Applying cluster identification algorithm and simulation to generate ...

Construction Management and Economics (February 2005) 23, 199–213

Applying cluster identification algorithm and simulation to generate probabilistic network schedules for design projects WEI-CHIH WANG* and REN-JYE DZENG Department of Civil Engineering, National Chiao Tung University, 1001, Ta-Hsueh Road, Hsin-Chu 300, Taiwan Received 13 November 2003; accepted 17 September 2004

Scheduling of a design project is complex because design activities often have information dependencies between each other. This study proposes a network-based model to schedule design projects and generate probabilistic project durations. The proposed model applies a modified cluster identification algorithm to evaluate information dependencies between design activities to facilitate the establishment of a schedule network (and regroup activities to support the assignment of design work); it also uses a simulation approach to incorporate the effect on duration of the uncertain number of design iterations. The model is implemented in four stages, which are breaking down the design work; evaluating the dependencies; identifying concurrent activities; and estimating the durations of activities and simulating the duration of design project. The advantages of the proposed model are demonstrated through its application to an example project, which was reviewed by industrial practitioners. Practitioners felt that the generated detailed scheduling data could help them to control their design work more precisely than a bar chart. Additionally, the simulated probabilistic project duration provided them with an awareness of the risk involved in meeting the contractual deadline. Keywords: Cluster identification algorithm, design schedule, information dependency, simulation, and project management

Introduction Constructing a building or facility depends on a design project and a construction project. Although many scheduling models, such as bar charts (Moder et al., 1983; Chrzanowski and Johnston, 1986) and network techniques (El-sersy, 1992; O’Brien, 1993; Ahuja et al., 1994), have been described to manage the duration of a construction project, little effort has been made to control the schedule of the design project probably because the cost associated with the design work is only 3–10% of the total project cost (Eldin, 1991). Time is not easily saved during the construction work because the primary aim of construction scheduling is to ensure that the fieldwork proceeds according to the original schedule. However, slightly improving the control of the design schedule may greatly reduce the total duration of the project. Current practice typically uses a bar chart method to represent the schedule of a design project. Each bar * Author for correspondence. E-mail: [email protected]

covers several months and represents a design activity. Some responsible design managers may further state points of expected percentage completions (such as, 25%, 50%, 75% and 100%) or control points (for example, drawing begun, drawings ready for engineering review, signing by project manager, incorporation of client’s comments, and ready for bid/construction) as milestones in each design activity (Choo et al., 2004). The simple bar-chart method cannot effectively support the schedule control of the design work, probably for two main reasons. First, the bar chart does not include enough detail to enable the timely detection of schedule slippage in a design activity. Second, the effects on the project completion date of progress delays in individual activities cannot easily be determined without explicitly showing the logical relationships among activities. Consequently, construction projects are frequently delayed because design deliverables (such as drawings, specifications, material take-off sheets and others) are delivered late (Chang, 2002). Therefore, the overall project deadline is frequently postponed.

Construction Management and Economics ISSN 0144-6193 print/ISSN 1466-433X online # 2005 Taylor & Francis Group Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0144619042000301393

200 A critical-path-method (CPM) network-based schedule (O’Brien, 1993), which is familiar to most practitioners, can present apparent scheduling data (for example, early start time and early finish time of an activity, and the logical relationships between activities), such that the CPM network-based schedule is a potential means of improving the control of design duration. However, using a conventional CPM network analysis to plan design activities is complicated chiefly because design activities often have different degrees of information dependencies between each other, such that the design process involves an uncertain number of iterations (Luh et al., 1999; Austin et al., 2000; Liau and Wang, 2000, Chua et al. 2003, Choo et al. 2004). Thus, a large amount of design information passes among activities many times until owner’s needs or regulatory requirements are met. Such iterative information dependency makes difficult to define the logical relationships between activities in the network as well as to evaluate the duration of each activity. Generally, while professionals employed to design a project should have the talent to handle the technical issues and coordination responsibilities, design deliverables are often delayed. Current scheduling practice in design projects must thus be improved. This work proposes a new network-based scheduling model of design projects, in which a revised cluster identification algorithm is applied to establish a schedule network and a simulation is performed to account for the effect of uncertainty in the number of design iterations on the duration of the project. Additionally, a design project comprises various systems, including architectural, civil, structure, mechanical, electrical and many others (Chua et al. 2003). These systems are designed by not only several functional departments in a single engineering firm, but also, very frequently, by many subcontracted engineering firms. Effective design management depends on properly breaking down the design work into packages (each with one or several systems), to help a head design manager distribute the design work to a range of design teams (including functional departments and subcontracted firms). Therefore, the systems may be advantageously grouped to reduce the number of interorganizational interfaces among the teams. The revised cluster identification algorithm of the proposed model regroups activities (e.g. systems) to facilitate the assignment of design work.

