Critical Path

Graduate Institute of Construction Engineering and Management, National Central University, No. 300, Jhongda Rd. , Jhongli City, Taoyuan County 32001, Taiwan b R&D Center for Construction Project Management, Chung Hua University, No. 707, Sec. 2, WuFu Rd. , Hsinchu, 300 Taiwan Received 7 February 2010; received in revised form 12 June 2011; accepted 16 June 2011 Abstract Assessing schedule delay's impact on total project duration to distribute delay liability remains a controversy.None of existing delay analysis methods is perfect because including an element of assumptions, subjective assessment and theoretical projection. Windows-based delay analysis methods are excellent in identifying and measuring construction schedule delays. Based on a previous study identifying potential problems in available windows-based delay analysis methods, this study proposes an innovative windows-based delay analysis method, called the effect-based delay analysis method (the EDAM method).The EDAM meth od performs delay analysis using extracted windows and determines delay impacts by considering the effects of delays on the critical path(s). According to its application to hypothetical cases and comparisons with other methods, the EDAM method is efficient in delay analysis and effective in solving concurrent delays and determining schedule shortened. The proposed EDAM method is a good alternative for schedule delay analysis for construction projects.  © 2011 Elsevier Ltd. and IPMA. All rights reserved. Keywords: Delay analysis; Claim; Schedule analysis; Construction project 1.Introduction Construction projects generally have highly complicated situations during execution, involve many project stakeholders and interfaces, and are influenced by many external factors. Therefore, schedule delays in construction projects are common and affect total project duration in unpredictable ways. Delay information and evidence are usually recorded and represented in different records, documen ts and schedules during the construction phase. Selecting a suitable delay analysis method and analyzing delay information accurately are essential tasks in any delayed construction project.Current delay analysis methods analyze delay liabilities based on delay information and evidence. Various analysis methods have been developed, such as global impact, as-planned, impacted as-planned, net ? Corresponding author. Tel. : +886 3 4227151Ãâ€"34040; fax: +886 3 4257092. E-mail address: [email  protected] edu. tw (J. -B. Yang). impact, time impact, collapsing, isolated delay type, snapshot, window analysis and isolated collapsed but-for (Bordoli and Baldwin, 1998; Gothand, 2003; Hegazy and Zhang, 2005; Kim et al. 2005; Mbabazi et al. , 2005; Ng et al. , 2004; Yang and Yin, 2009; Zack, 2001). Farrow (2007) had clearly claimed that none of the delay analysis methodologies is perfect because they all include an element of assumptions, subjective assessment, and theoretical projection. Ge nerally, a delay analysis method attempts to discover delay information derived from as-planned and as-built schedules, those are the bases for resolving delay disputes and claims.However, existing delay analysis methods still have the following shortcomings: (1) concurrent delays cannot be recognized or calculated by some of existing methods; (2) the critical path method cannot be executed in analysis and critical path changes cannot be considered; (3) the relative cost of float consumption is not considered; (4) analysis is not contemporaneous with delay timing; and (5) most methods focus only on the delayed activities, and ignoring the effects of time-shortened activities on total project duration (Arditi and Pattanakitchamroon, 263-7863/$ – see front matter  © 2011 Elsevier Ltd. and IPMA. All rights reserved. doi:10. 1016/j. ijproman. 2011. 06. 003 386 J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 2006; Bordoli and Baldwi n, 1998; Gothand, 2003; Mbabazi et al. , 2005; Ng et al. , 2004; Yang and Yin, 2009). Furthermore, Arditi and Pattanakitchamroon (2006), in discussing how to select a delay analysis method, concluded that selecting a feasible analysis method depends on a variety of factors, including information availability, time of analysis, methodology apabilities, time, funds and effort allocated for analysis. Based on a empirical study in UK, six group factors (project characteristics, contractual requirements, characteristics of baseline program, cost proportionality, timing of the analysis and record availability) influencing the selection of delay analysis methodologies were identified (Braimah and Ndekugri, 2008). In summary, although some advanced delay analysis methods have been developed, including a few commercial systems, existing delay analysis methods cannot satisfy the practical requirements of delay analysis.That is, practitioners still require an alternative method