Quantitative impact analysis of priority policy applied to BIM-based design validation 应用于基于 BIM 的设计验证的优先政策定量影响分析
Seung-Ha Huh ^("a "){ }^{\text {a }}, Namhyuk Ham ^("b,* "){ }^{\text {b,* }}, Ju-Hyung Kim ^("a "){ }^{\text {a }}, Jae-Jun Kim ^("a "){ }^{\text {a }}^("a "){ }^{\text {a }} Department of Architectural Engineering, Hanyang University, Seoul 04763, Republic of Korea ^("a "){ }^{\text {a }} 汉阳大学建筑工程系,大韩民国首尔 04763^(b){ }^{\mathrm{b}} Department of Digital Architecture and Urban Engineering, Hanyang Cyber University, Seoul 04763, Republic of Korea ^(b){ }^{\mathrm{b}} 汉阳网络大学数字建筑与城市工程系,大韩民国首尔 04763
A R T I C L E I N F O
Keywords: 关键词:
Priority queueing model 优先排队模式
BIM RFIs BIM RFI
BIM staffing BIM 人员配置
Waiting avoidance cost 避免等待的成本
BIM ROI BIM 投资回报率
Abstract 摘要
Building information modeling (BIM) design validation is primarily aimed at responding quickly to serious design errors. A prompt response to BIM request for information (RFI) can significantly enhance the BIM return on investment (ROI). Although prior research has identified additional factors to consider while assessing the benefits of BIM coordination, it was not possible to conduct an economic assessment. Therefore, this study fills this gap by conducting an economic assessment of the introduction of priority policies in BIM coordination using priority queue model. The findings demonstrate that the introduction of priority policies can impact the optimal BIM staffing and the engineers’ waiting cost for high-priority RFIs. We quantify the BIM ROI that can be improved by introducing the priority policy in BIM coordination, using time and cost metrics derived from the queue model. 建筑信息模型 (BIM) 设计验证的主要目的是快速应对严重的设计错误。对 BIM 信息请求 (RFI) 的及时响应可显著提高 BIM 投资回报率 (ROI)。虽然之前的研究已经确定了在评估 BIM 协调效益时需要考虑的其他因素,但却无法进行经济评估。因此,本研究利用优先队列模型对 BIM 协调中优先政策的引入进行了经济评估,从而填补了这一空白。研究结果表明,引入优先权政策会影响最佳 BIM 人员配置和工程师对高优先级 RFI 的等待成本。我们利用从队列模型中得出的时间和成本指标,量化了在 BIM 协调中引入优先策略后可提高的 BIM 投资回报率。
1. Introduction 1.导言
Unexpected events can occur in construction projects. Among them, design errors are a major risk factor for reworks and schedule delays [1]. Failure to eliminate or manage risk factors during the early stages of a construction project can significantly affect the success of the project [2]. 建筑项目中可能会出现意外事件。其中,设计错误是造成返工和工期延误的主要风险因素[1]。如果不能在建筑项目的早期阶段消除或管理风险因素,就会严重影响项目的成功[2]。
Building Information Modeling(BIM) is considered one of the means to reduce economic losses due to design errors [3]. The benefits of using BIM include fast and accurate design visualization and accuracy at every stage of the design phase [4]. Owing to these benefits, the use of BIM has increased [5]. Moreover, several studies have been conducted to reduce the waste of resources while using BIM [6-8]. 建筑信息模型(BIM)被认为是减少因设计错误造成经济损失的手段之一[3]。使用 BIM 的好处包括快速、准确的设计可视化以及设计阶段每个阶段的准确性[4]。由于这些优点,BIM 的使用量不断增加[5]。此外,还开展了多项研究,以减少使用 BIM 时的资源浪费[6-8]。
However, despite numerous benefits of using BIM, its adoption has been slow due to the difficulties experienced while operating and maintaining it [9]. The adoption of BIM can provide information as needed. However, this incurs additional costs [10] and requires BIM experts [11]. To implement ideal BIM, BIM staff should be assigned to handle the required information and manage issues raised by various project participants [6,10,11]. Therefore, human resource allocation is important to address uncertainty in construction projects [12]. Human resource allocation is a key component of project success. However, there are not enough quantitative tools to efficiently allocate the 然而,尽管使用 BIM 有诸多好处,但由于在操作和维护方面遇到困难,其采用速度一直很慢[9]。采用 BIM 可以根据需要提供信息。然而,这会产生额外的成本[10],并且需要 BIM 专家[11]。要实现理想的 BIM,应指派 BIM 工作人员处理所需的信息并管理各项目参与者提出的问题 [6,10,11]。因此,人力资源分配对于解决施工项目中的不确定性非常重要[12]。人力资源配置是项目成功的关键因素。然而,目前还没有足够的量化工具来有效地分配人力资源[13]。
resources [13]. Following the emphasis placed on the importance of BIM staff, human resource allocation can influence project performance or effectiveness can become a major research topic. 资源[13]。在强调 BIM 人员的重要性之后,人力资源配置对项目绩效或效果的影响可能会成为一个重要的研究课题。
Few studies have analyzed BIM ROI, including the effect of BIM staff. Neelamkavil et al. [14] included new variables in addition to the 6 performance indicators of BIM ROI analysis. LEE et al. [8] argued that BIM ROI analysis using BIM RFI should include a detailed analysis of the number of workers, quality of management, etc. Accordingly, Ham et al. [6] quantified BIM staff by tracking the BIM RFI of the actual project and analyzing the effect of BIM staff on the waiting time of project engineers. The their study applied the first come first served (FCFS) rule to the order in which the BIM staff process request for information(FRI). However, design errors have different effects on projects depending on the type, location, and time of discovery [1]. Paik et al. [58], Chahrour et al. [59] analyze BIM project data to prioritize coordination issues. The result of focusing on the priorities of BIM design coordination is improved productivity and economics of the design process. However, Chahrour et al. [59] cited the need for detailed value analysis and management of benefit realization in addition to the cost savings that can be achieved with BIM process coordination and conflict detection. Paik et al. [58] identified priorities for BIM design coordination issues, but no economic analysis was performed on them. 很少有研究分析 BIM 投资回报率,包括 BIM 人员的影响。Neelamkavil 等人[14]在 BIM 投资回报率分析的 6 个性能指标之外加入了新的变量。LEE 等人[8]认为,使用 BIM RFI 进行 BIM 投资回报率分析应包括对工人数量、管理质量等的详细分析。因此,Ham 等人[6]通过跟踪实际项目的 BIM RFI 来量化 BIM 人员,并分析 BIM 人员对项目工程师等待时间的影响。他们的研究对 BIM 人员处理信息请求(FRI)的顺序采用了先来后到(FCFS)规则。然而,设计错误会因类型、地点和发现时间的不同而对项目产生不同的影响[1]。Paik 等人[58]、Chahrour 等人[59]通过分析 BIM 项目数据来确定协调问题的优先次序。关注 BIM 设计协调优先级的结果是提高了设计过程的生产率和经济性。然而,Chahrour 等人[59] 指出,除了通过 BIM 流程协调和冲突检测可以节约成本外,还需要进行详细的价值分析和效益实现管理。Paik 等人[58]确定了 BIM 设计协调问题的优先次序,但没有对其进行经济分析。
Previous studies have revealed that there are additional items to 以往的研究表明,还需要
https://doi.org/10.1016/j.autcon.2023.105031
Received 29 August 2022; Received in revised form 19 June 2023; Accepted 15 July 2023 2022 年 8 月 29 日收到;2023 年 6 月 19 日收到修订稿;2023 年 7 月 15 日接受
Available online 26 July 2023 可于 2023 年 7 月 26 日在线查阅
0926-5805/⑳23 Elsevier B.V. All rights reserved. 0926-5805/⑳23 Elsevier B.V. 保留所有权利。保留所有权利。
consider in evaluating the benefits of BIM coordination in various ways. However, economic feasibility evaluation is not progressing because specific items cannot be presented. For example, the introduction of priorities in BIM process coordination can make a difference in the wait times of engineers and the performance of BIM staff. An additional item to consider in previous studies are the introduction of priorities for BIM process coordination. The specific item is the performance change that can change due to additional items. If so, it is necessary to analyze the change in the number of BIM staff and the waiting cost of engineers according to the application of the priority rule to BIM coordination. 在评估 BIM 协调的效益时,需要考虑各种方式。然而,由于无法提出具体项目,经济可行性评估没有取得进展。例如,在 BIM 流程协调中引入优先级,可使工程师的等待时间和 BIM 人员的工作表现有所不同。在以往的研究中,引入 BIM 流程协调的优先级是需要考虑的额外项目。具体项目是绩效变化可能因附加项目而改变。如果是这样,就有必要分析根据 BIM 协调优先规则的应用,BIM 人员数量和工程师等待成本的变化。
Accordingly, this study aims to improve the performance of BIMbased design validation by applying the priority queuing model from the field of management science. It aims to improve BIM ROI by analyzing the queue model performance indicators according to the RFI processing order of BIM staff, and quantifying the change in the number of BIM staff and the waiting cost of project engineers. 因此,本研究旨在通过应用管理科学领域的优先排队模型来提高基于 BIM 的设计验证绩效。其目的是根据 BIM 人员的 RFI 处理顺序分析排队模型性能指标,量化 BIM 人员数量的变化和项目工程师的等待成本,从而提高 BIM 投资回报率。
This study first presents a theoretical review of BIM and management issues. Research issues are identified by reviewing previous studies on human resource allocation in construction, BIM design validation, and BIM ROI, and by critically reviewing existing approaches, including the discussion of the queuing model. We further present a detailed framework for comparing performance indicators according to the BIM RFI processing sequence using a queuing model for quantitative analysis when priority rules are applied. We discuss, including detailed descriptions of two real-world projects, where BIM was applied in the construction phase, to use the model. 本研究首先对 BIM 和管理问题进行了理论回顾。通过回顾以往关于建筑业人力资源分配、BIM 设计验证和 BIM 投资回报率的研究,以及对现有方法的批判性回顾,包括对排队模型的讨论,确定了研究问题。我们进一步提出了一个详细的框架,用于根据 BIM RFI 处理顺序比较性能指标,在应用优先规则时使用排队模型进行定量分析。我们讨论了该模型的使用,包括对两个在施工阶段应用了 BIM 的实际项目的详细描述。
2. Literature review 2.文献综述
2.1. Effect of BIM-based design validation 2.1.基于 BIM 的设计验证效果
In a construction project, risks and uncertainties are the highest at the beginning of the project [15]. Recognizing risks and uncertainties at the design stage does not significantly affect the cost, while recognizing them at the construction stage increases the risk significantly [2]. The use of BIM in the design phase can improve the overall process [16]. Consequently, the use of BIM at the beginning of the project can significantly influence on the project and minimize costs. 在建筑项目中,项目开始阶段的风险和不确定性最高[15]。在设计阶段认识到风险和不确定性不会对成本产生重大影响,而在施工阶段认识到风险和不确定性则会大大增加风险[2]。在设计阶段使用 BIM 可以改善整个流程[16]。因此,在项目开始阶段使用 BIM 可以对项目产生重大影响,并最大限度地降低成本。
BIM-based coordination is an important step prior to construction, as the building is equipped with many mechanical, electrical and plumbing (MEP) systems [17]. The general concept of coordinating construction design involves defining the location and dimensions of building components to avoid clash between two or more disciplines including architecture, structural, mechanical, electrical, plumbing, and fire protection [18]. This allows for the identification of potential conflicts early and the avoidance of conflicts that affect project costs and schedules. 基于 BIM 的协调是施工前的一个重要步骤,因为建筑物配备了许多机械、电气和管道系统 (MEP)[17]。协调施工设计的一般概念包括定义建筑构件的位置和尺寸,以避免两个或多个专业(包括建筑、结构、机械、电气、管道和消防)之间的冲突[18]。这样可以及早发现潜在冲突,避免冲突影响项目成本和进度。
In the construction sector, the Design-Bid-Build (DBB) approach is the most common industry standard for project delivery [19]. The DBB approach can separate architects from contractors to build projects, which are used for most public and private projects [20], but can result in risks such as fragmentation and discontinuity, which are well-known in the AEC industry [21]. This DBB method problem can be improved through the introduction of BIM [21]. 在建筑领域,设计-招标-建造(DBB)方法是最常见的项目交付行业标准[19]。DBB 方法可以将建筑师与承包商分开来建设项目,大多数公共和私人项目都采用这种方法[20],但可能会导致分散和不连续性等风险,这在 AEC 行业是众所周知的[21]。这种 DBB 方法的问题可以通过引入 BIM 得到改善[21]。
However, BIM does not fit well with the current widespread procurement system (ex:DBB) [21]. Although the Design-Build (DB) method allows for overlap between design and construction phases and allows for easy adjustment of design errors [22], the DBB method is difficult to use to maximize the benefits of BIM-based coordination [23]. The DBB approach results in a certain level of separation between the design phase and the construction phase [16]. Consequently, the DB method can easily adjust design errors. However, there is not enough time for BIM-based coordination when using DBB method. BIM-based design validation is performed in a short period before construction begins [6]. When suing BIM, construction modelers inevitably discover errors and inconsistencies as they create architectural information 然而,BIM 与当前广泛使用的采购系统(例如:DBB)并不十分匹配[21]。虽然设计-建造(DB)方法允许设计阶段和施工阶段重叠,并允许轻松调整设计错误[22],但 DBB 方法很难最大限度地发挥基于 BIM 的协调优势[23]。DBB 方法导致设计阶段与施工阶段之间存在一定程度的分离[16]。因此,DB 方法很容易调整设计错误。然而,在使用 DBB 方法时,没有足够的时间进行基于 BIM 的协调。基于 BIM 的设计验证是在施工开始前的短时间内进行的[6]。在使用 BIM 时,施工建模人员在创建建筑信息时不可避免地会发现错误和不一致之处。
models [24]. Resolving all design errors in a short period from the detailed design to the pre-construction stage requires a lot of additional cost. However, the use of BIM must be done within BIM contract costs. 模型[24]。要在短时间内解决从详细设计到施工前阶段的所有设计错误,需要大量的额外成本。然而,BIM 的使用必须在 BIM 合同成本范围内进行。
In many studies, the number of BIM RFIs was tracked for the economic analysis of the adoption of BIM [6-8,10]. Barlish et al. [7] design errors were analyzed by dividing them into error identification potential, effect on schedule, and effect on quality. Consequently, there were differences in schedule, quality, possibility of error identification, direct cost, and indirect cost depending on design errors. However, the effect of each design error was not considered in the BIM ROI analysis. Ham et al. [6] improved BIM ROI by quantifying the BIM workforce through the number of RFIs in three projects. However, there was a precondition that the effects of design errors were not considered and were managed in the order in which they were discovered. 许多研究跟踪了 BIM RFI 的数量,用于采用 BIM 的经济分析[6-8,10]。Barlish 等人[7]将设计错误分为错误识别可能性、对进度的影响和对质量的影响进行分析。结果表明,设计错误在进度、质量、错误识别可能性、直接成本和间接成本方面都存在差异。但是,在 BIM 投资回报率分析中没有考虑每个设计错误的影响。Ham 等人[6]通过三个项目中的 RFI 数量来量化 BIM 劳动力,从而提高了 BIM 投资回报率。然而,前提条件是不考虑设计错误的影响,并按照发现错误的顺序进行管理。