Review of models of the design process The design of a building or facility can be divided into three phases – conceptual design, schematic design and

Wang and Dzeng detailed design. During the conceptual and schematic design phases, a prime designer (architect/engineer or A/E) seeks to incorporate information from a wide range of disciplines; represent candidate solutions; and generate new states from the current ones based on the available information to meet the owner’s requirements, including for example, the budget and general spatial arrangements (Baldwin et al., 1999; Rivard and Fenves, 2000). These two early phases ensure that the design deliverables can satisfy the owner’s needs. A simple bar chart method that allows milestones or due dates of design deliverables to be set may suffice. Moreover, a more complicated technique (such as the network-based scheduling model) may not be required because these two phases are frequently short (perhaps one to three months altogether). As the detailed design phase, the required design work is explicitly stated; the design deliverables must be met to prevent future construction work from being delayed. The importance of efficient design management to ensuring the smooth running of a project is being increasingly appreciated. Much research has been undertaken to better control the design process, and thus increases the effectiveness of the management of design duration. For example, Sanvido and Norton (1994) proposed a building design process model that indicated the tasks (such as acquire design projects, plan and control design, acquire resources and services, and others) involved in a successful design. Their model also identified the flow of information and knowledge that supports the development of the design. Some researchers have addressed the design process problems in a collaborative environment, including for example, miscommunication among designers and incompatibility of design data caused by changes to the design (Peng, 1994; Frankenberger and Badke-Schaub, 1998; Mokhtar et al., 2000; Hegazy et al., 2001). Chang (2001) developed performance indices to quantify whether a design project was ahead of or behind schedule from planned and actual design manhours. Such schedule indices are most useful at the overall project level, but they do not provide the detailed information about the scheduling of design activities. With reference to the uncertainty in the number of iterations among design activities, Luh et al. (1999) developed an optimization-based methodology that combines Lagrangian relaxation, stochastic dynamic programming and optimization to schedule the design process of a manufacturing product project. Considering design iterations and information dependency, Austin et al. (1994, 1999, 2000) described a planning methodology (Analytical Design Planning Technique; ADePT) to help plan the building design process. The core part of ADePT is a dependency

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Cluster identification algorithm and simulation structure matrix analysis that can help to order the design tasks into the optimum sequence to minimize the number of iterations within the multi-disciplinary design process. ADePT is now employed commercially, with its own web-based software application called PlanWeaver (refer to http://www.adeptmanagement.com). In PlanWeaver, the optimized matrix can be delivered as a project delivery schedule by linking the matrix to a project scheduling software application, such as Microsoft Project or Primavera. Furthermore, a computer tool called DePlan, has been developed by integrating the strategic nature of ADePT with the operational approach of Last Planner (Choo et al., 2004). With a focus on viewing design as the flow of information (parameter perspective), an Internet-based framework called the process-parameter-interface (PPI) model was developed to address the design management issues associated with improving design process scheduling and increasing the efficiency of collaboration (Chua et al., 2003). Briefly, several design process models have been developed to handle each of the design characteristics (including information dependency, the number of design iterations and the collaborative environment) using various techniques (including for example, information modeling methods, optimization and computer tools) to improve the management of the design. A good design process model may lead to the effective schedule control of design work.

NET-Design model This section presents the proposed model (NET-Design) to generate a network-based schedule for a design project.

are used as a basis for developing a concurrent design plan, such that more groups can work concurrently, compressing the design schedule. Unlike other studies, in which a sequencing algorithm (such as, ADePT) is applied to determine the optimum sequence of activities by minimizing the number of iterations, this investigation employs a clustering approach (described below) to regroup activities and facilitate the management of design teams; it applies the concept of concurrence to support design scheduling. Additionally, several previously developed models decompose the design work into various levels of detail in a very early modeling step, according to a work breakdown structure. The proposed model herein will further break down the design work only if more parallel groups of activities can be obtained (refer to Figure 1). That is, an activity may not be appropriate for further disaggregation if it depends weakly on other activities (such an one that can be performed concurrently with others), and so it is then likely to be assigned to a single team. (Such activities are PCW, CH, BG, SG, UPW and WWT in the example project. See Section 4.) Stages of modelling Figure 1 shows the four stages of the modeling in the NET-Design. The model first divides all of design work into design activities. Second, the information dependencies between these activities are evaluated. Third, the model applies a modified cluster identification algorithm to support determine these activities’ network precedence relationships for establishing a schedule network (i.e. precedence diagram). Finally, a

Clustering design activities As stated earlier, various design teams commonly undertake the tasks in a design project. From the perspective of high-level management, a head design manager may prefer to control the total design progress by communicating with only a few team managers, instead of numerous design engineers who work on their own activities. Hence, design activities that are strongly related to each other (and so must be executed in a particular order) should be grouped together and assigned to a single design team. Then, the team manager (rather than the head manager) can coordinate the highly-dependent activities of a particular team. If different teams perform these highly dependent activities, then the number of organizational interfaces is likely to be high. Activities of different groups depend weakly on dependencies and can overlap. These groups