for complex cas es. Windows-based delay analysis methods perform delay analysis according to some extracted time frames, called windows. Traditional windows-based method, the windows analysis method, has been recognized as the most creditable delay analysis method (Gothand, 2003; Kim et al. , 2005). US courts have generally accepted some types of windows-based method, as they can calculate the impact of various delays, namely, the non-excusable delays (NE delays) and excusable delays (ED delays).Based on the viewpoint of a contractor, excusable delays are further divided into excusable compensable delays (EC delays) and excusable non-compensable delays (EN delays) (Zack, 2000; Mohan and Al-Gahtani, 2006). For above delay types, analysis results generated by windows-based methods provide a clear liability allocation to contract parties. This information is valuable for dispute resolution. For a complex construction project, three types of delays (NE, EC and EN delays), might exist simultaneously.Whi le the information for identifying all types of delays is available, the allocation of total project delay to above delay types provides more clear delay liability identification. Furthermore, for a contractor, to allocate all delays into these delay types improves its ability to get possible delayed-related expenditure back although the situations for compensable/non-compensable depend primarily on the terms of the contract (Trauner et al. , 2009). It is beneficial to a contractor to distinguish compensable and non-compensable delays. Namely, a perfect delay analysis method is targeted to identify these delay types accurately.To provide an alternative delay analysis method for resolving concurrent delays and liability distribution problems and for overcoming the time-consuming drawback of analyzing delays in a day-by-day manner, this study proposes a novel windows-based delay analysis method, called the effect-based delay analysis method (EDAM), which is a systematic analysis metho d that considers the impact of delays on the critical path(s) of a project. 2. Available windows-based delay analysis methods Several windows-based delay analysis methods have been developed in the past two decades.All windows-based delay analysis methods can be divided into two categories: (1) performing delay analysis starting backward from an as-built schedule and (2) performing delay analysis starting forward from an as-planned schedule. The popular methods in the category of starting forward from an as-planned schedule include the windows analysis method (called traditional windows analysis (TWA) hereinafter), the modified windows analysis (MWA) method, the delay analysis method using delay section (DAMUDS) method and the daily windows delay analysis (DWDA) method.The TWA method performs delay analysis using extracted schedule windows, rather than by analyzing delay events in a one-by-one manner forward from the as-planned schedule or backward from the as-built schedule. The MW A method improves analytical processes by the TWA method and uses algorithms to calculate delay liability. The DAMUDS method tries to overcome two limitations in existing methods, namely inadequate accounting of concurrent delays and inadequate accounting of time-shortened activities.The DWDA method calculates clear delay liabilities to the contractor and owner based on day-by-day delay analysis of critical path(s) along the project duration. Kao and Yang (2009) compared the above four windowsbased delay analysis methods using an illustrative case. They determined that the four methods are dynamic delay analysis methods that perform real-time critical path analysis. The TWA and MWA methods are less reliable than the DAMUDS and DWDA methods, since they may lose essential information when the analysis period is long and may be unable to detect critical path changes.The DWDA method analyzes delay information in a day-by-day manner that is the same as as-built situations, but requires c onsiderable effort during analysis. The DAMUDS method is more efficient than the DWDA method even though both yield the same analysis results. Detailed compared information can be found elsewhere (Kao and Yang, 2009). Other windows-based methods belonging to the category of starting backward from an as-built schedule, such as the isolated collapsed but-for delay analysis method (Yang and Yin, 2009), have been developed for facilitating delay analysis problems by similar approaches.However, these methods perform delay analysis moving backward from an as-built schedule, not forward from an as-planned schedule. The approaches of using as-planned schedule or as-built schedule may derive different final analytical results. This study does not compare the results by the methods belonging to the category of starting backward from an as-built schedule to those by the developed EDAM method. 3. Problems in windows-based delay analysis methods 3. 