Ajibade et al. [61] studied the frequency of occurrence of RFI and the time of occurrence of RFI according to the characteristics of the project. It was revealed that the larger and more complex the project, the more RFIs and the longer the processing time. Importantly, they found research data that the processing of RFIs is related to the number and level of staffing. The question of how to estimate and prepare the staff needed to handle RFIs was raised as a future study. Vishal et al. [60] presented a framework for classifying and specifying functional and technical requirements for a BIM server to serve as a platform. Based on the contingency theory, it is argued that the collaboration requirements would vary from project to project, and, hence, support technical requirements should be an integral part of the BIM-server development rather than an afterthought. Therefore, in order to maximize the technological benefits of using BIM, it is essential to identify the potential impact of design errors on a project and address them in order of priority. Ajibade 等人[61]根据项目的特点研究了 RFI 发生的频率和 RFI 发生的时间。结果显示,项目越大、越复杂,RFI 就越多,处理时间就越长。重要的是,他们发现研究数据表明 RFI 的处理与人员配置的数量和水平有关。他们提出了如何估算和准备处理 RFI 所需的人员这一问题,并将其作为今后的研究课题。Vishal 等人[60]提出了一个框架,用于分类和指定 BIM 服务器作为平台的功能和技术要求。根据权变理论,他们认为不同项目的协作要求会有所不同,因此,支持技术要求应该是 BIM 服务器开发的一个组成部分,而不是事后才想到的。因此,为了最大限度地发挥使用 BIM 的技术优势,必须识别设计错误对项目的潜在影响,并按优先顺序解决这些问题。
2.2. Priority queueing model in management science 2.2.管理科学中的优先排队模型
Management skills and workforce planning can significantly affect productivity in construction management [25]. The workflow management(WfM) system is the most successful type of systems that support collaborative work [26]. The WfM system is evaluated in terms of lead time, service time, latency and resource utilization, and the above adjustments can improve efficiency [27]. The WfM system has its roots in computer science and management science [28], and queue networks are used for the quantitative analysis of efficiency [28-30]. 管理技能和劳动力规划会极大地影响施工管理的生产率[25]。工作流管理系统(WfM)是支持协同工作的最成功的系统类型[26]。WfM 系统从准备时间、服务时间、延迟和资源利用率等方面进行评估,上述调整可以提高效率[27]。WfM 系统起源于计算机科学和管理科学[28],队列网络被用于效率的定量分析[28-30]。
Queueing theory is a mathematical theory focused on modeling and analysis serving random demand; queuing model is an abstract description of these systems [31]. It can be considered statistically through several performance measures, including the average latency of a queue or system, and the number of expected waits or incoming services [30]. 队列理论是一种数学理论,侧重于为随机需求提供建模和分析服务;队列模型是对这些系统的抽象描述[31]。它可以通过几种性能指标进行统计,包括队列或系统的平均延迟、预期等待或传入服务的数量 [30]。
The queuing theory describes the types of waits as shown in Fig. 1 [32], and expresses the types of queuing systems that actually appear [32]. Customers arrive at the queue system randomly for service. Typically, one or more servers provide the service. Each customer leaves the queue after being individually served by the server. 排队理论描述了如图 1 所示的等待类型[32],并表达了实际出现的排队系统类型[32]。顾客随机到达队列系统寻求服务。通常,一个或多个服务器提供服务。每个顾客在接受服务器的单独服务后离开队列。
Queue systems are subject to time-dependent changes in system 队列系统会随着时间的推移而发生变化。
Fig. 1. Basic queueing system ( CC represents a customer, and SS a server). 图 1.基本排队系统( CC 代表顾客, SS 代表服务器)。
parameters such as arrival rate or number of servers [33]. Unusual parameters such as arrival rate and number of servers include patients and medical staff performing care, port overload and port size. Changing time-dependent parameters can significantly affect the performance of a queuing system [6,33][6,33]. Table 1 presents research areas that use timedependent queuing systems. 到达率或服务器数量等参数[33]。到达率和服务器数量等非正常参数包括进行护理的病人和医务人员、端口过载和端口大小。改变与时间相关的参数会显著影响队列系统的性能 [6,33][6,33] 。表 1 列出了使用随时间变化的排队系统的研究领域。
Bailey et al. [34] minimized the waiting time of customers to increase customer satisfaction by adjusting the appointment time of outpatients. Cayirli et al. [35] minimizes the waiting and idle time between the patient being served at the hospital and the medical staff performing the treatment through the queueing model. Buzacott et al. [36] presented a solution to a design optimization problem that occurs in a manufacturing system using a queuing model. Zhang et al. [37] performed quantitative analysis through the queuing model to solve the port overload problem with the port size expansion and minimum input. Kim et al. [38] proposed a 4D digital twin framework through the performance index analysis of the queuing model. Wee et al. [39] quantitatively analyzed the effect of the construction team allocation on the performance of frame construction using the queuing theory. Kim et al. [40] quantitatively analyzed the apartment frame construction period and applied the queuing theory to determine the validity of the estimated period. Bailey 等人[34] 通过调整门诊病人的预约时间,最大限度地减少了顾客的等待时间,从而提高了顾客满意度。Cayirli 等人[35]通过排队模型最大限度地减少了在医院接受服务的病人与进行治疗的医务人员之间的等待和空闲时间。Buzacott 等人[36] 利用排队模型提出了制造系统中出现的设计优化问题的解决方案。Zhang 等人[37]通过排队模型进行了定量分析,解决了端口过载问题,并扩大了端口尺寸和最小输入量。Kim 等人[38]通过排队模型的性能指标分析提出了 4D 数字孪生框架。Wee 等[39]利用排队理论定量分析了施工队伍分配对框架施工性能的影响。Kim等人[40]定量分析了公寓框架施工工期,并应用排队理论确定了估计工期的正确性。
Lin et al. [41] improved the error detection process and error correction process of the software system by using a priority queuing model. Kim et al. [42] analyzes the queue network in the call center to prioritize high-value customers to avoid client loss. Ingolfsson et al. [43] examined the structure of patrol car shifts and personnel scheduling methods that model stochastic and time-varying demand processes. Nan et al. [44] examined the resource optimization problem for multimedia cloud. By comparing priorities and multi-service scenarios, they achieved the minimum response time for cloud resources and derived the minimum resource cost. De Souza et al. [45] integrates users of different priority classes into the system queue to support different patients according to the medical severity of the Emergency Medical Service (EMS). Through this, they evaluated the performance of the average travel time and average waiting time of various user classes. Lin 等人[41]利用优先队列模型改进了软件系统的错误检测过程和纠错过程。Kim 等人[42]分析了呼叫中心的队列网络,以优先处理高价值客户,避免客户流失。Ingolfsson 等人[43]研究了巡逻车轮班结构以及模拟随机和时变需求过程的人员调度方法。Nan 等人[44]研究了多媒体云的资源优化问题。通过比较优先级和多服务场景,他们实现了云资源的最小响应时间,并得出了最小资源成本。De Souza 等人[45]根据紧急医疗服务(EMS)的医疗严重程度,将不同优先级的用户整合到系统队列中,以支持不同的病人。为此,他们评估了不同用户等级的平均旅行时间和平均等待时间的性能。
As shown in Table 1, the queueing model is useful for quantitatively analyzing systems in various fields. However, it is important to note that studies on better resource optimization and performance improvement were conducted through comparative analysis when the priority rule 如表 1 所示,排队模型对于定量分析各领域的系统非常有用。但需要注意的是,在优先权规则为 "0 "或 "0 "时,通过比较分析,可以更好地优化资源和提高性能。
Table 1 表 1
Research areas that use time-dependent queuing systems. 使用随时间变化的排队系统的研究领域。
Application area 应用领域
Researcher 研究员
Type of service 服务类型
排队数据类型
Type of queueing
data
Type of queueing
data| Type of queueing |
| :--- |
| data |
Bailey et al. 贝利等人
Consultant 顾问
Patients 患者
Health care 医疗保健
[34]
Cayirliet al.
Doctor 医生
Patients 患者
[35]
Buzacott et al. Buzacott 等人
Part 部分
Manufacturing 制造业
[36]
Zhang et al.
Port 港口
systems 系统
Application area Researcher Type of service "Type of queueing
data"
Bailey et al. Consultant Patients
Health care [34]
Cayirliet al. Doctor Patients
[35] Buzacott et al. Part Manufacturing
[36] Zhang et al. Port systems| Application area | Researcher | Type of service | Type of queueing <br> data |
| :--- | :--- | :--- | :--- |
| | Bailey et al. | Consultant | Patients |
| Health care | [34] | | |
| | Cayirliet al. | Doctor | Patients |
| [35] | Buzacott et al. | Part | Manufacturing |
| [36] | Zhang et al. | Port | systems |
rather than the FCFS rule, which is the basic assumption of the queueing model. 而不是 FCFS 规则,后者是队列模型的基本假设。
Recently, studies applying the queuing model have also begun to emerge in the construction field. However, there is no study that quantitatively analyzes resource optimization and performance improvement in the construction field by applying the priority rule. Schwarz et al. [33] provide an overview of approaches for the performance evaluation of time-dependent queueing systems. According to their study, all areas of application, a systematic test of other evaluation approaches may represent a worthwhile investigation. They argue that the opportunity for the development of other evaluation approaches lies in the combination of existing ideas concerning approximation. The development of new approaches can be a combination of priority policy items and BIM ROI items. The optimal BIM staffing and the variation in engineer waiting costs for high priority RFIs can be used for systematic testing. 最近,建筑领域也开始出现应用排队模型的研究。然而,目前还没有应用优先权规则对建筑领域的资源优化和性能提升进行定量分析的研究。Schwarz 等人[33]概述了与时间相关的排队系统性能评估方法。根据他们的研究,在所有应用领域,对其他评估方法进行系统测试可能是一项值得研究的工作。他们认为,开发其他评估方法的机会在于结合现有的近似思想。新方法的开发可以是优先政策项目和 BIM 投资回报率项目的结合。最佳 BIM 人员配置和高优先级 RFI 的工程师等待成本变化可用于系统测试。
Therefore, this study quantitatively analyzes the effect of BIM-based design verification to which the priority rule is applied. This includes a comparison of basic performance analyses such as L,Lq,W,Wq\mathrm{L}, \mathrm{Lq}, \mathrm{W}, \mathrm{Wq}, and Wq , based on the study of Ham et al. [6] with FCFS rules applied, which is the basic assumption of the queue model. Additionally, the quantitative analysis of optimal server input (ex: BIM staff) and customer waiting costs(ex: project engineers) under priority rules quantifies BIM ROI that can be improved. 因此,本研究定量分析了应用优先级规则的基于 BIM 的设计验证的效果。这包括根据 Ham 等人的研究[6],在应用 FCFS 规则(这是队列模型的基本假设)的情况下,对 L,Lq,W,Wq\mathrm{L}, \mathrm{Lq}, \mathrm{W}, \mathrm{Wq} 和 Wq 等基本性能分析进行比较。此外,对优先级规则下的最佳服务器输入(例如:BIM 人员)和客户等待成本(例如:项目工程师)进行量化分析,以量化可提高的 BIM 投资回报率。
2.3. Performance improvement scenario in BIM based design validation 2.3.基于 BIM 的设计验证中的性能改进方案
The adoption of BIM incurs additional costs. Therefore, owners and managers in the Architecture, Engineering, and Construction (AEC) industry are primarily concerned with ROI [10]. ROI analysis is used to evaluate a proposed investment [24]. Various studies have been conducted to calculate and improve BIM ROI. Cost savings from BIM adoption have generally been estimated based on RFI, design changes, and construction duration or delays [7,8,46]. Lee et al. [8] analyzed BIM ROI based on the cost of avoiding rework owing to design errors. Lu et al. [47] calculated cost savings by comparing BIM and non-BIM projects. Giel et al. [26] calculated BIM ROI through tracking RFI. Ahn et al. [11] show that BIM ROI can be improved through the importance of BIM experts and process improvement. 采用 BIM 会产生额外成本。因此,建筑、工程和施工(AEC)行业的业主和管理人员主要关注投资回报率[10]。投资回报率分析用于评估建议的投资[24]。为了计算和提高 BIM 投资回报率,已经开展了多项研究。一般根据 RFI、设计变更和施工工期或延误来估算采用 BIM 所节省的成本[7,8,46]。Lee 等人[8]根据避免因设计错误造成返工的成本分析了 BIM 投资回报率。Lu 等人[47]通过比较 BIM 项目和非 BIM 项目,计算了节省的成本。Giel 等人[26]通过跟踪 RFI 计算了 BIM 投资回报率。Ahn 等人[11]的研究表明,BIM 投资回报率可以通过 BIM 专家的重要性和流程改进来提高。
In the studies mentioned above, only traceable data, such as labor costs and capital costs, were considered BIM investment costs. However, Jin et al. [48] confirmed through a survey that BIM practitioners’ experience of using BIM and collaboration based on priorities increases BIM ROI. Ham et al. [6] analyzed the RFI response latency of project participants and improved BIM ROI by quantifying the number of BIM staff. [6,48][6,48] revealed that the analysis of latency and cost according to priority policies and workforce quantification should be considered for the increase of ROI. 在上述研究中,只有人工成本和资本成本等可追溯数据被视为 BIM 投资成本。然而,Jin 等人[48]通过调查证实,BIM 从业人员的 BIM 使用经验和基于优先级的协作提高了 BIM 投资回报率。Ham 等人[6]分析了项目参与者的 RFI 响应延迟,并通过量化 BIM 人员数量提高了 BIM 投资回报率。 [6,48][6,48] 发现,为提高投资回报率,应考虑根据优先级政策和劳动力量化分析延迟和成本。
In fact, the optimal scenario was derived in many studies by considering the problem of determining how and when to execute each activity to minimize the total cost [49-51]. Time-cost trade-offs have long been studied because they are the two most important quantifiable goals in construction projects [51]. Klerides et al. [49] proposed a programming approach to the time-cost trade-off problem of examining various scenarios and accommodating variations by applying priority rules. El-Rayes et al. [50] developed an optimal model between time, cost and quality by optimizing activity priority information and activity cost to improve construction quality. Hu et al. [51] presented a complex time-cost-quality optimization model based on correlations between construction activities. 事实上,在许多研究中,最佳方案都是通过考虑确定如何以及何时执行每项活动以最小化总成本而得出的[49-51]。长期以来,人们一直在研究时间成本权衡问题,因为这是建筑项目中两个最重要的可量化目标[51]。Klerides 等人[49]针对时间成本权衡问题提出了一种编程方法,即研究各种方案,并通过应用优先权规则来适应各种变化。El-Rayes 等人[50]通过优化活动优先级信息和活动成本,建立了时间、成本和质量之间的最优模型,以提高施工质量。Hu 等人[51]根据施工活动之间的相关性提出了一个复杂的时间-成本-质量优化模型。
The best-case scenario for improving BIM ROI is to find a trade-off between time and cost. It is difficult to solve many design errors discovered through the verification of BIM design in a short time. The degree of rework caused by design errors depends on how long the errors remain undetected [52]. Peansupap et al. [53] classified the rank of the effect of design errors from negligible levels (1) to severe levels (5) in the 提高 BIM 投资回报率的最佳方案是在时间和成本之间找到平衡点。通过 BIM 设计验证发现的许多设计错误很难在短时间内解决。设计错误造成的返工程度取决于错误未被发现的时间长短[52]。Peansupap 等人[53]将设计错误的影响等级划分为可忽略等级(1)到严重等级(5)。