Figure 1

Implementation stages of the proposed model

202 three-point estimation method is taken to represent the probabilistic duration of each activity, and simulation is used to derive the probabilistic duration of the project. Stage 1: Breakdown of design work Design work is divided into design activities, using a document review or an expert interview. The document review method is appropriate for a design project that is similar to a familiar or previous one for which a breakdown of the design work is available. When a model user is unsure about the breakdown, interviews with experts (including for example, experienced designer managers or system planners) may be required. These activities may be discipline-based activities (such as architectural, structural, landscaping, mechanical and electrical) or system-based activities (such as process cooling water and ultra-purifying water). For example, a design project may be divided into seven system-based activities (that is, S1, S2, S3, S4, S5, S6 and S7), following a review of documents and interviews with experts. Stage 2: Evaluation of dependencies The second stage is to assess the information dependencies between activities. The dependency assessment is to facilitate the determination of activity sequences. Experts are helpful in this stage. The dependencies between the activities are identified and represented by a binary successor-predecessor matrix A, such as matrix (1). The activities listed on the left and the top of matrix (1) represent predecessors and successors, respectively. A value ‘1’ in a cell specifies that the design of the corresponding successor depends on the design of the corresponding predecessor. The absence of a value in the cell indicates that the corresponding successor does not depend on the predecessor. For example, matrix (1) states that S3 should be designed before S2 (S3RS2) because the design of S2 depends on the design of S3. Notably, the use of a matrix allows each pair of activities to be completely evaluated. When the activities are broken into greater details, the relationships between detailed activities can be better clarified, increasing the likelihood of a correct and complete identification of dependency. However,

Wang and Dzeng whether such a detailed level of activities is considered depends on a design manager’s management style or needs. As mentioned earlier, NET-Design suggests that any activity should be decomposed, yielding more parallel groups of activities. In NET-Design, all strong dependencies are assumed to have been captured by setting a threshold to ignore weak dependencies in the design of a complex product. Nevertheless, the example given by matrix (1) is simplified for illustration. Real-life activities involve more dependencies. Stage 3: Identification of concurrent activities for establishing schedule network When the dependencies among the activities have been evaluated, a modified Cluster Identification Algorithm (CIA) is applied to separate the activities into groups (Kusiak and Chow, 1987). Activities within a single group depend strongly on each other and must be performed in order. In contrast, activities in different groups can be designed concurrently. This grouping facilitates the definition of the precedence relationships among activities. The output of this stage is an established schedule network. (See Section 3.5 for illustrations.) After this stage is completed, an activity that depends strongly on other activities must be broken down further. For example, a civil/structural/architectural activity may be separated into civil, structural, architectural, landscaping, decoration, and interior subactivities, which are performed by different designers. Then, stages (1)–(3) are repeated (Figure 1). Breaking down an activity with a high dependency sum is to separate the activity’s sub-activities with high dependency from weakly dependent ones. Such separation isolates the part of the activity that is not suited to concurrent design, so that the remaining sub-activities may be designed concurrently. Stage 4: Estimation of activity durations and simulation of design duration In NET-Design, the three-point estimation method of PERT (Program Evaluation and Review Technique), which is familiar to most construction practitioners (Moder et al., 1983), is used to represent a statistical distribution of the duration of each design activity. The three-point estimation requires an optimistic value (adi ), a pessimistic value (bdi ), and the most likely value (cdi ) of the duration variable (di) of activity i (i51, 2… I) to be estimated. Notably, these durations are estimated by the person (design manager or system planner) who is in charge of the activities. His or her judgement is based on work experience, the subjective consideration of the personnel available to him and various other factors

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Cluster identification algorithm and simulation (such as the complexity of the project). Additionally, the effects of uncertainty in the number of design iterations within an activity and among activities on the duration are assumed to be approximately described by the probabilistic distributions of activities. A simulation approach is adopted to evaluate the probabilistic duration of the design project (Carr, 1979; Moder et al., 1983; Ahuja and Nandakumar, 1985). A simulation includes a procedure for generating random durations that follow the distribution of di, and then applies the CPM forward and backward calculations to obtain the total duration of the project, dTot. This procedure is performed many hundred times, with dTot being computed each time. A cumulative probability distribution of total project duration can then be constructed from the values of dTot. This distribution is used to estimate the probability of completing a design project within a particular duration. A simulation language, STate and ResOurce Based Simulation of COnstruction ProcEsses or Stroboscope (Martinez, 1996), is used to execute the simulation procedure described in NET-Design. In addition to Stroboscope’s powerful capabilities to dynamically access the state of the simulation, Stroboscope has an add-on that allows the definition of CPM networks with probabilistic durations and the calculation of various statistics about the project and activities. This procedure is implemented on a Pentium III PC with 256 Mbytes of RAM in a Windows XP environment. Analysing 22 duration variables of the example project 10 000 times takes around 15 minutes. The run-time can be reduced using faster PCs and by refining the source code of the model. Modified cluster identification algorithm (MCIA) After the dependencies among the activities are evaluated, stage 3 of NET-Design uses a modified CIA to group the activities. The original CIA has been applied in a wide range of areas, including biology, data reorganization, medicine, pattern recognition, groupings parts of automated systems and production flow analysis (Kusiak and Chow, 1987). This CIA is based on a binary object-feature incidence matrix, whose columns represent objects and whose rows represent features. The object-feature matrix of the original CIA is herein changed into an object-object (successor-predecessor) matrix used to evaluate whether the objects exhibit any dependency (Dzeng, 2003). Figure 2 shows the steps of the modified version of CIA (MCIA), which are described below. Step 1

Determine the cluster dependency threshold T, which is determined by the NET-Design user to control the cluster size.

