is because, in random network topologies, the citation relationships among standards are irregular and highly entangled. This structural randomness means that as the Technical Committee increases its $ATC$, the marginal coordination gain is small: additional resources are often assigned to standards that are only weakly interdependent, so their simultaneous revision hardly improves system-wide coherence. At the same time, the complex, unpredictable dependencies greatly amplify scheduling conflicts; overlapping revision tasks and prolonged waiting times become more frequent, lengthening the overall project duration. Beyond a certain $ATC$ threshold, these scheduling inefficiencies outweigh the modest coordination benefits, causing the $\mathit{CISS}$ to decline rather than increase. In short, the disorderly citation patterns in random networks dilute the value of extra resources and can even degrade $\mathit{CISS}$ when $ATC$ is pushed too high. This suggests that for a scale-free large-scale standard citation network, the $\mathrm{C}\mathrm{I}\mathrm{S}\mathrm{S}$ can be improved by increasing the $ATC$ of TC during the revision cycle, regardless of the network’s average degree. However, for random citation, maintaining a low level of $ATC$ is a good strategy for gaining $\mathrm{C}\mathrm{I}\mathrm{S}\mathrm{S}$ and resource efficiency.

5.2.5. Parameter Sensitivity Analysis

In practice, the revision duration ${dr}_i$ and the standard implementation transition period ${dp}_i$ fluctuate according to the actual situation; thus, there must be a certain degree of uncertainty. In this section, a parameter sensitivity analysis is conducted based on Example 5.1, focusing on two key parameters: ${dr}_i$ and ${dp}_i$. While keeping all other parameters unchanged, the two parameters ${dr}_i$ and ${dp}_i$ were globally perturbed within the range defined by the original parameters, i.e., the same perturbation magnitude was applied to these two parameters of the same type, and their relative relationship remained unchanged. The perturbation magnitudes were set to −50%, −25%, 0%, +25%, and +50% (rounded to the nearest integer).

The PSO algorithm was run 10 times in each group of experiments, and the optimal value of the degree of coordination was computed and checked against the baseline parameter (i.e., $∆=0$). The average duration fluctuated with different $∆$ values, as shown in Figure 10.

In general, the fluctuations of different work period parameters have varying degrees of influence on the $\mathit{CISS}$ in the standard revision project cycle, as shown in Figure 10. When Δ < 0, the degree of coordination is more sensitive to the fluctuations of the work period parameters. When the parameter perturbation amplitude reaches −50%, the degree of coordination is significantly negatively affected. The sensitivity of coordination to the fluctuations of the work period parameters is smaller when Δ > 0, and the degree of coordination changes the least at a perturbation amplitude of +25%. Regardless of the direction and proportionality of the parameter perturbation, the sensitivity of the degree of coordination remains low, with its absolute deviation always below 4%. The coordination optimization model for SRPSP proposed in this study shows high robustness to the fluctuations of the key schedule parameters ${dr}_i$ and ${dp}_i$. The above analysis shows that the model can still maintain high stability and coordination within a certain range of parameter fluctuations, thereby verifying its reliability and validity. The model achieves the highest stability when the fluctuation threshold of the coordination parameter is ±5%; therefore, TC standards administrators can use this model to plan their standards revision programs.

6. Conclusions

In contemporary society, the efficient operation of almost every industry is fundamentally dependent on standards. As standards are normative documents for achieving optimal operations within a specific scope, the coordination of standards systems is important for ensuring the consistency and interoperability of interdependent standards throughout their lifecycle. This study proposed an SRPSP model to address the operational challenges faced by TCs. Based on the classical RCPSP, we extended its framework by integrating two dimensions: system dynamic characteristics, where revision tasks propagate through the reference network, and value-driven characteristics, featuring non-economic optimization objectives. The characteristics of standards revision projects were identified, and an SRPSP model was formulated to manage such context-specific coordination tasks. A key contribution of this study is the development of the $CISS$, a measurable indicator for assessing coordination degree among standards across their evolving lifecycle and enabling improvement of standard optimization strategies. The proposed SRPSP model maximizes the average $\mathrm{C}\mathrm{I}\mathrm{S}\mathrm{S}$ over revision cycles and is solved using a PSO algorithm, which balances computational efficiency with coordination requirements. Its validation and effectiveness were confirmed through computational experiments on the BeiDou Satellite Navigation Standardization System (managed by TC544), and a parameter sensitivity test is conducted to show consistent performance under varying conditions.

Through computational experiments, this study first compared the applicability of the proposed model with traditional project scheduling models that prioritize minimizing makespan as the optimization target for SRPSP. The results demonstrated that our model generates revision plans that significantly outperform duration-centric approaches. Then, through analyzing scenarios characterized by three key parameters of standard citation networks—network topology (scale-free vs. stochastic), network scale, and average node degree—distinct optimization strategies were identified: For small-scale networks, maintaining a revision capacity threshold of $ATC=3$ achieves optimal $CISS$ while balancing resource efficiency. Lower capacity risks systemic incoherence, whereas higher capacity leads to resource waste. For large-scale, scale-free networks, increasing the revision capacity ($ATC$) consistently enhances the $CISS$ throughout revision cycles, regardless of the network’s average degree. The proposed model effectively mitigates the negative impacts of standard revisions on the systemic effect of the standard system in practical TC governance, ensuring sustained alignment among standards throughout revision processes. This approach not only improves the practical utility of standards but also optimizes TC management efficiency, offering actionable strategies to enhance both the operational performance of revision plans and the governance capabilities of standardization bodies. By bridging the gap between operations research and standard management practices, this study advances project scheduling methodologies for standardized governance and provides technical committees with powerful tools for managing complex standard systems.

Despite the benefits, our model is not without limitations. It exclusively addresses coordination failures between standards triggered by revision activities and explicitly excludes consideration of the secondary revision of standards, though real-world complexities—such as accelerated technological obsolescence or frequent regulatory shifts—often necessitate multiple revision cycles that compound scheduling challenges. While the PSO algorithm guarantees solution feasibility, its computational efficiency may degrade substantially when scaling to accommodate both network expansion and secondary revision scenarios, manifesting particularly in prolonged initialization phases. Future research could further expand the findings of this study by developing more complex standard scheduling models that account for domain-specific characteristics and more complex standard revision scenarios, as well as optimizing the efficiency of algorithmic solutions.