study on the effect levels owing to design errors. Therefore, among the many design errors discovered through the verification of BIM design, there are design errors that must be managed first. Resolving high-level design errors first and delaying low-level design errors can be the best way through which to minimize the total cost of the project. 设计错误造成的影响程度的研究。因此,在通过 BIM 设计验证发现的众多设计错误中,有一些设计错误必须先行管理。先解决高层次的设计错误,延迟解决低层次的设计错误,是将项目总成本降至最低的最佳途径。
Therefore, this study quantitatively analyzes the effectiveness of the verification of the BIM design with priority rules. To find a time-cost trade-off when the priority rule is applied, the performance is compared with the performance applied by the FCFS rule in Ham et al. (6), and the optimal number of BIM staff is sought according to the performance. Additionally, we analyzed the avoidance cost of engineers’ waiting for high-priority design errors. Changing the optimal number of BIM staff under the priority rule and reducing the waiting cost of engineers for higher priorities can reduce the total cost of the project. This is the best-case scenario where BIM ROI is improved. 因此,本研究定量分析了采用优先规则验证 BIM 设计的有效性。为了找到应用优先规则时的时间成本权衡,我们将其性能与 Ham 等人(6)中的 FCFS 规则所应用的性能进行了比较,并根据性能寻求最佳的 BIM 人员数量。此外,我们还分析了工程师等待高优先级设计错误的避免成本。改变优先级规则下的最佳 BIM 人员数量,减少工程师对高优先级的等待成本,可以降低项目的总成本。这是提高 BIM 投资回报率的最佳情况。
3. Problem statement from a preliminary investigation 3.初步调查中的问题陈述
This section identifies the problem through preliminary research on two real-world projects. For both projects, BIM design validation was conducted in the pre-construction stage after detailed design. Through this, 1228 design errors were found in project A and 908 design errors were found in project B (Table 2). The research was conducted under the premise of solving all the design errors found through BIM design validation in the pre-construction stage. 本节通过对两个实际项目的初步研究来确定问题所在。这两个项目都在详细设计后的施工前阶段进行了 BIM 设计验证。通过这项工作,在项目 A 中发现了 1228 个设计错误,在项目 B 中发现了 908 个设计错误(表 2)。研究的前提是解决施工前阶段通过 BIM 设计验证发现的所有设计错误。
The Haeundae L project is a high-rise construction project with a maximum height of 412 m , in which Company A participated as a general contractor. Landmark tower ( 5 stories below ground to 101 above, 412 m above the ground) comprising a tourist hotel, a residence hotel, an observatory, etc., residential tower A ( 5 below the ground - 85 above, 339 m ) for apartment houses and ancillary facilities, residential tower B (underground), It comprises a podium(1st floor - 7th floor), comprising 5 floors - 85 floors above ground, 333 m ), and commercial facilities. Haeundae L 项目是 A 公司作为总承包商参与的最高高度为 412 米的高层建筑项目。地标塔楼(地下 5 层至地上 101 层,地上 412 米)包括旅游酒店、住宅酒店、天文台等;住宅楼 A(地下 5 层至地上 85 层,339 米)包括公寓和附属设施;住宅楼 B(地下)包括裙楼(1 层至 7 层)(地上 5 层至 85 层,333 米)和商业设施。
Project A was conducted in a fast-track method. Furthermore, a CoreWall, which divides the plane into a core part and an outer peripheral part and divides it into construction, was adopted. For high-rise buildings, it is important to shorten the construction period and manage the process [54]. It is important to manage design errors in the early stages of the project owing to the nature of the high-rise building and the fasttrack project. However, there was a risk that the construction company could bear additional costs other than the contract amount during the quality review process of design documents in the pre-construction stage after detailed design. Accordingly, Company A signed a contract with 项目 A 采用快速施工法。此外,还采用了将平面分为核心部分和外围部分并分段施工的 CoreWall。对于高层建筑来说,缩短工期和进行过程管理非常重要[54]。由于高层建筑的性质和快速通道项目的特点,在项目初期对设计错误进行管理非常重要。然而,在详细设计之后的施工前阶段,在设计文件的质量审查过程中,建筑公司有可能承担合同金额之外的额外费用。因此,A 公司与
Company C for BIM-based construction services worth KRW 3,200,000,0003,200,000,000. The contract period was from September 2015 to June 2018 (34 months). 6 BIM staffs were deployed to address the low design quality. During this process, 1228 design errors were found. Table 3 shows the classification of the discovered design errors by construction type. Design errors can result in serious losses if not addressed in advance [6]. Therefore, BIM staff must resolve 1228 design errors found through design validation before construction. C 公司提供基于 BIM 的建筑服务,价值 3,200,000,0003,200,000,000 韩元。合同期为 2015 年 9 月至 2018 年 6 月(34 个月)。为解决设计质量低的问题,部署了 6 名 BIM 工作人员。在此过程中,发现了 1228 个设计错误。表 3 按建筑类型对发现的设计错误进行了分类。如果不提前解决设计错误,可能会造成严重损失[6]。因此,BIM 工作人员必须在施工前解决通过设计验证发现的 1228 项设计错误。
The Gwangmyeong Ikea project is the first Ikea store project in Korea. The main structures consist of pre-cast concrete structures and steel structures. The building with a total floor area of 135,000m^(2)135,000 \mathrm{~m}^{2} has 53,739m^(2)53,739 \mathrm{~m}^{2} store floors, excluding parking lots, and consists of a show room, a warehouse space, a restaurant and a children’s play area. 光明宜家项目是韩国第一个宜家商店项目。主要结构由预制混凝土结构和钢结构组成。建筑总面积为 135,000m^(2)135,000 \mathrm{~m}^{2} ,有 53,739m^(2)53,739 \mathrm{~m}^{2} 个楼层,不包括停车场,由一个展厅、一个仓库空间、一个餐厅和一个儿童游乐区组成。
This project discovered many risks of MEP clash during the design document review process in the pre-construction stage after detailed design. MEP coordination is critical to project success as it requires significant time and human resources [55,56]. Accordingly, Company W signed a BIM-based construction support service with Company F. Before contracting the BIM-based construction support service, the LOD (Level of Detail) of the project stayed at 300. A more detailed BIM model was required to present the results applicable for immediate construction and detailed design review required in the construction phase. Therefore, in the pre-construction stage, the process of increasing the detail level of the BIM model to 400 or higher was conducted. 该项目在详细设计后的施工前阶段的设计文件审查过程中发现了许多 MEP 冲突的风险。MEP 协调对项目成功至关重要,因为它需要大量的时间和人力资源[55,56]。因此,W 公司与 F 公司签订了基于 BIM 的施工支持服务合同。在签订基于 BIM 的施工支持服务合同之前,项目的 LOD(详细程度)保持在 300。需要更详细的 BIM 模型来展示适用于即时施工和施工阶段所需的详细设计审查的结果。因此,在施工前阶段,将 BIM 模型的详细程度提高到 400 或更高。
The contract period was from July 2013 to September 2014 (15 months). This BIM-based construction support service contract includes Master Model Management, MEP Conflict check, and Solution. One BIM staff was assigned to solve the low design quality. During this process, 904 MEP clash errors were found. Table 4 shows the MEP clash errors of Project B discovered through the BIM design validation. 合同期为 2013 年 7 月至 2014 年 9 月(15 个月)。这份基于 BIM 的施工支持服务合同包括主模型管理、MEP 冲突检查和解决方案。一名 BIM 工作人员负责解决设计质量低的问题。在此过程中,发现了 904 个 MEP 冲突错误。表 4 显示了通过 BIM 设计验证发现的项目 B 的 MEP 冲突错误。
Both case projects had a common problem. As both projects used the DBB delivery method, risks had to be managed in the pre-construction stage according to the design quality. To review all design errors within the short period of the pre-construction stage after the design, high BIM staff labor costs are incurred. It is important to keep the BIM investments within the set contract amount budget limits. 这两个案例项目都有一个共同的问题。由于两个项目都采用了 DBB 交付方式,因此必须在施工前阶段根据设计质量管理风险。在设计完成后的施工前阶段的短时间内审查所有设计错误,会产生高昂的 BIM 人员人工成本。将 BIM 投资控制在既定的合同金额预算范围内非常重要。
To quantify the effect of BIM on labor productivity in [57], issues such as too much activity or biased budgets of the BIM staff must be addressed in the data collection stage to obtain the right level of detail. However, Ham et al. [6] is the only study that uses the FCFS rule that can quantify the number of BIM staff. 要量化[57]中 BIM 对劳动生产率的影响,必须在数据收集阶段解决 BIM 人员活动过多或预算有偏差等问题,以获得正确的详细程度。然而,Ham 等人的研究[6] 是唯一使用 FCFS 规则对 BIM 人员数量进行量化的研究。
In fact, construction companies do not process design errors discovered through the validation of the BIM design in order. Therefore, from a practical point of view, the BIM design validation performance should be analyzed when the priority order of design error handling 事实上,建筑公司并没有按顺序处理通过 BIM 设计验证发现的设计错误。因此,从实际角度出发,在分析 BIM 设计验证性能时,应按设计错误处理的优先顺序排列
Table 3 表 3
Project A Design Errors by Work Type. 按工种划分的项目 A 设计错误。
Work type 工作类型
classification of design errors 设计错误的分类
Number of occurrences 发生次数
Structure 结构
drawing Discrepancy 绘图差异
345
658
Ambiguity 模糊性
158
Omission 疏忽
155
drawing Discrepancy 绘图差异
185
Architecture 建筑学
Ambiguity 模糊性
88
373
Omission 疏忽
100
MEP
drawing Discrepancy 绘图差异
2
21
Ambiguity 模糊性
18
Omission 疏忽
1
Multiple process resolvable design errors involving more than one stakeholder 涉及一个以上利益相关者的多个流程可解决的设计错误
Between structure and architecture 结构与建筑之间
36
176
Between structure and MEP 结构与机电工程之间
102
Between architecture and MEP 建筑与机电工程之间
22
Between structure, architecture, and MEP 结构、建筑和机电工程之间的关系
16
total 总计
1228
Work type classification of design errors Number of occurrences
Structure drawing Discrepancy 345 658
Ambiguity 158
Omission 155
drawing Discrepancy 185
Architecture Ambiguity 88 373
Omission 100
MEP drawing Discrepancy 2 21
Ambiguity 18
Omission 1
Multiple process resolvable design errors involving more than one stakeholder Between structure and architecture 36 176
Between structure and MEP 102
Between architecture and MEP 22
Between structure, architecture, and MEP 16
total 1228| Work type | classification of design errors | Number of occurrences | |
| :---: | :---: | :---: | :---: |
| Structure | drawing Discrepancy | 345 | 658 |
| | Ambiguity | 158 | |
| | Omission | 155 | |
| | drawing Discrepancy | 185 | |
| Architecture | Ambiguity | 88 | 373 |
| | Omission | 100 | |
| MEP | drawing Discrepancy | 2 | 21 |
| | Ambiguity | 18 | |
| | Omission | 1 | |
| Multiple process resolvable design errors involving more than one stakeholder | Between structure and architecture | 36 | 176 |
| | Between structure and MEP | 102 | |
| | Between architecture and MEP | 22 | |
| | Between structure, architecture, and MEP | 16 | |
| total | | | 1228 |
Table 4 表 4
Project B MEP clash errors by Work Type. 项目 B 按工程类型划分的 MEP 冲突错误。
Work type 工作类型
classification of MEP clash errors MEP 冲突错误分类
发生次数
Number of
occurrences
Number of
occurrences| Number of |
| :--- |
| occurrences |
Between Structure and MEP 结构与机电工程之间
131
Between Structure and Electronic 结构与电子之间
47
MEP 冲突分类 建筑与 MEP 之间的冲突
MEP clash
classification
Between Architecture and MEP
MEP clash
classification Between Architecture and MEP| MEP clash | |
| :--- | :--- |
| classification | Between Architecture and MEP |
2
建筑与电子之间
Between Architecture and
Electronic
Between Architecture and
Electronic| Between Architecture and |
| :--- |
| Electronic |
0
Total 总计
Between Architecture and MEP 建筑与机电工程之间
23
Between MEP and Electronic 在 MEP 和电子之间
701
Work type classification of MEP clash errors "Number of
occurrences"
Between Structure and MEP 131
Between Structure and Electronic 47
"MEP clash
classification Between Architecture and MEP" 2
"Between Architecture and
Electronic" 0
Total Between Architecture and MEP 23
Between MEP and Electronic 701| Work type | classification of MEP clash errors | Number of <br> occurrences |
| :--- | :--- | :--- |
| | Between Structure and MEP | 131 |
| Between Structure and Electronic | 47 | |
| MEP clash <br> classification Between Architecture and MEP | 2 | |
| | Between Architecture and <br> Electronic | 0 |
| Total | Between Architecture and MEP | 23 |
| | Between MEP and Electronic | 701 |
rather than the FCFS rule is applied. The validation performance of the BIM design when priorities are applied shows different results than when FCFS rules are applied. The research method is described in the following section. 而不是 FCFS 规则。在应用优先级时,BIM 设计的验证性能显示出与应用 FCFS 规则时不同的结果。下一节将介绍研究方法。
4. Research method 4.研究方法
In this section, we present the research methods used to address the research problems found in the Literature review and preliminary investigation(Fig. 2). We tracked all RFIs recorded from A and B projects. In addition, according to the progress and characteristics of the project, priority classification criteria were set for handling design errors (priority classification criteria are listed in the case study). 在本节中,我们将介绍用于解决文献综述和初步调查中发现的研究问题的研究方法(图 2)。我们对 A 和 B 项目中记录的所有 RFI 进行了跟踪。此外,我们还根据项目的进度和特点,制定了处理设计错误的优先级分类标准(优先级分类标准已在案例研究中列出)。
First, all RFIs were classified according to classification criteria, and characteristics were identified of the queueing model(M/M/s model, priority model) to analysis performance when priority rules are applied to the order of RFI responses. Through performance analysis of the two selected models, we analyze the effect of BIM RFI processing order on the optimal number of BIM staffs. 首先,根据分类标准对所有 RFI 进行分类,并确定排队模型(M/M/s 模型、优先模型)的特征,以分析优先规则应用于 RFI 响应顺序时的性能。通过对所选两个模型的性能分析,我们分析了 BIM RFI 处理顺序对最佳 BIM 人员数量的影响。
Second, analyze changes in the engineers’ waiting cos as highpriority design errors are addressed first. The reduction in waiting costs can be considered waiting avoidance cost of engineers through the use of BIM. Therefore, we quantitatively analyze the input(BIM staff) for using BIM and the output(waiting avoidance cost of engineer) through the use of BIM. 其次,分析工程师在优先处理高优先级设计错误时等待成本的变化。等待成本的减少可视为工程师通过使用 BIM 而避免的等待成本。因此,我们对使用 BIM 的投入(BIM 人员)和使用 BIM 的产出(避免工程师等待成本)进行了定量分析。
4.1. M//M//sM / M / s queue model 4.1. M//M//sM / M / s 队列模型