Figure 2 Steps in implementing the modified cluster identification algorithm

Step 2

Remove from the aforementioned successorpredecessor matrix A the activities whose dependency sum (D) exceed T, and store these activities in matrix A*. The D of an activity is the number of other activities that are dependent on the activity. D is the maximum of Ds and Dp. Ds of an activity is the number of its succeeding activities, which can be determined

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Step 3 Step 4

Step 5 Step 6 Step 7 Step 8

Step 9

Wang and Dzeng by summing the numbers in its row in the matrix. Dp of an activity is the number of its preceding activities, which can be determined by summing the numbers in its column in the matrix. Matrix (1) displays examples of Ds and Dp for each of the activities. The reason for this early removal is to find a separable cluster that includes an activity depending on most other activities. Such an activity, when applying performing the MCIA, may yield fewer clusters than would have been obtained. Hence, some users of the model may wish to remove any such over-dependent activity before performing the matrix analysis. Set the iteration number, k51. Select any row i of the matrix A(k) (where A(k) denotes matrix A at iteration k) and draw a horizontal line hi through it. At each entry ‘1’ on the intersection with the horizontal line hi, draw a vertical line vj. At each entry crossed by the vertical line vj, draw a horizontal line hi. Repeat steps 5 and 6 until no singly crossed entries ‘1’’’ remain. Transform matrix A(k) into A(k+1) by removing all the twice-crossed entries ‘1’. Add all the twice-crossed entries ‘1’ to A*. If matrix A(k+1)50 (such that all its elements equal zero), stop; otherwise, set k5k+1 and return to step 4. Iterations from step 4 to 9 are called matrix analysis.

Each activity whose D exceeds T is removed in step 2, and becomes a separated cluster, which is uninvolved in the subsequent matrix analysis. A value of T that is too high may lead to the generation of too few clusters, each of which is too large (including too many activities). Conversely, a T that is too low may yield too many clusters, such that each cluster is too small. Both situations contradict the purpose of using the MCIA. The suitable T depends on the user and the configuration of the matrix. Half of the total number of activities is a recommended starting value for T (Kusiak and Chow, 1987).

Illustrative example of the MCIA This section uses the previously described seven systembased activities to demonstrate the MCIA. Consider a cluster dependency threshold of 3.5 (half of seven activities). The following shows how the MCIA processes the example matrix (1) with seven activities. Step 1

Set T53.5.

Step 2

S1 is the only activity whose D (Ds57) exceeds 3.5. Thus, remove S1 from A, and store it in A*. A* now includes {S1}.

Notably, Dp may exceed Ds in the determination of D. In that case, such an activity with high Dp (with several predecessors) must be temporarily removed form step 2. An ‘End’ activity is an example of such an activity. If an activity (for example, S1 or ‘End’) with a high dependency on others is not removed, then a large cluster (a group that includes such an activity and many other dependent activities) will form. Large clusters yield fewer parallel work groups. Step 3 Steps 4–7

Set the iteration number k51. Select row S 2 of matrix A (1); draw horizontal line h2 through it, and then draw vertical line v2. Entry ‘1’ at cell (S3, S2) is crossed only once. Thus, draw h3 and then v3. (See matrix (2)).

Steps 8–9

Removing the {S2, S3} cluster from matrix A(1) yields matrix A(2). A* now consists of {S1} and {S2, S3}. Steps 4–7 Select row S4 of matrix A(2); draw horizontal line h4 through it, and then draw vertical line v4. (See matrix (3)).

Steps 8–9 Removing {S4} from matrix A(2) yields matrix A(3). A* now comprises {S1}, {S2, S3} and {S4}. Steps 4–7 Select row S5 of matrix A(3); draw horizontal line h5 through it, and then draw vertical lines v5 and v6. Entry ‘1’ at cell (S6, S6) is crossed only once. Therefore, draw h6. (See matrix (4)).

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Cluster identification algorithm and simulation Remove {S5, S6} from matrix A(3). A* now comprises {S1}, {S2, S3}, {S4} and {S5, S6}. Steps 4–7 Select row S7 of matrix A(4); draw horizontal line h7 through it, and then draw vertical line v7. (See matrix (5)).

Steps 8–9

Steps 8–9

Remove {S7} from matrix A(4). A* now consists of {S1}, {S2, S3}, {S4}, {S5, S6} and {S7}. Since A(4)50, stop.

Matrix (6) presents the final results of clustering. In the matrix, these seven activities are decomposed into five clusters, represented by grey blocks. Except for cluster S1, all clusters are mutually independent; that is, they can be concurrently designed. Notably, at this stage, S1 depends strongly on other activities, and thus may have to be further segregated. The details of such segregation are demonstrated using the application example discussed in the later section.

relationships among the seven activities; S1 precedes other activities; S3RS2; S4 can be designed concurrently with S2, S3, S5, S6 and S7; S5RS6, and S7 can be designed concurrently with S2,S6. Therefore, a precedence network of this design project can be constructed, as displayed in Figure 3.

Example Example project

Notably, the cell representation in the matrix is directional. That is, a ‘1’ in a cell reveals that its corresponding activity in the left of the matrix precedes the corresponding activity on the top of the matrix, rather than the other around. The MCIA includes a ‘redundant’ ‘1’ in each of the diagonal cells (implying that an activity depends on itself) to ensure that all activities will be processed. The algorithm will not work effectively if these redundant ‘1’s are absent from the diagonal cells. For instance, if the ‘1’s are removed from matrix (1) (matrix (69)), steps 4–7 will only result in groups {S1}, {S2, S3} and {S5, S6}; groups {S4} and {S7} will not be identified.

The proposed NET-Design model was applied to a semiconductor wafer fab design project in northern Taiwan. The total construction cost was about US$ 160 million, including the cost of the fab’s structure, mechanics, electrical system and clean room, but excluding that of the production equipment (Dzeng, 2003). The duration of the design project was seven months (210 days). The design was contracted out to several specialized engineering firms, all of which had contracts directly with the client. The client used ‘design start’, 30%, 60%, 80%, and 100% design completion as milestones to control the duration of the project. A simple bar chart was used to represent the planned and actual progress of the design project.

Establishment of design network schedule The aforementioned clustered groups help to determine quickly the logical relationships among activities. That is, matrix (6) shows the following precedence

Figure 3

Derived schedule network with seven activities

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Evaluations Stage 1: Breakdown of design work The design is broken down into nine system-base activities, including civil/structural/architectural (CSA), mechanical/electrical/plumbing (MEP), clean room (CR) and special systems. The special systems include process cooling water (PCW), ultra pure water (UPW), wastewater treatment (WWT), bulk gas (BG), special gas (SG), and chemical handling (CH) systems. This breakdown corresponds to the tendered packages of the design project. Stage 2: Evaluation of dependencies Two managers involved in the project help to evaluate the dependencies among the nine system-based activities, which are summarized in Table 1. Dependencies are of one of five degrees - extreme (E), strong (S), half (H), weak (W), and non-existent (N). For example, CR affects CSA’s structural and architectural layout subsystems. CSA is considered to be approximately half-dependent on CR. That is, the design of CR affects about half of the work involved in designing CSA. Thus, CRRCSA with a ‘half’ dependency. Also, for example, the design of CR strongly impacts MEP’s ice water, product gas, general electricity, heat ventilation air conditioning, and fire prevention subsystems. That is, MEP depends strongly on CR because the design of CR influences over half of the work involved in designing MEP. Thus, CRRMEP with a ‘strong’ dependency. The numbers in parentheses in Table 1 are the binary values in the cells, using ‘weak dependent’ as the threshold. Therefore, the values in the cells in the above two examples (CR vs. CSA and CR vs. MEP) both equal one (although the levels of the dependencies in both examples differ, being ‘half’ and ‘strong’), represented as

Table 1

H(1) and S(1), respectively. Column 11 (Ds) in the table states the sum of dependencies of the successors of each activity in Column 1. The bottom row (Dp) presents the sum of dependencies of predecessors of each activity in the first row. According to the table, CSA and MEP have the highest dependency sums (58). Stage 3: Identification of concurrent activities for establishing schedule network If the cluster dependency threshold T is set to five (about half of the nine activities), then CSA and MEP are removed from the matrix A (i.e. Table 1) before the matrix analysis is performed. The shaded blocks in Table 1 refer to the clustering results of the MCIA. The table indicates that CR is the first activity, followed by CSA and MEP, followed by the remaining activities (PCW, CH, BG, SG, UPW and WWT), which can all be designed concurrently. Figure 4 shows an initial network that represents the logical relationships among these activities. Notably however, in Figure 4, CSA depends on MEP and MEP depends on CSA. Such a cyclic dependency violates the logic of CPM network-based scheduling, and implies that these two activities should be broken down further. CSA and MEP are also broken down further because of their high dependency sums. An incidental benefit of these breakdowns is that they elucidate which parts (i.e., sub-activities) of the activities can be designed in parallel or sequentially. Repetition of stages 1–3 CSA is further broken down into four sub-activities, including CSA1 (architectural structure), CSA2 (architectural layout), CSA3 (architectural exterior wall), and CSA4 (architectural landscape). MEP is further broken down into nine sub-activities, including MEP1 (chiller

Dependencies between activities in the example project Successor (1)

Predecessor

CSA MEP CR PCW CH BG SG UPW WWT Dp

CSA (2)

MEP (3)

E (1) S (1) H (1)

S (1) E (1) S (1)

CR (4)

PCW (5)

CH (6)

BG (7)

SG (8)

UPW (9)

WWT (10)

Ds (11)

H (1) W (1)

H (1) W (1)

H (1) W (1)

S (1) W (1)

H (1) H (1)

H (1) H (1)

(8) (8) (3) (1) (1) (1) (1) (1) (1)

E (1) E (1) E (1) E (1) E (1) E (1) E (1)

(3)

(3)

Notes: E: extreme, S: strong, H: half, W: weak.