In a queuing system, the time between customer arrivals is referred to as inter-arrival time. It is almost impossible to predict when the next customer will arrive in a typical queuing system. However, there is enough data about the customers arriving at the queuing system, you can estimate the average number of customers arriving per unit time. This is referred to as the ‘average arrival rate’ and is denoted by the Greek letter ’ lambda\lambda '. Because lambda\lambda is the average rate of the arrival of customers arriving at the waiting system, the mean of the probability distribution 在排队系统中,顾客到达之间的时间称为到达间隔时间。在典型的排队系统中,几乎不可能预测下一位顾客何时到达。但是,如果有足够的关于到达排队系统的顾客的数据,就可以估算出单位时间内到达的顾客的平均数量。这就是 "平均到达率",用希腊字母" lambda\lambda "表示。由于 lambda\lambda 是到达等待系统的顾客的平均到达率,因此概率分布的平均值为
Research Method 研究方法
Performance analysis of queueing model according to the design error processing sequence 根据设计误差处理顺序对排队模型进行性能分析
BIM staffs’ Performance quad\quad Engineers’ waiting time BIM 人员的表现 quad\quad 工程师的等待时间
BIM Design Validation Performance Analysis under Priority Rules 优先规则下的 BIM 设计验证性能分析
Fig. 2. Research method. 图 2.研究方法。
over the time between arrivals is 1//lambda1 / \lambda. Customers arrive randomly. The exponential distribution is a probability distribution that adequately describes the random arrival property and is referred to as the ‘Markovian property’. 1//lambda1 / \lambda 。客户随机到达。指数分布是一种能充分描述随机到达特性的概率分布,被称为 "马尔可夫特性"。
A system with only one server is referred to as a single server system, and a system with two or more servers is referred to as a multi-server system. In a basic queuing system, each customer is individually serviced by one server. The time from the start of the customer’s service to the moment it is completed is referred to as service time. The queuing model assumes that service times have a uniform probability distribution across all servers. Table 5 shows the server and queue model assumptions. 只有一台服务器的系统称为单服务器系统,有两台或更多服务器的系统称为多服务器系统。在基本的排队系统中,每个客户都由一台服务器单独提供服务。从客户服务开始到服务结束的时间称为服务时间。队列模型假定所有服务器的服务时间具有均匀的概率分布。表 5 显示了服务器和队列模型假设。
The symbol for the mean of the service time probability distribution is 1//mu.mu1 / \mu . \mu represents the average number of customers that one server can serve per unit time. This is referred to as the average service rate. For example, if 1//mu1 / \mu is 30 min , then the average service rate (mu)(\mu) is 2 customers/h. In the queuing model, M=M= exponential distribution (Markovian) as a symbol representing the probability distribution for arrival-to-arrival times and service times. 服务时间概率分布均值的符号为 1//mu.mu1 / \mu . \mu 代表一名服务器在单位时间内能服务的客户平均数量。这被称为平均服务率。例如,如果 1//mu1 / \mu 为 30 分钟,则平均服务速率 (mu)(\mu) 为 2 个客户/小时。在排队模型中, M=M= 指数分布(马尔可夫分布)作为一个符号,代表了到达到到达时间和服务时间的概率分布。
The M/M/1 model is a single server model with one server. Both arrival-to-arrival and service times follow an exponential distribution. If ss is the symbol for the number of servers, then the M//M//sM / M / s model is a model with servers of ss. The first symbol (M) is the probability distribution over the arrival interval, and the second symbol (M) is the probability distribution over the service time. (M) denotes an exponential distribution with Markovian properties. The performance of the standby system can be analyzed by the number of customers waiting and the waiting time of the customers. Table 6 presents the notation used in this study. M/M/1 模型是一种只有一台服务器的单服务器模型。到达-到达时间和服务时间都服从指数分布。如果 ss 是服务器数量的符号,那么 M//M//sM / M / s 模型就是服务器数量为 ss 的模型。第一个符号 (M) 是到达间隔的概率分布,第二个符号 (M) 是服务时间的概率分布。(M) 表示具有马尔可夫特性的指数分布。备用系统的性能可以通过等待的客户数量和客户等待时间来分析。表 6 列出了本研究中使用的符号。
In a waiting system, customers are unproductive members of the organization while waiting. Customers care about how long they have to wait for service, and customer satisfaction can be expressed in appropriate waiting times. Therefore, it is important to control the waiting time of customers. The basic equations for deriving L,L_(q),WL, L_{q}, W, and W_(q)W_{q} from the queue model are: (1)-(5). 在等待系统中,顾客在等待期间是组织中的非生产性成员。顾客关心的是等待服务的时间,而顾客满意度可以用适当的等待时间来表示。因此,控制顾客的等待时间非常重要。从队列模型中推导出 L,L_(q),WL, L_{q}, W 和 W_(q)W_{q} 的基本方程是(1)-(5). L=lambda W\mathrm{L}=\lambda W ( lambda\lambda mean arrival rate) L=lambda W\mathrm{L}=\lambda W ( lambda\lambda 平均到达率) L_(q)=(P_(0)(lambda//mu)^(s)rho)/(s!(1-rho)^(2))=(P_(0)lambda^(s+1))/((s-1)!mu^(s-1)(s mu-lambda)^(2))L_{q}=\frac{P_{0}(\lambda / \mu)^{s} \rho}{s!(1-\rho)^{2}}=\frac{P_{0} \lambda^{s+1}}{(s-1)!\mu^{s-1}(s \mu-\lambda)^{2}} W=W_(q)+(1)/(mu)W=W_{q}+\frac{1}{\mu} W_(q)=L_(q)//lambdaW_{q}=L_{q} / \lambda P_(0)=(1)/(sum_(n=0)^(s-1)((lambda//mu)^(n))/(n!)+((lambda//mu)^(s))/(s!)((1)/(1-lambda//s mu)))P_{0}=\frac{1}{\sum_{n=0}^{s-1} \frac{(\lambda / \mu)^{n}}{n!}+\frac{(\lambda / \mu)^{s}}{s!}\left(\frac{1}{1-\lambda / s \mu}\right)}
The relational expression of (1) was first proved by D.C. Little and is referred to as Little’s formula. The above relation is important because if one performance of L,L_(q),WL, L_{q}, W, and W_(q)W_{q} is obtained from these relations, the other performance can be obtained. (1) 的关系式由 D.C. Little 首次证明,被称为 Little 公式。上述关系式非常重要,因为如果从这些关系式中得到 L,L_(q),WL, L_{q}, W 和 W_(q)W_{q} 的一个性能,就可以得到另一个性能。
Table 5 表 5
Assumptions of the queueing model. 队列模型的假设。
Table 6 表 6
Notation. 记号
Model description 型号说明
lambda\lambda
Mean arrival rate 平均到达率
1/ג
Average of the probability distribution of the inter-arrival time 到达间隔时间概率分布的平均值
mu\mu
Mean service rate 平均服务率
1/ mu\mu
Average of the probability distribution of service time 服务时间概率分布的平均值
Average waiting time of each customer in the system 系统中每位客户的平均等待时间
W_(q)W_{q}
Average waiting time of each customer in the queue 队列中每位顾客的平均等候时间
Probabilities 概率
P
Vector of state probabilities 状态概率向量
TC
Average total cost per unit time 单位时间平均总成本
SC
Average service cost per unit time 单位时间平均服务成本
Economic analysis indicators 经济分析指标
WC
Average waiting cost per unit time 单位时间平均等待成本
Cs
Cost of one server per unit time 单位时间内一台服务器的成本
Cw
Waiting cost per unit time for each customer in the queuing system 排队系统中每位顾客单位时间内的等待成本
Model description lambda Mean arrival rate
1/ג Average of the probability distribution of the inter-arrival time
mu Mean service rate
1/ mu Average of the probability distribution of service time
s Number of servers
"rho=
lambda//s mu" Utilization factor
L No. of tasks in the system
Performance indicators L_(q) No. of tasks in the queue
W Average waiting time of each customer in the system
W_(q) Average waiting time of each customer in the queue
Probabilities P Vector of state probabilities
TC Average total cost per unit time
SC Average service cost per unit time
Economic analysis indicators WC Average waiting cost per unit time
Cs Cost of one server per unit time
Cw Waiting cost per unit time for each customer in the queuing system| Model description | $\lambda$ | Mean arrival rate |
| :---: | :---: | :---: |
| | 1/ג | Average of the probability distribution of the inter-arrival time |
| | $\mu$ | Mean service rate |
| | 1/ $\mu$ | Average of the probability distribution of service time |
| | s | Number of servers |
| | $\begin{aligned} & \rho= \\ & \lambda / s \mu \end{aligned}$ | Utilization factor |
| | L | No. of tasks in the system |
| Performance indicators | $L_{q}$ | No. of tasks in the queue |
| | W | Average waiting time of each customer in the system |
| | $W_{q}$ | Average waiting time of each customer in the queue |
| Probabilities | P | Vector of state probabilities |
| | TC | Average total cost per unit time |
| | SC | Average service cost per unit time |
| Economic analysis indicators | WC | Average waiting cost per unit time |
| | Cs | Cost of one server per unit time |
| | Cw | Waiting cost per unit time for each customer in the queuing system |
4.2. Priority queue model 4.2.优先队列模型
In the queuing model with priority, queuing rules are based on priority. The order in which customers are selected from the queue for service is determined by a predetermined priority. Important customers are prioritized. When one server serves one customer, the customer with the highest priority is selected and served. The distribution of arrival interval times and service times for each priority class assumes an exponential distribution. Priority queuing assumes that the average service time is the same for all classes. However, average arrival rates may vary by class. 在有优先权的排队模式中,排队规则以优先权为基础。从队列中选择客户提供服务的顺序由预先确定的优先级决定。重要客户优先。当一台服务器为一位客户提供服务时,优先级最高的客户会被选中并得到服务。每个优先级的到达间隔时间和服务时间的分布假设为指数分布。优先排队假定所有类别的平均服务时间相同。然而,平均到达率可能因等级而异。
There are two priority queue models namely non-preemptive and preemptive. Non-preemptive means that when a higher-priority customer arrives in the system, a lower-priority customer in service continues to be served until the moment the service is complete. Therefore, once a server starts serving a customer, they do not stop until completion. Preemptive means that whenever a higher-priority customer enters the system, lower-priority customers in service are evicted. The server immediately begins servicing new, high-priority customers. If both models ignore the distinction for customers at different priority levels, they are the same as the M//M//sM / M / s model except in the order of service. 有两种优先队列模式,即非抢占式和抢占式。非抢占式是指当一个优先级较高的客户到达系统时,系统会继续为优先级较低的客户提供服务,直到服务完成。因此,服务器一旦开始为客户提供服务,就不会停止,直到服务完成。抢占式指的是,每当有优先级较高的客户进入系统时,正在服务的优先级较低的客户就会被驱逐。服务器立即开始为新的高优先级客户提供服务。如果这两种模式都忽略了不同优先级客户的区别,那么除了服务顺序外,它们与 M//M//sM / M / s 模式是一样的。
The difference from the M//M//s\mathrm{M} / \mathrm{M} / \mathrm{s} model is the distribution of waiting time derived from the first-come-first-served service rule. If you have a priority rule, the variance of the waiting time distribution is even greater. This is because the waiting time of the customer with the highest priority will be shorter than that of the first-come-first-served basis, and the waiting time of the customer with the lowest priority will be larger. In the queue model, the probability distribution of service time is determined by the properties of the queue system. 与 M//M//s\mathrm{M} / \mathrm{M} / \mathrm{s} 模型的不同之处在于先到先得服务规则得出的等待时间分布。如果有优先权规则,等待时间分布的方差会更大。这是因为优先级最高的客户的等待时间会短于先到先得基础上的等待时间,而优先级最低的客户的等待时间会更长。在队列模型中,服务时间的概率分布是由队列系统的特性决定的。
How long it takes for BIM staffs to process a project engineer’s design errors may vary from design error to design error. However, this study uses an exponential distribution as the probability distribution of service times (time taken to process design errors). A priority queuing model can be used, assuming a certain probability distribution of service times and times between arrivals of customers (ex: design errors). Both arrival-to-arrival and service times and performance indicators such as L,L_(q),WL, L_{q}, W, and W_(q)W_{q} are used. BIM 人员处理项目工程师设计错误所需的时间可能因设计错误而异。不过,本研究采用指数分布作为服务时间(处理设计错误所需时间)的概率分布。假设服务时间和客户到达时间(例如:设计错误)之间存在一定的概率分布,则可使用优先排队模型。到达到到达时间和服务时间以及 L,L_(q),WL, L_{q}, W 和 W_(q)W_{q} 等性能指标均可使用。
The comparison of performance metrics in the queue model is as follows: First, we analyze the performance of the BIM staff according to the application of priority rules and FCFS rules. This allows for the analysis of the performance of BIM staff when priority rules are applied. Second, a quantitative comparison of waiting avoidance costs for highpriority design errors in FCFS rules and priority rules is possible. 队列模型的性能指标比较如下:首先,我们根据优先级规则和 FCFS 规则的应用情况分析 BIM 人员的绩效。这样就可以分析在应用优先规则时 BIM 工作人员的绩效。其次,可以对 FCFS 规则和优先级规则中高优先级设计错误的等待避免成本进行量化比较。
In this research, the preemptive queue model was excluded from the performance analysis. Through the BIM design validation, all BIM RFIs discovered in a short period of time from the detailed design to the preconstruction stage were tracked. There are no new RIFs to discover. Therefore, the non-preemptive queue model is suitable for performance analysis that handles design errors discovered through design verification. The priority queue model is the same as the M//M//sM / M / s model, except that there is a priority, and the service order and waiting time are distributed accordingly. 在本研究中,性能分析不包括抢先队列模型。通过 BIM 设计验证,跟踪了从详细设计到施工前阶段短时间内发现的所有 BIM RFI。没有新的 RIF 需要发现。因此,非优先队列模型适用于处理通过设计验证发现的设计错误的性能分析。优先队列模型与 M//M//sM / M / s 模型相同,只是有一个优先级,服务顺序和等待时间也相应分配。
If the average waiting time in the system of a class k customer in a steady state is W_(k)W_{k}, then s=s= number of servers, mu=\mu= average service rate per server, lambda_(i)=\lambda_{i}= average arrival rate of class ii customers, 如果稳定状态下 k 类客户在系统中的平均等待时间为 W_(k)W_{k} ,则 s=s= 服务器数量, mu=\mu= 每台服务器的平均服务速率, lambda_(i)=\lambda_{i}=ii 类客户的平均到达速率、
{:[lambda=sum_(i=1)^(N)lambda_(i)","r=(lambda )/(u)","" is in Relational Expressions "(6)∼(9).],[W_(k)=(1)/(AB_(k-1)B_(k))+(1)/(mu)","k=1","2","dots","N","" in this expression "(6)]:}\begin{aligned}
& \lambda=\sum_{i=1}^{N} \lambda_{i}, \mathrm{r}=\frac{\lambda}{u}, \text { is in Relational Expressions }(6) \sim(9) . \\
& W_{k}=\frac{1}{A B_{k-1} B_{k}}+\frac{1}{\mu}, k=1,2, \ldots, N, \text { in this expression }(6)
\end{aligned}
A=s!(s mu-lambda)/(r^(s))sum_(j=0)^(s-1r^(j))+s mu,B_(0)=1A=s!\frac{s \mu-\lambda}{r^{s}} \sum_{j=0}^{s-1 r^{j}}+s \mu, B_{0}=1, B_(k)=1-(sum_(i=1)^(k)lambda_(i))/(s mu)B_{k}=1-\frac{\sum_{i=1}^{k} \lambda_{i}}{s \mu}, This result assumes (6) B_(k)=1-(sum_(i=1)^(k)lambda_(i))/(s mu)B_{k}=1-\frac{\sum_{i=1}^{k} \lambda_{i}}{s \mu} ,这个结果假设 (6) sum_(i=1)^(k)lambda_(i) < s mu\sum_{i=1}^{k} \lambda_{i}<s \mu.