(1)

(3)

(3)

(3)

(3)

(3)

(3)

Cluster identification algorithm and simulation

207 influences the design of the box girders in CSA1 (i.e. CRRCSA1). The location of the platform of the CR equipment also determines the layout of CSA2 (i.e. CRRCSA2). Second, matrix (9) displays the dependencies among each sub-activity of CSA and MEP and the other activities. For example, the design of PCW requires information on the loading capacity of the slabs (CSA1) and the layout of structural elements and spaces (CSA2); accordingly, PCW should be a successor for CSA1 and CSA2 (i.e., CSA1RPCW and CSA2RPCW).

Figure 4 Initial schedule network of the example project

equipment), MEP2 (process exhaust system, including general exhaust, acid exhaust and volatile organic compound exhaust subsystems), MEP3 (electrical equipment), MEP4 (high-voltage equipment), MEP5 (heating, ventilation and air conditioning), MEP6 (fire protection system), MEP7 (grounding system), MEP8 (closed circuit television video equipment) and MEP9 (plumbing system). Matrix (7) specifies the dependencies among the decomposed sub-activities, as evaluated by the same managers. Notably, matrix (7), with an average of 3.4 (541/12) dependencies, is obtained from a pruned dependency matrix. According to Figure 4, activity CR precedes CSA and MEP, which precede all of the other activities. Thus, the evaluated dependencies can be divided into the following two parts. (See matrices (8) and (9)). First, matrix (8) presents the dependencies between CR and each subactivity of CSA and MEP. For example, special consideration of the micro vibration associated with CR

Then, matrices (7) and (9) can be treated as the aforementioned Matrix A, and should be further processed by the MCIA to find the clustered groups. Notably, matrix (8) does not need to be applied by the MCIA because the matrix explicitly specifies the precedence relationships among activities (CRRCSA1, CRRCSA2, CRRMEP1, CRRMEP2, CRRMEP3, CRRMEP5 and CRRMEP6). Table 2 shows the precedence relationships among the activities, based on matrices (7), (8), and (9). Figure 5 depicts a schedule network that is this established.

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Stage 4: Estimation of activity durations and simulation of design duration The aforementioned managers (one from the A/E firm and the other from the M/E firm) and several disciplinary designers are asked to help further by providing threepoint duration estimates of each design activity in this example project. Consider CSA1 (architectural structure) for example. The A/E manager estimates that 35 days is the most likely duration for designing CSA1 given the allocated design personnel, the scale and complexity of the project, the micro-vibration requirements of the fab structure, possible coordination with other design discipline-based or system-based activities, and the manager’s own past experience of fab design projects. The duration is optimistically estimated to be only 28 days if more design engineers are allocated and the coordination is smooth, while it is pessimistically increased to 45 days if the conditions are mostly unfavourable. The left part of Table 3 lists the estimates of the durations of the activities. The results of the simulation indicate that the minimum and maximum durations of the project are approximately 156 and 213 days, corresponding to cumulative probabilities of zero and one, respectively. Figure 6 plots the simulated cumulative probability distribution of the project duration. The project can be completed within the contractual duration (5210 days)

Table 2

with a probability of around 99.98%. This high probability of success represents a low risk in meeting the design deadline. Additionally, the expected duration and standard deviation of the project are estimated to be 184 and 7.7 days, respectively. The mean (mi) of the duration variable (di) of each activity i is derived as follows (Moder et al., 1983) to identify the critical activities from the CPM calculations. mdi ~

ðadi z4cdi zbdi Þ 6

ð10Þ

According to the calculated values of mi (in the right part of Table 3), the total duration of the project is 180.5 days. And the critical path is StartRCRRCSA2RMEP3RMEP6RCSA4RCHR End. Focusing attention on these activities that are most constraining on the schedule facilitates the application of the principle of management by exception.

Double-checking the MCIA results In the proposed NET-Design, some activities (such as CSA and MEP in the example project) are broken down if they depend strongly on other activities. Then, the aforementioned stages 1–3 are repeated. A means of double-checking whether the MCIA evaluations are correct is to segregate each activity into sub-activities in

Logical relationships between activities in the example project

Based on matrix (7)

Based on matrix (8)

CSA2RCSA3 CSA2RCSA1 CSA2RMEP1 CSA2RMEP3 CSA2RMEP4

CRRCSA1 CRRCSA2 CRRMEP1 CRRMEP2 CRRMEP3 CRRMEP5 CRRMEP6

CSA3RCSA4 CSA3RMEP2 CSA4RMEP9 MEP1RMEP7 MEP1RCSA1 MEP2RMEP7 MEP3RMEP1 MEP3RMEP2 MEP3RMEP5 MEP3RMEP6 MEP3RMEP8 MEP5RMEP7 MEP6RMEP7 MEP6RCSA4 MEP8RMEP7

Based on matrix (9) CSA1RPCW CSA1RUPW CSA1RWWT CSA2RPCW CSA2RCH CSA2RBG CSA2RSG CSA2RUPW CSA2RWWT CSA3RBG CSA4RSG CSA4RCH CSA4RSG CSA4RWWT MEP1RPCW MEP1RUPW

MEP2RCH MEP2RSG MEP3RPCW MEP3RCH MEP3RBG MEP3RSG MEP3RUPW MEP3RWWT MEP5RUPW MEP5RWWT MEP6RCH MEP6RSG MEP6RUPW MEP6RWWT MEP7RPCW MEP7RUPW MEP7RWWT

209

Cluster identification algorithm and simulation

Figure 5 Established schedule network of the example project

Table 3

Estimated duration data of each activity in the example project

Activity

Description

Optimistic duration

Most likely duration

Pessimistic duration

Mean

Standard deviation

CSA1 CSA2 CSA3 CSA4 MEP1 MEP2 MEP3 MEP4 MEP5

Architectural structure Architectural layout Architectural exterior wall Architectural landscape Chiller equipment Process exhaust system Electrical equipment High-voltage equipment Heating ventilation and air conditioning Fire protection system Grounding system Closed circuit television video equipment Plumbing system Clean room Process cooling water Ultra pure water Wastewater treatment Bulk gas Special gas Chemical handling

28 14 10 7 7 10 20 10 28

35 24 14 10 10 14 28 14 35

45 30 20 12 12 20 40 20 45

35.5 23.3 14.3 9.80 9.80 14.3 28.7 14.3 35.5

2.8 2.7 1.7 0.8 0.8 1.7 3.3 1.7 2.8

20 7 14

28 10 21

40 12 30

28.7 9.80 21.3

3.3 0.8 2.7

20 30 20 25 25 20 20 30

28 45 30 35 35 30 30 45

40 60 40 45 45 40 40 60

28.7 45 30 35 35 30 30 45

3.3 5.0 3.3 3.3 3.3 3.3 3.3 5.0

MEP6 MEP7 MEP8 MEP9 CR PCW UPW WWT BG SG CH

Notes: Unit: days

stage 1. And all the activities and sub-activities are evaluated to determine dependencies and are together identified for concurrency. For example, in Table 1, CSA and MEP are segregated into 13 sub-activities,

CSA1–CSA4 and MEP1–MEP9, respectively; and these 13 sub-activities and seven other activities (CR, PCW, UPW, WWT, BG, SG and CH) are together evaluated for their dependencies. Restated, the MCIA steps are

210

Wang and Dzeng respectively. The PERT distribution, also plotted in Figure 6, is slightly to the left of the simulation distribution, showing that the duration generated by PERT is more optimistic than that generated by the simulation. This optimism of PERT follows from PERT’s merging bias (Moder et al., 1983). However, this PERT was acceptable to the practitioners because of its simplicity.

Other discussions Figure 6 Cumulative probability duration distributions of the example project

applied to 20 (513+7) activities, while the original approach involves only nine (52+7) activities. The method and the current model yield the same results when applied to the example project. Notably however, the alternative method that analyses more activities simultaneously requires that more care be taken to prevent human processing errors. Feedback from practitioners Although the proposed model was not actually applied in the example project, the practitioners who participated in this study appreciated the practical issues raised by the evaluation results. Practitioners felt that the generated detailed scheduling data (including, for example, expected early start and early finish times) concerning each design activity can help them to control their design work more precisely than can a bar chart. Additionally, the simulated probabilistic project duration provides them with an awareness of the risk involved in meeting the contractual deadline. Nevertheless, all practitioners suggested that a computerized application could simplify the modeling. This suggestion will be addressed in future research. Finally, most practitioners were concerned by their lack of familiarity with the simulation algorithms. Therefore, the PERT approach is directly provided herein. In a PERT, the input data, which are the means of the duration variables, can be obtained using Equation (10); the standard deviation (si) of each duration variable (di), is derived as (Moder et al., 1983): bdi {adi ð11Þ 6 Based on the calculated values mi and si (in the right part of Table 3), the PERT analysis finds that the minimum, expected and maximum durations of the example project are around 154, 180 and 207 days, sdi ~