Therefore, grade kk can reach a steady state. Because Little’s formula can be applied by rank, let L_(k)L_{k} be the average number of rank kk customers in the queued system at steady state, which is L_(k)=lambda_(k)W_(k),k=1,2,dots,NL_{k}=\lambda_{k} W_{k}, k=1,2, \ldots, N. The average wait time in the queue for Tier kk customers is W_(k)W_{k} minus 1//mu1 / \mu, and the average queue length is multiplied by lambda_(k)\lambda_{k}. If the performance of LL, L_(q),WL_{q}, W, and W_(q)W_{q} is found, the other performance can be found as well. Therefore, we can analyze the performance of the queue. 因此,等级 kk 可以达到稳定状态。由于利特尔公式可以按等级应用,设 L_(k)L_{k} 为稳定状态下排队系统中等级 kk 客户的平均人数,即 L_(k)=lambda_(k)W_(k),k=1,2,dots,NL_{k}=\lambda_{k} W_{k}, k=1,2, \ldots, N 。等级 kk 客户在队列中的平均等待时间为 W_(k)W_{k} 减去 1//mu1 / \mu ,平均队列长度乘以 lambda_(k)\lambda_{k} 。如果找到了 LL 、 L_(q),WL_{q}, W 和 W_(q)W_{q} 的性能,那么其他性能也可以找到。因此,我们可以分析队列的性能。
The existing research on BIM ROI improvement through BIM RFI tracking was conducted without considering the effect of design errors on the project. However, each design error has a different effect on the project depending on the location and type of construction. Therefore, design errors that can cause delays or affect projects must be categorized and prioritized to be addressed. Priority resolution may reduce BIM staffing or reduce waiting time for high priority design errors. Through the expression in (10), it is possible to quantitatively analyze the total cost when the priority and the FCFS rules are applied. 现有关于通过 BIM RFI 跟踪提高 BIM 投资回报率的研究没有考虑设计错误对项目的影响。然而,根据施工地点和类型的不同,每个设计错误对项目的影响也不同。因此,必须对可能导致延误或影响项目的设计错误进行分类,并按优先级加以解决。优先解决可减少 BIM 人员配置或减少高优先级设计错误的等待时间。通过(10)中的表达式,可以定量分析应用优先级和 FCFS 规则时的总成本。
minimum TC=SC+WC\mathrm{TC}=\mathrm{SC}+\mathrm{WC}, 最小值 TC=SC+WC\mathrm{TC}=\mathrm{SC}+\mathrm{WC} 、
TC: Average total cost per unit time. TC:单位时间内的平均总成本。
SC: Average service cost per unit time. SC:单位时间内的平均服务成本。
WC: Average waiting cost per unit time. WC:单位时间内的平均等待成本。
The waiting cost of the project engineer according to the BIM RFI processing sequence can be analyzed by the Eqs. (12), (13). Cs is the cost for one BIM employee per unit time. Cw is the waiting cost of project participants per unit time, s=s= number of servers, and L=L= average number of customers in the queuing system. Therefore, the minimum TC considering both the service and waiting cost can be determined by estimating the constants Cs and Cw , and finding the value of s that satisfies the eq. 根据 BIM RFI 处理顺序,项目工程师的等待成本可由式(12)、(13)分析。Cs 是一名 BIM 员工在单位时间内的成本。Cw 为单位时间内项目参与者的等待成本, s=s= 为服务器数量, L=L= 为排队系统中客户的平均数量。因此,考虑到服务成本和等待成本的最小 TC 可以通过估算常数 Cs 和 Cw 来确定,并找出满足公式 s=s=的 s 值。 SC=Cs^(**)s\mathrm{SC}=\mathrm{Cs}^{*} \mathrm{~s}, WC=Cw^(**)L\mathrm{WC}=\mathrm{Cw}^{*} \mathrm{~L},
Minimum TC =Cs^(**)s+Cw**L=\mathrm{Cs}^{*} \mathrm{~s}+\mathrm{Cw} * \mathrm{~L} 最低 TC =Cs^(**)s+Cw**L=\mathrm{Cs}^{*} \mathrm{~s}+\mathrm{Cw} * \mathrm{~L}
In this study, we consider the waiting cost of engineers to evaluate the performance with the priority policy and the FCFS policy applied. The evaluation of the waiting cost that engineers can avoid due to the introduction of the priority policy can be analyzed by Eq. (14). The point 在本研究中,我们考虑了工程师的等待成本,以评估优先级策略和 FCFS 策略的性能。对工程师因引入优先策略而避免的等待成本的评估可通过式(14)进行分析。点
to consider here is that the priority (n=1)(n=1) is processed first, but the priority (n=2)(n=2) is processed after the priority (n=1)(n=1) is processed first. 这里需要考虑的是,优先级 (n=1)(n=1) 优先处理,而优先级 (n=2)(n=2) 则在优先级 (n=1)(n=1) 优先处理后处理。
WC(FCFS) - WC(Priority) = engineer waiting avoidance cost due to the introduction of the priority policy (14) WC(FCFS)-WC(Priority) = 由于采用优先政策而避免的工程师等待成本 (14)
(14) *number of design errors by priority(n) = Engineers total waiting avoidance cost by priority(n), (15). (14) *优先级(n)的设计错误数 = 优先级(n)的工程师避免等待总成本,(15)。
5. Case study 5.案例研究
5.1. Data collection & classification 5.1.数据收集与分类
Table 7 shows the design errors collected by BIM staff through the validation of the BIM design in each project. Project A data was collected using BIM reports and RFI recorded by BIM staff. In project A, 1228 BIM design errors were found through the validation of the BIM design. Project B data was collected using automatic clash checking via Navisworks and RFI recorded by BIM staff. In project B, 904 MEP clash errors were found through the MEP clash review. 表 7 載列 BIM 人員在每個項目中,透過驗證 BIM 設計所收集到的設計誤 差。項目 A 的數據是根據建築信息模擬人員記錄的建築信息模擬報告和無線射頻表達意見收集。在项目 A 中,通过 BIM 设计验证发现了 1228 项 BIM 设计错误。项目 B 的数据是通过 Navisworks 的自动冲突检查和 BIM 人员记录的 RFI 收集的。在项目 B 中,通过 MEP 冲突审查发现了 904 个 MEP 冲突错误。
The performance when priority rules are applied to the design error handling sequence can be considered a result of BIM staffing performance to handle BIM design error and a reduction in project engineer wait time for high priority design error. To compare performance when FCFS rules and priority rules are applied, there is need to determine the number of employees who have collected BIM FRIs over a given period of time. 在设计错误处理顺序中应用优先规则时的绩效,可视为处理 BIM 设计错误的 BIM 人员配置绩效以及项目工程师对高优先级设计错误的等待时间减少的结果。要比较采用 FCFS 规则和优先规则时的绩效,需要确定在特定时间段内收集了 BIM FRI 的员工人数。
Converting the collected BIM RFI through the input period of the BIM staff ( 1 month =22=22 days) allows for the calculation of the number of design errors processed by the BIM staff. This is the average arrival rate of the design errors that the BIM staff must handle in the queuing model. Project A has an average arrival rate of 22.74 and Project B has an average arrival rate of 11.58 . 将收集到的 BIM RFI 通过 BIM 人员的输入期(1 个月 =22=22 天)进行转换,可计算出 BIM 人员处理的设计错误数量。这就是排队模型中 BIM 人员必须处理的设计错误的平均到达率。项目 A 的平均到达率为 22.74,项目 B 的平均到达率为 11.58。
Ham et al. [6] interviews the BIM staff; they can handle an average of three BIM design errors per day. This study applied Ham et al. [6] interview to compare the performance under the FCFS rule. Therefore, project A applied the service rate of BIM staff to 3 cases per day ( mu=3\mu=3 ). In an interview with BIM staff who conducted the MEP interference review of Project B, they were able to handle 15 BIM design errors per day on average. Therefore, the BIM staff service rate for project B was applied at 15 cases per day (mu=15)(\mu=15). Ham 等人[6]采访了 BIM 工作人员;他们平均每天可以处理三个 BIM 设计错误。本研究采用 Ham 等人[6]的访谈来比较 FCFS 规则下的绩效。因此,项目 A 将 BIM 人员的服务率定为每天 3 个案例( mu=3\mu=3 )。在与项目 B 进行机电工程干扰审查的 BIM 人员访谈时,他们平均每天能够处理 15 个 BIM 设计错误。因此,项目 B 的 BIM 人员服务率为每天 15 个案例 (mu=15)(\mu=15) 。
In the multi-server queuing model, the server utilization (rho)(\rho) must satisfy rho <= 1\rho \leqq 1 to be in a stable state capable of performing normal services. However, the rho\rho value of Project A(s=6)\mathrm{A}(\mathrm{s}=6) is 1.26 . Therefore, the project cannot reflect the results of the queuing model. Accordingly, Ham et al. [6] performed the analysis by increasing the number of BIM staff to s=s= 11, who performed BIM-based design verification in the preconstruction stage. Therefore, we analyze the performance of the queuing model to which the priority rule is applied using s=11s=11 for the performance of project A in this study. 在多服务器队列模型中,服务器利用率 (rho)(\rho) 必须满足 rho <= 1\rho \leqq 1 才能处于能够提供正常服务的稳定状态。然而,项目 A(s=6)\mathrm{A}(\mathrm{s}=6) 的 rho\rho 值为 1.26。因此,该项目无法反映排队模型的结果。因此,Ham 等人[6] 通过将 BIM 人员数量增加到 s=s= 11 人进行了分析,他们在施工前阶段进行了基于 BIM 的设计验证。因此,我们在本研究中针对项目 A 的性能,使用 s=11s=11 分析了应用优先规则的排队模型的性能。
Project B had an average arrival rate ( 11.58 cases/day) that was lower than the average service rate ( 15 cases/day). Therefore, only one BIM staff was able to respond to all BIM design errors. The server idle rate is 0.23;77%0.23 ; 77 \% can be spent processing design errors and 23%23 \% processing other tasks. 项目 B 的平均到达率(11.58 例/天)低于平均服务率(15 例/天)。因此,只有一名 BIM 人员能够处理所有 BIM 设计错误。服务器空闲率为 0.23;77%0.23 ; 77 \% ,可用于处理设计错误和 23%23 \% 处理其他任务。
Table 7 表 7
Descriptions of BIM staffing in real-world projects. 描述真实世界项目中的 BIM 人员配置。
Project 项目
A
B
Total BIM RFIs BIM RFI 总数
1228
904
BIM staff input period BIM 工作人员投入期
54 days 54 天
78 days 78 天
Number of BIM staff members(s) BIM 工作人员人数
6
1
Mean arrival rate (lambda)(\lambda) 平均到达率 (lambda)(\lambda)
22.74
11.58
Mean service rate(mu)\operatorname{rate}(\mu) 平均服务 rate(mu)\operatorname{rate}(\mu)
3
15
Server utilization rate (rho)(\rho) 服务器利用率 (rho)(\rho)
1.26
0.77
Server idle rate (1-rho)(1-\rho) 服务器空闲率 (1-rho)(1-\rho)
N/A 不适用
0.23
Project A B
Total BIM RFIs 1228 904
BIM staff input period 54 days 78 days
Number of BIM staff members(s) 6 1
Mean arrival rate (lambda) 22.74 11.58
Mean service rate(mu) 3 15
Server utilization rate (rho) 1.26 0.77
Server idle rate (1-rho) N/A 0.23| Project | A | B |
| :--- | :--- | :--- |
| Total BIM RFIs | 1228 | 904 |
| BIM staff input period | 54 days | 78 days |
| Number of BIM staff members(s) | 6 | 1 |
| Mean arrival rate $(\lambda)$ | 22.74 | 11.58 |
| Mean service $\operatorname{rate}(\mu)$ | 3 | 15 |
| Server utilization rate $(\rho)$ | 1.26 | 0.77 |
| Server idle rate $(1-\rho)$ | N/A | 0.23 |
5.2.1. Project AA design error priority classification 5.2.1.项目 AA 设计错误优先级分类
1228 design errors were discovered in project A. It is difficult to resolve all the design errors in a short period of time before construction after detailed design. Therefore, to classify design errors, 1228 design errors were categorized into 3 types through collaboration with 7 process management experts and quality control experts. 在项目 A 中发现了 1228 项设计错误。在详细设计完成后施工前的短时间内,很难解决所有的设计错误。因此,为了对设计错误进行分类,我们与 7 位过程管理专家和质量控制专家合作,将 1228 项设计错误分为 3 类。
As a result of categorizing design errors, 1056 design errors were classified as simple design errors (Type 1) that can be resolved at the design stage. The remaining 172 design errors were classified as likely to cause dismantling and reconstruction (Type 2) if not discovered prior to construction. It was further confirmed that the 32 design errors that occurred in Landmark Tower could affect the subsequent process owing to the accumulation of rework, resulting in fatal delay(Type 3). For a detailed description of the design errors discovered through the validation of the BIM design of project A, see the study in [6] 在对设计错误进行分类后,1056 项设计错误被归类为简单设计错误(第 1 类),可在设计阶段解决。其余 172 项设计错误被归类为可能导致拆除和重建(第 2 类),如果在施工前没有发现的话。经进一步确认,置地广场大厦出现的 32 个设计错误可能会影响后续工序,造成返工积累,导致致命延误(第 3 类)。关于项目 A 的 BIM 设计验证中发现的设计错误的详细描述,请参阅[6]中的研究。
Fig. 3 shows a design error that may cause fatal construction delays (Type 3). Discrepancy of absence information on boundary differences at tower boundaries can result in serious construction problems. Therefore, Table 8 shows the design error priority criteria for project A. Simple design errors can be classified as priority 3 (3st), which can be handled last. Design errors that have the potential to cause dismantling and rebuilding can be classified as Priority 2 (2st). Design errors with potential delays owing to the accumulation of rework can be classified as Priority 1(1st). 图 3 显示了可能造成致命施工延误的设计错误(第 3 类)。塔楼边界的边界差异信息不一致可能导致严重的施工问题。因此,表 8 列出了项目 A 的设计错误优先级标准。简单的设计错误可归类为优先级 3(3st),可最后处理。有可能导致拆除和重建的设计错误可列为优先级 2(2st)。有可能造成返工而延误工期的设计错误可列为优先级 1(第 1 级)。