NET-Design considering overlaps between activities The previously described matrix includes only binary values (i.e. zero and one). That is, the design activities are assumed to be independent of, or to follow each other. However, in realty, dependencies among design activities are more complicated. For example, the design of a clean room in a wafer fab project impacts the design of parts of the CSA activity, but not of all of it. Restated, their dependencies may not be characterized as a finish-to-start relationship. When a dependency is not binary, it may be described in various measurements, including a percentage of overlap between activities and the type of network logic (for example, in a start-to-start relationship). Table 4 presents examples of measuring dependency. In the table, Column 2 measures the dependency as a percentage of overlap of activities; Column 3 presents the corresponding time-scaled logical relationship, and Column 4 displays the cell value in the matrix. In the example 2-1 of the table, if an activity can begin only when a large part of the preceding activity has been completed, then the overlap between the activities can be considered to be small; therefore, their dependency is strong, and the value in the corresponding cell is 0.75 (overlapping percentage can be 0–33%). Additionally, in the example 4-1, if an activity can start after a small fraction of its preceding activity has been completed, then the overlap can be said to be large; thus, the dependency is weak, and the value in the corresponding cell is 0.25 (overlapping percentage can be 66,100%). Overlapping activities may also exhibited other types of relationships, as indicated by examples 2-2, 2-3, 3-2, 3-3, 4-2 and 4-3 in Column 3 in Table 4. The value in a cell represents the strength of a dependency between the corresponding predecessor and successor. The matrix analysis of the MCIA requires that the cell values are binary, so the user must determine a threshold between zero and one to distinguish strong relationships from weak ones. A future extension of this work to incorporate this overlapping is suggested.

211

Cluster identification algorithm and simulation Table 4

Example of overlapping of activities associated with various levels of dependency

delay in the aforementioned sub-optimal design case (in which the execution of certain activities may be repeated). However, in the infeasible case (in which the entire design may be totally changed), the NET-Design algorithms should be re run to generate a new design schedule. Nevertheless, the explicit incorporation of design iterations should be further considered, although more complex modeling and simulation algorithms may be required. Tendering clustered design activities

Iterations within an activity and across activities Design iterations may occur within each of the activities, and across them. Decisions (such as regarding changing system requirements to meet a limited budget) made in the preceding activities may constrain the design search space in subsequent activities to such an extent that design may be sub-optimal or even infeasible. Accordingly, some uncertain design iteration loops may arise, possibly across a number of activities. Thus, iterations within and across activities should have a great impact on the ability to arrive at a precise duration estimate of a design project (Austin et al., 1994, 1999, 2000). The current NET-Design assumes that the duration effects ‘within’ or ‘across’ iterations can be specified by a duration distribution of each activity, based on the threepoint duration estimation. The pessimistic duration of each activity may be increased by considering the possible consequences of other upstream and downstream activities to improve the modeling of the duration effects due to the iterations. Hence, the far-right tail of the project duration distribution (as presented in Figure 6) will then be extended to indicate the extra risk of an unexpected

In NET-Design, a group of strongly mutually dependent activities is recommended to be distributed to a single design team to reduce the number of interfaces among teams. For example, in the example project, MEP1 and PCW depend strongly on each other (MEP1RPCW). Hence, NET-Design recommends assigning the two systems to a single team who has the specialty to design both systems. Assigning the design of such two systems to a single team instead of two teams reduces the burden of design interface management from the head design manager. However, such an assignment may not always be practical. For instance, CSA1 also precedes PCW, but two teams with different specialties frequently design them. Even though these activities are highly correlated, they should still be distributed across two teams, between which an interface exists. Nevertheless, the identified interface should still receive substantial attention from management, regardless of whether or not the recommendation is acted upon. Interfaces among different design teams should receive much of the head design manager’s attention. Similarly, interfaces among activities within a team should receive the attention of the manager of the team.

Conclusions Many design projects are currently scheduled using the bar chart method. Such a simple method is ineffective in controlling the schedule of design work. This study has contributed to how the two techniques, modified cluster identification algorithm (taken from the manufacturing domain) and simulation (taken from the manufacturing and construction domains) can be combined to produce a four-stage model (NET-Design) for generating a probabilistic schedule of design project. In NET-Design, activities that exhibit strong information dependencies on each other cannot be designed concurrently. Activities that depend weakly on each other can be designed concurrently. Regrouping activities that depend strongly on each other yields strategies in work assignment and tendering, such that the number of inter-organizational

212 interfaces is reduced. This work considers an example project to demonstrate the feasibility of applying the proposed model. Some other directions of potential future research were also identified during the course of this study. First, since practitioners may find using qualitative language to describe dependencies to be more comfortable, a method (such as fuzzy CIA, Hoppner, 1999) to transform such qualitative description into quantitative data (cell values) should be explored. Second, as the design-build method of project delivery begins to dominate (Fredrickson, 1998), the model may be expandable to one that integrates both design and construction schedules.

Acknowledgements The writers thank the reviewers for their careful evaluation and thoughtful comments. J. J. Pan and Partners, Architects and Planners are appreciated for providing valuable information and feedback on the proposed model and helping evaluate the example project. Mr B. Y. Lin and Mr S. M. Hsieh (former graduate students of National Chiao Tung University) are also appreciated for helping to process the application data.

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