904 design errors were found in project B. The 904 design errors were categorized into three types namely A, B, and C, through collaboration with project participants. As a result of categorizing design errors, 35 interference errors were classified as negligible interference (Type 1) from the construction point of view. A total of 674 interference errors were classified as single process interference (Type 2) within each work type. A total of 195 interference errors were classified as interference (Type 3) requiring consultation with other types of work. 通过与项目参与方合作,将这 904 项设计错误分为 A、B 和 C 三类。在对设计错误进行分类后,从施工角度来看,有 35 个干扰错误被归类为可忽略不计的干扰(类型 1)。在每个工种中,共有 674 个干扰错误被归类为单一过程干扰(第 2 类)。共有 195 个干扰错误被归类为需要与其他工种协商的干扰(第 3 类)。
The following Fig. 4 is an example of interference (Type 3) that requires consultation between types of work. It is an interference error found through BIM; however, it cannot be found on the drawing owing to interference between Structure and MEP. Therefore, Table 9 shows the priority criteria for project B. From a construction point of view, negligible interference can be classified as Priority 3 (3st). Interferences that are self-resolving in a single process can be classified as priority 2 (2st). Interference that requires consultation with other types of work can be classified as priority 1 (1st). 下图 4 是干扰(类型 3)的一个示例,需要在各工种之间进行协商。这是一个通过 BIM 发现的干扰错误,但由于结构和 MEP 之间的干扰,在图纸上无法发现。因此,表 9 列出了项目 B 的优先级标准。从施工角度来看,可忽略不计的干扰可归类为优先级 3(3st)。可在单一工序中自行解决的干扰可列为优先级 2(2st)。需要与其他工种协商的干扰可列为优先级 1(1st)。
5.3. Basic performance analysis of queuing models 5.3.队列模型的基本性能分析
5.3.1. Project A basic performance analysis 5.3.1.项目 A 基本绩效分析
Assuming 11 BIM staffs assigned to project A, rho\rho is 0.69 , which satisfies rho <= 1\rho \leqq 1 to reach a steady state. Therefore, the performance of project A can be analyzed through the queuing model as shown in Table 10. The default performance when FCFS rules are applied is L=7.99\mathrm{L}=7.99 cases, Lq=\mathrm{Lq}= 0.41 cases, W=0.35\mathrm{W}=0.35 days, Wq=0.01\mathrm{Wq}=0.01 days. In other words, the average waiting time for a BIM RFI to be processed is 0.35 days (based on 8 h worked per day, 2.8 h ). 假设为项目 A 分配 11 名 BIM 人员, rho\rho 为 0.69,满足 rho <= 1\rho \leqq 1 ,达到稳定状态。因此,项目 A 的性能可通过队列模型进行分析,如表 10 所示。应用 FCFS 规则时的默认性能为: L=7.99\mathrm{L}=7.99 例, Lq=\mathrm{Lq}= 0.41 例, W=0.35\mathrm{W}=0.35 天, Wq=0.01\mathrm{Wq}=0.01 天。换句话说,处理 BIM RFI 的平均等待时间为 0.35 天(按每天工作 8 小时,即 2.8 小时计算)。
When the priority rule is applied to the design error handling sequence, the performance is different from that when the FCFS rule is applied. The high-priority(1st) performance is L=0.20,Lq=0.00,W=\mathrm{L}=0.20, \mathrm{Lq}=0.00, \mathrm{~W}=0.33,Wq=0.000.33, \mathrm{Wq}=0.00, which significantly improves the performance of L and Lq. This means that few customers (L=0.20)(\mathrm{L}=0.20) are in service and can be processed as soon as they enter the server. This improves high-priority performance by delaying low-priority design errors. Through this, the risk of serious design errors such as re-construction and delay in construction can be eliminated in advance. 当优先级规则应用于设计错误处理序列时,其性能与应用 FCFS 规则时不同。高优先级(1st)性能为 L=0.20,Lq=0.00,W=\mathrm{L}=0.20, \mathrm{Lq}=0.00, \mathrm{~W}=0.33,Wq=0.000.33, \mathrm{Wq}=0.00 ,这大大提高了 L 和 Lq 的性能。这意味着, (L=0.20)(\mathrm{L}=0.20) 服务中的客户很少,他们一进入服务器就能得到处理。这就通过延迟低优先级的设计错误,提高了高优先级的性能。通过这种方式,可以提前消除重新施工和延误施工等严重设计错误的风险。
Ham et al. [6] proposed a method to optimize BIM staff by applying Ham 等人[6]提出了一种优化 BIM 人员的方法,通过应用
Fig. 3. Example of fatal delay design error (Type 3) 图 3.致命延迟设计错误示例(类型 3)
Table 8 表 8
Project A design error priority classification. 项目 A 设计错误优先级分类。
Division 分部
Categorize design error types 对设计错误类型进行分类
Number of design errors 设计错误数量
Priority (n) 优先权 (n)
Type 1 第一类
Simple design errors 简单的设计错误
1056
3 st 3站
Type 2 第二类
Rework design errors 返工设计错误
140
2 st 2站
Type 3 类型 3
Delay design errors 延迟设计错误
32
1 st
Total 总计
1228
Division Categorize design error types Number of design errors Priority (n)
Type 1 Simple design errors 1056 3 st
Type 2 Rework design errors 140 2 st
Type 3 Delay design errors 32 1 st
Total 1228 | Division | Categorize design error types | Number of design errors | Priority (n) |
| :--- | :--- | :--- | :--- |
| Type 1 | Simple design errors | 1056 | 3 st |
| Type 2 | Rework design errors | 140 | 2 st |
| Type 3 | Delay design errors | 32 | 1 st |
| Total | | 1228 | |
FCFS rules to project A. In design error handling under FCFS rules, 10 BIM staff were best suited for Project A. Table 11 shows the above performance. However, design errors may have different effects depending on the location and type of error. Therefore, to quantitatively analyze the performance of BIM personnel when the priority rule is applied, we derived the performance of the priority queuing model for ss=8-11=8-11. Table 12 shows the above performance. 在 FCFS 规则下的设计错误处理方面,10 名 BIM 人员最适合项目 A。然而,设计错误可能会因错误的位置和类型不同而产生不同的影响。因此,为了定量分析 BIM 人员在应用优先规则时的表现,我们得出了 ss=8-11=8-11 的优先排队模型的表现。表 12 显示了上述性能。
When 8 BIM staff (s=8)(s=8) were assigned to project A, the performance of high priority (1st, 2st) was L=0.21,0.96\mathrm{L}=0.21,0.96, which demonstrated 当 8 名 BIM 人员 (s=8)(s=8) 被分配到项目 A 时,高优先级(第 1、第 2)的绩效为 L=0.21,0.96\mathrm{L}=0.21,0.96 ,这表明
significant improvement compared with L=22.86\mathrm{L}=22.86 when FCFS rules were applied. High-priority design errors are very unlikely to exist in the system and are resolved without waiting as soon as they enter the server. The performance of low-priority design errors (3st) was improved compared with the performance when the FCFS rule was applied with L =21.34=21.34. However, it is the same as the FCFS rule because design errors with higher priority are processed first. The utilization rate of the server is rho=0.94\rho=0.94, and the server spends almost all of their time handling incoming design errors every hour. 与应用 FCFS 规则时的 L=22.86\mathrm{L}=22.86 相比,有了明显改善。高优先级设计错误在系统中存在的可能性很小,一旦进入服务器,无需等待即可解决。与应用 FCFS 规则时的性能相比,低优先级设计错误(3st)的性能有所提高,L =21.34=21.34 。 不过,它与 FCFS 规则相同,因为优先级较高的设计错误会被优先处理。服务器的利用率为 rho=0.94\rho=0.94 ,服务器每小时几乎要花费全部时间处理传入的设计错误。
When 9 BIM staff (s=9)(s=9) were assigned to project A , the performance of high priority(1st, 2st) was L=0.20,0.92L=0.20,0.92, which showed significant improvement compared with L=10.41\mathrm{L}=10.41 when FCFS rules were applied. High-priority design errors are highly unlike to exist in the system and are resolved without waiting as soon as they enter the server. The performance of low-priority design errors (3st) was improved compared with the performance when the FCFS rule was applied with L=9.26\mathrm{L}=9.26. However, it is the same as the FCFS rule because design errors with higher priority are processed first. The server utilization rate is rho=0.84\rho=0.84; 当 9 名 BIM 人员 (s=9)(s=9) 被分配到项目 A 时,高优先级(第 1、第 2 位)的表现为 L=0.20,0.92L=0.20,0.92 ,与应用 FCFS 规则时的 L=10.41\mathrm{L}=10.41 相比有显著改善。高优先级设计错误极不可能存在于系统中,一旦进入服务器,无需等待即可解决。与应用 FCFS 规则时的性能相比,低优先级设计错误(3st)的性能提高了 L=9.26\mathrm{L}=9.26 。 但是,它与 FCFS 规则相同,因为优先级较高的设计错误会被优先处理。服务器利用率为 rho=0.84\rho=0.84 ;
Fig. 4. Example of requiring consultation with other types of work(Type 3). 图 4.要求与其他类型的工作进行协商的示例(类型 3)。
Table 9 表 9
Project B MEP interference error classification. 项目 B MEP 干扰错误分类。
Number of
interferences| Number of |
| :--- |
| interferences |
优先权 (n)
Priority
(n)
Priority
(n)| Priority |
| :--- |
| (n) |
Type 1 第一类
从施工角度看,干扰可忽略不计 每种工种内的单一工序干扰,需要与其他工种协商
negligible interference from the
construction point of view
single process interference within
each work type
requiring consultation with other
types of work
negligible interference from the
construction point of view
single process interference within
each work type
requiring consultation with other
types of work| negligible interference from the |
| :--- |
| construction point of view |
| single process interference within |
| each work type |
| requiring consultation with other |
| types of work |
35
3st 第3个
Type 3 类型 3
195
2st 第2
Total 总计
typ 类型
typ| typ |
| :--- |
1st 第 1
Division "MEP Interference Review
Classification Criteria" "Number of
interferences" "Priority
(n)"
Type 1 "negligible interference from the
construction point of view
single process interference within
each work type
requiring consultation with other
types of work" 35 3st
Type 3 195 2st
Total "typ" 1st | Division | MEP Interference Review <br> Classification Criteria | Number of <br> interferences | Priority <br> (n) |
| :--- | :--- | :--- | :--- |
| Type 1 | negligible interference from the <br> construction point of view <br> single process interference within <br> each work type <br> requiring consultation with other <br> types of work | 35 | 3st |
| Type 3 | 195 | 2st | |
| Total | typ | 1st | |
Table 10 表 10
Project A queuing model performance (FCFS/Priority). 项目 A 队列模型性能(FCFS/优先级)。
it is busy handling design errors that arrive every hour. However, there is an idle time of 0.16 (Based on 8 h work //1.28h/ 1.28 \mathrm{~h} ). 它忙于处理每小时出现的设计错误。但是,空闲时间为 0.16(基于 8 小时工作 //1.28h/ 1.28 \mathrm{~h} )。
When 10 BIM staff (s=10)(s=10) were assigned to project A, both highand low-priority design errors outperformed FCFS rule-applied performance. The utilization rate of the server was rho=0.75;3//4\rho=0.75 ; 3 / 4 of the working hours deal are spent on design errors while 1//41 / 4 of idle time exists. 当 10 名 BIM 人员 (s=10)(s=10) 被分配到项目 A 时,高优先级和低优先级设计错误的表现都优于 FCFS 规则应用的表现。服务器的利用率为 rho=0.75;3//4\rho=0.75 ; 3 / 4 ,其中 rho=0.75;3//4\rho=0.75 ; 3 / 4 工作时间用于处理设计错误, 1//41 / 4 为闲置时间。
It is important to analyze the performance according to the change in the number of servers under the priority rule. High-priority ( n=1,2n=1,2 ) design errors are addressed by BIM staff as soon as they occur. However, low-priority design errors improve performance with the number of servers. The above analysis can be interpreted in two ways. If the processing of low-grade design errors can be postponed, 8 BIM staff can be assigned project A. Second, if low-grade design error handling needs to be improved, 9 BIM staff should be assigned project A. The criteria of priority and the input of BIM staff may be applied differently depending on the conditions and site of the project. However, the performance under the priority rule was quantitatively analyzed through the queuing model that the performance was better than the performance when the 根据优先级规则下服务器数量的变化分析性能非常重要。高优先级( n=1,2n=1,2 )的设计错误一旦发生,BIM 人员就会立即处理。然而,低优先级的设计错误会随着服务器数量的增加而提高性能。上述分析可以有两种解释。如果低等级设计错误的处理可以推迟,则可指派 8 名 BIM 人员负责项目 A;其次,如果低等级设计错误的处理需要改进,则应指派 9 名 BIM 人员负责项目 A。然而,通过排队模型对优先规则下的绩效进行定量分析,结果表明其绩效优于优先规则下的绩效。
FCFS rule was applied. 采用了 FCFS 规则。
5.3.2. Project B basic performance analysis 5.3.2.项目 B 基本绩效分析
The server utilization rate of project BB is stable with rho=0.77\rho=0.77. Therefore, the performance of project BB can be analyzed using the queuing model as shown in Table 13. When the FCFS rule is applied to the MEP interference error handling sequence, the performance is L=\mathrm{L}=3.39,Lq=2.62,W=0.29,Wq=0.223.39, \mathrm{Lq}=2.62, \mathrm{~W}=0.29, \mathrm{Wq}=0.22. This means that the average waiting time for a BIM RFI to be processed is 0.29 days (based on 8 h worked per day, 2.3 h ). 项目 BB 的服务器利用率与 rho=0.77\rho=0.77 保持稳定。因此,项目 BB 的性能可使用队列模型进行分析,如表 13 所示。当 FCFS 规则应用于 MEP 干扰错误处理序列时,性能为 L=\mathrm{L}=3.39,Lq=2.62,W=0.29,Wq=0.223.39, \mathrm{Lq}=2.62, \mathrm{~W}=0.29, \mathrm{Wq}=0.22 。这意味着 BIM RFI 处理的平均等待时间为 0.29 天(按每天工作 8 小时,2.3 小时计算)。
MEP interference error handling performance under priority rules has significantly improved. The performance of the interference error with the highest priority (n=1)(n=1) is L=0.32,Lq=0.15,W=0.12,Wq=\mathrm{L}=0.32, \mathrm{Lq}=0.15, \mathrm{~W}=0.12, \mathrm{Wq}= 0.06 . As soon as they enter the server, they can be processed by BIM staff. 优先级规则下的 MEP 干扰错误处理性能显著提高。最高优先级 (n=1)(n=1) 的干扰错误处理性能为 L=0.32,Lq=0.15,W=0.12,Wq=\mathrm{L}=0.32, \mathrm{Lq}=0.15, \mathrm{~W}=0.12, \mathrm{Wq}= 0.06。只要进入服务器,BIM 人员就可以对其进行处理。
The performance of the interference error with the second priority ( nn=2=2 ) is L=2.65,Lq=2.07,W=0.30\mathrm{L}=2.65, \mathrm{Lq}=2.07, \mathrm{~W}=0.30 days, and Lq=0.24\mathrm{Lq}=0.24. Although the number of customers in the system is small compared with the performance of the FCFS rule, waiting time is high because the highest-priority interfering errors are handled first. 第二优先级的干扰错误( nn=2=2 )的性能为 L=2.65,Lq=2.07,W=0.30\mathrm{L}=2.65, \mathrm{Lq}=2.07, \mathrm{~W}=0.30 天, Lq=0.24\mathrm{Lq}=0.24 。虽然与 FCFS 规则的性能相比,系统中的客户数量较少,但由于优先级最高的干扰错误首先得到处理,因此等待时间较长。
The performance of the lowest priority (n=3)(n=3) interference error was L=0.42,Lq=0.39,W=0.94\mathrm{L}=0.42, \mathrm{Lq}=0.39, \mathrm{~W}=0.94, and Wq=0.88\mathrm{Wq}=0.88. The number of customers in the server is small. However, the performance of W and Wq is low. This is because interference errors with higher priority are processed first. The good performance for L and Lq was attributed to the low priority interference count of 35 in Table 9. 最低优先级 (n=3)(n=3) 干扰错误的性能为 L=0.42,Lq=0.39,W=0.94\mathrm{L}=0.42, \mathrm{Lq}=0.39, \mathrm{~W}=0.94 , Wq=0.88\mathrm{Wq}=0.88 。服务器中的客户数量较少。然而,W 和 Wq 的性能却很低。这是因为优先级较高的干扰错误会被优先处理。L 和 Lq 的良好性能归功于表 9 中 35 的低优先级干扰计数。
Unlike project A, project B had only one BIM staff. Therefore, it is impossible to determine the decline in BIM staff when priority rules are applied. However, we can quantitatively analyze that performance when priority rules are applied is superior to performance when FCFS rules are applied. The next section, analyzes the engineers’ avoidance cost for high-priority design errors. 与项目 A 不同,项目 B 只有一名 BIM 人员。因此,无法确定采用优先规则时 BIM 人员的减少情况。不过,我们可以定量分析出,采用优先规则时的绩效优于采用 FCFS 规则时的绩效。下一节将分析工程师避免高优先级设计错误的成本。
5.4. Engineers waiting cost analysis with priority rule applied 5.4.采用优先权规则的工程师等待成本分析
5.4.1. Project AA engineer waiting cost analysis 5.4.1.项目 AA 工程师等待成本分析
In the analysis of the engineers’ waiting cost according to the design error processing sequence, the engineers’ waiting avoidance cost for a high-priority design error should be quantified, A quick response to a high-priority design error results in avoiding engineer’s waiting cost. Accordingly, project A engineers’ waiting cost was quantified. 在根据设计错误处理顺序分析工程师等待成本时,应量化工程师避免高优先级设计错误的等待成本。因此,对项目 A 工程师的等待成本进行了量化。
Project A spent KRW 5 million per month for the labor cost of one BIM staff. This was KRW 227,272 per day (based on 22 working days per month, 8 h per day), which was KRW 28,409 per hour. The waiting cost (Cw) was the labor cost (KRW 270,333/day) of a professional engineer based on the 2017 engineering used in the performance analysis with FCFS rules applied in the study on [6]. Converting this to unit time, Cw (the cost wasted while the project engineer waits for BIM design error feedback) per hour is KRW 33,792. Therefore, it can be analyzed by applying (12) and (13). Table 14 shows the waiting cost according to the order of handling design errors. 项目 A 每月花费 500 万韩元支付一名 BIM 工作人员的人工成本。每天 227 272 韩元(按每月 22 个工作日,每天 8 小时计算),即每小时 28 409 韩元。等待成本(Cw)是专业工程师的人工成本(270,333 韩元/天),以 2017 年工程为基础,在性能分析中使用 FCFS 规则进行研究[6]。将其转换为单位时间,每小时的 Cw(项目工程师等待 BIM 设计错误反馈时浪费的成本)为 33 792 韩元。因此,可以应用(12)和(13)进行分析。表 14 显示了按照处理设计错误的顺序排列的等待成本。
When the FCFS rule is applied to the handling of BIM design errors, the waiting cost of engineers is KRW 269,998. When the priority rule is applied, the first, second and third priority waiting costs are KRW 6758, KRW 29,339, and KRW 233,164 respectively. Fig. 5 shows the cost of waiting for engineers. The verification of the BIM design is mainly aimed at managing high-risk design errors such as rework and delay in 当采用 FCFS 规则处理 BIM 设计错误时,工程师的等待成本为 269998 韩元。如果采用优先级规则,第一、第二和第三优先级的等待成本分别为 6758 韩元、29339 韩元和 233164 韩元。图 5 显示了工程师的等待成本。BIM 设计的验证主要是为了管理高风险的设计错误,如返工和延误。
Table 13 表 13
Project B queuing model performance(FCFS/priority). 项目 B 队列模型性能(FCFS/优先级)。
construction first. 先施工。
The design error with the highest priority (1st) avoid the waiting cost of KRW 263,240. Design errors with the second priority (2st) avoid the waiting cost of KRW 233,901. Design errors with the lowest priority (3st) are handled last. This is the same as the engineer waiting cost under the FCFS rules. The engineer waiting cost of the highest-priority design error was significantly reduced by 1//401 / 40 compared with the FCFS rule applied waiting cost. This study is aimed at improving BIM ROI by analyzing the performance when priority rules are applied to design errors discovered through the verification of the BIM design. Therefore, we analyze the engineer’s waiting avoidance cost. 优先级最高(1st)的设计错误可避免 263 240 韩元的等待成本。第二优先级(2st)的设计错误可避免 233,901 韩元的等待成本。优先级最低(3st)的设计错误最后处理。这与 FCFS 规则下的工程师等待成本相同。与 FCFS 规则应用的等待成本相比,最高优先级设计错误的工程师等待成本大幅降低了 1//401 / 40 。本研究旨在通过分析优先级规则应用于 BIM 设计验证过程中发现的设计错误时的性能,提高 BIM 投资回报率。因此,我们分析了工程师的避免等待成本。
The design errors with the highest priority(1st) for project A is 32 cases. The waiting cost of the FCFS rule is KRW 269,998, and the waiting cost of the design errors with the highest priority is KRW 6758. Therefore, waiting avoidance cost for the design errors with the highest priority through 263,240**32263,240 * 32 is KRW 8,423,6808,423,680. 项目 A 中优先级最高(1)的设计错误为 32 个。FCFS 规则的等待成本为 269998 韩元,优先级最高的设计错误的等待成本为 6758 韩元。因此,通过 263,240**32263,240 * 32 优先级最高的设计错误的等待避免成本为 8,423,6808,423,680 韩元。
The design errors with the second priority (2st) is processed after the design errors with the first priority (1st) is handled. The waiting cost of engineers is KRW 269,998-6758-29,339, so waiting avoidance cost is KRW 233,901. Therefore, the waiting avoidance cost for the design errors with the second priority through 233,901**140233,901 * 140 is KRW 32,746,14032,746,140. When the priority rule is applied to the design error processing sequence of project A, the engineer waiting cost of KRW 41,169,82041,169,820 is reduced. 在处理完第一优先级(1)的设计错误后,再处理第二优先级(2st)的设计错误。工程师的等待成本为 269998-6758-29339 韩元,因此避免等待成本为 233901 韩元。因此,通过 233,901**140233,901 * 140 第二优先级的设计错误的等待避免成本为 32,746,14032,746,140 韩元。当优先级规则应用于项目 A 的设计错误处理顺序时,工程师的等待成本 41,169,82041,169,820 就会降低。
The analysis of the engineers’ waiting cost according to the MEP interference error handling sequence should quantify the engineer’s waiting avoidance cost for high-priority interference errors. High priority interference errors reduce waiting cost compared with performance with FCFS rules. A quick response to a high-priority interference error results in avoiding the engineer’s waiting cost. Accordingly, we quantified the waiting cost for project BB engineer. 根据 MEP 干扰错误处理顺序对工程师等待成本的分析,应量化工程师避免高优先级干扰错误的等待成本。与 FCFS 规则相比,高优先级干扰错误降低了等待成本。对高优先级干扰错误的快速响应可避免工程师的等待成本。因此,我们量化了项目 BB 工程师的等待成本。
Project B spent KRW 5,000,000 per month for the labor cost of one BIM staff. This was KRW 227,272 per day (based on 22 working days per month, 8 h per day), which was KRW 28,409 per hour. The waiting cost (Cw) was the labor cost (KRW 270,333/day) of a professional engineer based on the 2017 engineering used in the performance analysis with FCFS rules applied in the study on [6]. Converting this to unit time, Cw 项目 B 每月花费 5,000,000 韩元支付一名 BIM 工作人员的人工成本。每天 227 272 韩元(按每月 22 个工作日,每天 8 小时计算),即每小时 28 409 韩元。等待成本(Cw)是专业工程师的人工成本(270,333 韩元/天),以 2017 年工程为基础,在性能分析中使用 FCFS 规则进行研究[6]。将其转换为单位时间,Cw
Fig. 5. Project A quantify the cost of waiting for engineers. 图 5.项目 A 量化等待工程师的成本。
(cost wasted while the project engineer waits for BIM design error feedback) per hour is KRW 33,792. Therefore, it can be analyzed by applying (12) and (13). Table 15 below shows the engineer’s waiting cost according to the order of handling interference errors (项目工程师等待 BIM 设计错误反馈时浪费的成本)每小时为 33 792 韩元。因此,可以应用(12)和(13)进行分析。下表 15 显示了工程师根据处理干扰错误的先后顺序而产生的等待成本
When the FCFS rule is applied to MEP interference error handling, the engineer’s waiting cost is KRW 114,555 . When the priority rule is applied, the first, second and third priority waiting costs are KRW 10,813 , KRW 89,549, and KRW 14,193 respectively. Fig. 6 shows the cost of waiting for engineers. 当 FCFS 规则应用于 MEP 干扰错误处理时,工程师的等待成本为 114 555 韩元。采用优先规则时,第一、第二和第三优先级的等待成本分别为 10,813 韩元、89,549 韩元和 14,193 韩元。图 6 显示了工程师的等待成本。
Interference errors with the highest priority (1st) avoid waiting cost of KRW 103,742. Interference errors with the second priority (2st) avoid waiting cost of 14,193 won. Interference errors with the lowest priority (3st) are handled last; this is the same as the engineer waiting cost under the FCFS rules. The waiting cost for the interference errors of the lowest priority (3st) was low because there were very few interference errors (35 cases). However, because high-priority interference errors are handled first, there is no waiting avoidance cost despite the low waiting cost of the lowest priority(3st). 最高优先级(1st)的干扰错误可避免 103 742 韩元的等待费用。第二优先级(2st)的干扰错误可避免 14 193 韩元的等待成本。优先级最低(3st)的干扰错误最后处理;这与 FCFS 规则下的工程师等待成本相同。最低优先级(3st)干扰错误的等待成本很低,因为干扰错误很少(35 例)。但是,由于高优先级的干扰错误会首先得到处理,因此尽管最低优先级(3st)的等待成本很低,但却没有避免等待的成本。
The engineer waiting cost of the highest-priority interference error was significantly reduced by 1//111 / 11 compared with the FCFS rule applied waiting cost. As with project A, we analyzed the engineer’s waiting avoidance costs to identify performance improvements under the priority rule. 与 FCFS 规则应用的等待成本相比,最高优先级干扰错误的工程师等待成本大幅降低了 1//111 / 11 。与项目 A 一样,我们分析了工程师的等待避免成本,以确定优先级规则下的性能改进。
The Interference error with the highest priority for project B is 195 cases. The waiting cost of the FCFS rule is KRW 114,555 , and the waiting cost of the design error with the highest priority is KRW 10,813 . Therefore, the avoidance cost for the interference error with the highest priority(1st) through 103,742*195 is KRW 20,229,690. The interference error with the second priority (2st) is KRW 114,555-10,813-89,549, which can avoid the waiting cost of KRW 14,193 . Therefore, the avoid cost for the interference error with the second priority through 14,193**67414,193 * 674 is KRW 9,566,0829,566,082. When the priority rule is applied to the interference error processing sequence of project BB, the engineer waiting cost of KRW 29,795,772 is reduced. 项目 B 中优先级最高的干扰错误为 195 个。FCFS 规则的等待成本为 114 555 韩元,优先级最高的设计错误的等待成本为 10 813 韩元。因此,通过 103,742*195 计算,优先级最高(第一级)的干扰错误的避免成本为 20,229,690 韩元。第二优先级(2st)的干扰误差为 114,555-10,813-89,549 韩元,可避免 14,193 韩元的等待成本。因此,通过 14,193**67414,193 * 674 避免第二优先级干扰误差的成本为 9,566,0829,566,082 韩元。当优先级规则应用于项目 BB 的干扰错误处理顺序时,工程师的等待成本为 29 795 772 韩元。
6. Comparative analysis 6.比较分析
In this section, two types of performance improvement when processing BIM RFI by applying priority are compared with the existing performance. As is/to be was used to compare performance when the FCFS and priority rules were applied. Output (benefit of BIM)/Input (cost of BIM)* 100%100 \% is used to calculate BIM ROI [1]. Decreasing input and increasing output can improve BIM ROI. 在本节中,我们将比较应用优先级处理 BIM RFI 时的两种性能改进与现有性能。采用 FCFS 和优先级规则时,使用 "现状"/"待定 "来比较性能。输出(BIM 效益)/输入(BIM 成本)* 100%100 \% 用于计算 BIM 投资回报率[1]。减少投入、增加产出可以提高 BIM 投资回报率。
First, the application of priority rules to the RFI processing sequence can reduce the number of optimal BIM staff. When FCFS rules are applied to project A, the optimal BIM staffing is 10 . However, applying the priority rule can reduce the optimal BIM staffing to 8-9 (Table 16). If there are 8 BIM staffs, the labor cost will be reduced by KRW 340,000,000340,000,000. If there are 9 BIM staffs, the labor cost will be reduced by KRW 170,000,000 (Fig. 7). It was confirmed that the design error handling performance analysis under the priority rule can reduce the BIM staff (Input) improved BIM ROI through reduced labor costs. 首先,在 RFI 处理顺序中应用优先级规则可以减少最佳 BIM 人员数量。对项目 A 采用 FCFS 规则时,最佳 BIM 人员配置为 10 人。然而,应用优先规则可将最佳 BIM 人员配置减少到 8-9 人(表 16)。如果有 8 名 BIM 人员,人工成本将减少 340,000,000340,000,000 韩元。如果有 9 名 BIM 人员,人工成本将减少 1.7 亿韩元(图 7)。由此证实,优先规则下的设计错误处理性能分析可以通过减少人工成本来减少 BIM 人员(投入),提高 BIM 投资回报率。
Second, project engineers’ waiting costs for high-priority RFIs are reduced. The reduction in waiting cost can be considered a waiting avoidance cost in the calculation of the BIM ROI. When the priority rule is applied to projects AA and BB, it is confirmed that the waiting cost (Output) of the project engineer is reduced. For projects A and B with 其次,减少了项目工程师等待高优先级 RFI 的成本。在计算 BIM 投资回报率时,等待成本的减少可视为避免等待成本。当优先级规则应用于项目 AA 和 BB 时,可以确认项目工程师的等待成本(输出)降低了。对于项目 A 和 B,其
Table 15 表 15
Project B engineer waiting cost. 项目 B 工程师等待费用。
Division As is (FCFS) To be (Priority)
Labor cost according to the FCFS(10) Priority(9) Priority(8)
optimal number of BIM 1,700,000,000 1,530,000,000 1,360,000,000
staff(KRW) 170,000,000-340,000,000 Improvement | Division | As is (FCFS) | To be (Priority) | |
| :--- | :--- | :--- | :--- |
| Labor cost according to the | FCFS(10) | Priority(9) | Priority(8) |
| optimal number of BIM | $1,700,000,000$ | $1,530,000,000$ | $1,360,000,000$ |
| staff(KRW) | $170,000,000-340,000,000$ Improvement | | |
Fig. 7. Changes in labor costs according to the number of BIM staff in project A. 图 7.项目 A 中人工成本随 BIM 人员数量变化的情况。
FCFS rules applied to the RFI processing sequence, engineers waiting costs are KRW 269,998 and KRW 114,555. However, it has been confirmed that high priority waiting cost of the engineers in projects A and B with priority rules has decreased significantly to KRW 6758 and KRW 10,813 (Fig. 8, Table 17). Calculating this, projects A and B can avoid the engineer’s waiting costs by KRW 41,169,820 and KRW 29,795,722 respectively. 如果将 FCFS 规则应用于 RFI 处理顺序,工程师的等待成本分别为 269998 韩元和 114555 韩元。然而,在采用优先规则的项目 A 和项目 B 中,工程师的高优先等待成本已大幅降至 6758 韩元和 10813 韩元(图 8,表 17)。由此计算,项目 A 和项目 B 可分别避免 41 169 820 韩元和 29 795 722 韩元的工程师等待成本。
Project A, where the priority rule was applied, could reduce BIM manpower (Input) by 1 or 2 people. Additionally, the waiting cost (Output) of the project engineer could save KRW 41,169,820 compared with the FCFS rule. Therefore, assuming that 8 BIM staffs are employed, KRW 340,000,000 (labor cost) +41,169,820+41,169,820 (engineer waiting avoidance cost) =381,169,820=381,169,820 can be saved. Assuming that 9 BIM staff are employed, KRW 170,000,000 +41,169,820=211,169,820+41,169,820=211,169,820 can be saved. 采用优先规则的项目 A 可减少 1 或 2 名 BIM 人力(投入)。此外,与 FCFS 规则相比,项目工程师的等待成本(产出)可节省 41 169 820 韩元。因此,假设聘用 8 名 BIM 人员,可节省 3.4 亿韩元(人工成本) +41,169,820+41,169,820 (避免工程师等待成本) =381,169,820=381,169,820 。假设聘用 9 名 BIM 人员,则可节省 +41,169,820=211,169,820+41,169,820=211,169,820 1.7 亿韩元。
Project B with a priority rule applied can save the engineers’ waiting cost of KRW 29,795,772 compared with the FCFS rule. However, because only one BIM staff was used for project B, labor cost savings for BIM staff cannot be confirmed. 与 FCFS 规则相比,采用优先规则的项目 B 可节省工程师等待成本 29 795 772 韩元。但是,由于项目 B 只使用了一名 BIM 人员,因此无法确认 BIM 人员节省的人工成本。
The prioritization of design errors resolution has value when 在下列情况下,优先解决设计错误具有价值
Fig. 8. Engineers waiting cost for FCFS rule and priority rule(1st). 图 8.FCFS 规则和优先级规则(1st)的工程师等待成本。
Table 17 表 17
Project B engineer waiting cost. 项目 B 工程师等待费用。
Waiting costs for project engineers 项目工程师的等待费用
As is (FCFS) 现状(FCFS)
To be (Priority 1st) 待定(第一优先级)
Project A (KRW) 项目 A(韩元)
269,998
6758
Project B(KRW) 项目 B(韩元)
114,555
10,813
Waiting costs for project engineers As is (FCFS) To be (Priority 1st)
Project A (KRW) 269,998 6758
Project B(KRW) 114,555 10,813| Waiting costs for project engineers | As is (FCFS) | To be (Priority 1st) |
| :--- | :--- | :--- |
| Project A (KRW) | 269,998 | 6758 |
| Project B(KRW) | 114,555 | 10,813 |
analyzing BIM ROI. The application of prioritization policies has been reported to have positive effects such as reducing the number of servers (Kim et al. [42]), enhancing service performance (Souza et al. [45]), improving task performance (William et al. [62]), and optimizing schedules (Liu et al. [41]). In previous studies, an economic benefits of BIM-based clash avoidance were evaluated by applying prioritization policy (Chahrour et al. [59]). This study focuses on the analysis the effects of prioritization policies from a micro perspective, specifically reducing number of servers (BIM staff) and improving the service performance (engineer’s wait avoidance). To evaluate the economic feasibility, the gap was derived by comparing the engineer waiting cost of the FCFS policy and that of the prioritization policy (Eq. 14). The derived gap represents the engineer’s wait avoidance cost for a high-priority RFI. Through the reduction in labor costs and the cost of engineer wait avoidance, the potential improvement in BIM ROI has been quantified. 分析 BIM 投资回报率。据报道,优先级策略的应用具有积极的效果,如减少服务器数量(Kim 等人[42])、提高服务性能(Souza 等人[45])、改善任务性能(William 等人[62])和优化进度(Liu 等人[41])。在之前的研究中,基于 BIM 的避免冲突的经济效益是通过应用优先级策略来评估的(Chahrour 等[59])。本研究侧重于从微观角度分析优先级策略的效果,特别是减少服务器(BIM 人员)数量和提高服务性能(避免工程师等待)。为评估经济可行性,通过比较 FCFS 政策和优先级政策的工程师等待成本得出差距(公式 14)。得出的差距代表工程师避免等待高优先级 RFI 的成本。通过降低人工成本和避免工程师等待的成本,可以量化 BIM 投资回报率的潜在改进。
7. Conclusions and further research 7.结论和进一步研究
This study proposes methods to enhance the BIM ROI in construction projects by analyzing the performance of BIM design validation using a priority queue model. The BIM RFI discovered through BIM design validation was tracked and all design errors were classified according to priority criteria. We derived the optimal BIM staffing by exploring the BIM staffing performance according to the priority policy application in the BIM RFI response order. In addition, we investigated changes in waiting costs for engineers with priority policies applied to BIM coordination. 本研究通过使用优先级队列模型分析 BIM 设计验证的性能,提出了在建筑项目中提高 BIM 投资回报率的方法。我们跟踪了通过 BIM 设计验证发现的 BIM RFI,并根据优先级标准对所有设计错误进行了分类。我们根据 BIM RFI 响应顺序中的优先级政策应用,探索了 BIM 人员配备的性能,从而得出了最佳 BIM 人员配备。此外,我们还研究了在 BIM 协调中采用优先策略后工程师等待成本的变化。
As expected, changes in the RFI response order have affected the engineer’s waiting costs. We confirmed the gap between priority policy and FCFS policy through performance change for engineer’s waiting time for high priority RFI. Studies that seek to improve BIM ROI through policy changes in the response order of BIM coordination should consider two evaluation criteria. 不出所料,RFI 响应顺序的变化影响了工程师的等待成本。通过工程师对高优先级 RFI 等待时间的绩效变化,我们确认了优先级政策与 FCFS 政策之间的差距。通过改变 BIM 协调响应顺序来提高 BIM 投资回报率的研究应考虑两个评估标准。
The first criteria is the optimal BIM staffing. We were able to reduce the optimal BIM staffing by applying the priority policy to Project A. The second criteria is the reduction in engineers’ waiting costs due to prompt responses to high-priority RFIs. The reduced waiting cost can be considered as the cost of avoiding waiting through the application of priority policies to BIM coordination. 第一个标准是最佳 BIM 人员配置。通过在项目 A 中应用优先政策,我们能够减少最佳 BIM 人员配置。第二个标准是由于对高优先级 RFI 的及时响应而减少了工程师的等待成本。减少的等待成本可视为通过在 BIM 协调中应用优先级政策而避免等待的成本。
The value and significance of this study is to quantify the impact of 这项研究的价值和意义在于量化以下方面的影响
RFI response order changes on project participants. The introduction of priority policies to BIM coordination has reduced organizational inappropriate workflows and reduced BIM staffing. Reducing the input (BIM staffing) and increasing the output (reducing engineer waiting costs, avoiding improper workflows) in BIM use is a good scenario to enhance BIM ROI. Improved BIM ROI leads to increased BIM adoption. 项目参与者的 RFI 响应顺序变化。在 BIM 协调中引入优先政策,减少了组织中不恰当的工作流程,减少了 BIM 人员配置。减少 BIM 使用中的投入(BIM 人员配备)和增加产出(减少工程师等待成本、避免不当工作流程)是提高 BIM 投资回报率的良好方案。BIM 投资回报率的提高会导致 BIM 应用的增加。
There are two things to consider in this study. First, we were able to apply queueing theory by setting the arrival time and service time of customers stochastically. Using the exponential distribution of the queuing model, it was possible to predict service time and waiting time. To use the queue model, the analysis was simplified by considering the arrival time of the customer (BIM RFI) as a single step with a mean arrival time. 这项研究有两点值得考虑。首先,我们能够应用排队理论,随机设定顾客的到达时间和服务时间。利用排队模型的指数分布,可以预测服务时间和等待时间。为了使用队列模型,我们将顾客(BIM RFI)的到达时间视为具有平均到达时间的单一步骤,从而简化了分析。
Second, the criteria for classifying design errors may vary depending on the characteristics, progress, and applied construction methods of the project. If different priority classification criteria are applied, different results may be obtained, and the priority classification criteria are refined, the results may vary. In addition, we analyzed the application of priority policies to two real case projects with BIM, but the application cases for various projects need to be analyzed. 其次,设计错误的分类标准可能因项目的特点、进度和应用的施工方法而异。如果采用不同的优先级分类标准,可能会得到不同的结果,而对优先级分类标准进行细化,结果也可能不同。此外,我们分析了优先级策略在两个使用 BIM 的实际案例项目中的应用,但还需要分析不同项目的应用案例。
Funding source 资金来源
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A1052050). 这项工作得到了韩国政府资助的韩国国家研究基金会(NRF)基金(MSIT)(编号:2021R1F1A1052050)的支持。
Declaration of Competing Interest 竞争利益声明
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 作者声明,他们没有任何可能会影响本文所报告工作的已知经济利益或个人关系。
Data availability 数据可用性
Data will be made available on request. 数据将应要求提供。
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Corresponding author at: Department of Digital Architecture and Urban Engineering, Hanyang Cyber University, 222, Seoul 04763, Republic of Korea. 通讯作者韩国汉阳网络大学数字建筑与城市工程系,222,首尔 04763。
E-mail address: nhham@hycu.ac.kr (N. Ham). 电子邮件地址:nhham@hycu.ac.kr (N. Ham)。
The time between arrivals is evenly distributed according to the probability distribution 到达时间间隔按照概率分布均匀分布
Arriving customers wait until service completion in the queue system 到达的客户在排队系统中等待服务完成
There is one infinite queue in the queuing system, which can accommodate an infinite number of customers. 排队系统中有一个无限队列,可以容纳无限多的顾客。
Waiting rules are first-come-first-served (FCFS) 等候规则为先到先得(FCFS)
A queue system has a fixed number of servers, each serving all customers. 队列系统有固定数量的服务器,每个服务器为所有客户服务。
Each customer is individually serviced on one server 每个客户在一台服务器上接受单独服务
Service times are distributed equally independently according to probability distribution 服务时间根据概率分布平均独立分布