1. Unable to identify critical path changes In general, whether an activity is on a critical path is an important signal when identifying its delay impact on total project duration.During the construction phase of a construction project, many situations e. g. , change order, activity appending or deleting by different site conditions, and critical path changes, affect the outcome of delay analysis. In J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 387 considering delay information only for those activities on the critical path(s) in the as-planned schedule, existing windowsbased delay analysis methods may ignore essential delay information from activities during critical path changes. 3. 2.Incapable of dealing with complicated delay situations An ideal delay analysis method should calculate delay information quickly, accurately and stably. Some windowsbased delay analysis methods perform delay analysis based on arbitrarily extracted windows, while others deal with limited delay sit uations. As construction projects become increasingly complex, proper delay analysis methods should deal with complicated delay situations (i. e. , concurrent delays, project acceleration and compression). Approaches for window extraction by the some mentioned windows-based delay analysis methods cannot effectively deal with complex delay situations. . 3. Inefficient delay analysis Windows-based delay analysis methods perform analysis using extracted windows. The times of delay analysis for different methods vary. The rule by the TWA and MWA methods is to select timing subjectively. Conversely, the DAMUDS and DWDA methods select analysis windows objectively. For a complicated delay case, the TWA and MWA methods might obtain wrong results when using inadequate windows; thus the DAMUDS and DWDA methods may waste considerable calculation effort due to numerous windows in a complex project with long duration.How to intelligently select analysis windows for available windowsbased delay a nalysis methods puzzles a delay analyst. 3. 4. Unclear liability allocation Available windows-based delay analysis methods can identify concurrent delays, but cannot clearly allocate delay liability. For example, the DAMUDS method uses the concept of contractor's float to represent the effects of a contractor on schedule management. Although the DAMUDS method can identify concurrent delays based on a contractor's perspective, it does not provide a clear liability allocation approach. 4.Methodology development 4. 1. Innovative concept To provide an alternative method for dealing with problems in existing windows-based delay analysis methods, this study proposes a novel windows-based delay analysis method, the EDAM method, which is a systematic analysis method based on existing windows-based delay analysis methods. The EDAM method performs delay analysis using extracted windows and determines delay impacts by considering the effects of delays on the critical path. Although the analyti cal processes of the EDAM method are similar to those in other method, the EDAM ethod solves the problems mentioned previously. The EDAM method consists of analytical procedures with baseline schedule development and algorithms for liability identification and calculation. 4. 2. Analytical procedures Fig. 1 shows the analytical processes in the EDAM method. The EDAM method uses an as-planned schedule as a basis for delay analysis, and requires clearly identified delay attributes (delay start, finish and liability) for delay liability calculation. Before delay impact calculation, the EDAM method applies the critical path method to determine a comparison baseline.Based on this comparison baseline, the EDAM method performs schedule analysis by considering two situations: with and without a delay in an analyzed period. If no delay occurred in an analyzed period, the EDAM method considers whether the performance of project acceleration exists. If a delay is identified in an analyzed peri od, a day-by-day delay analysis is executed to calculate the impact of a delay when the delay is on a critical path. In delay impact calculation, the concurrent delay is detected and its liability is then assigned to contract parties.Similar to the other windows-based methods, the EDAM method performs delay analysis using two viewpoints, namely, those of owner and contractor. Therefore, the EDAM method allocates delay liability for each contract party and collects the performance of project acceleration by the contractor for each analyzed period. The EDAM method performs schedule analysis until all analysis periods are complete. 4. 3. Baseline schedule development approach A baseline for delay impact calculation is determined using the following four approaches which determine the duration, start date, and finish date for each activity. Completed activity. The start and finish dates for completed activities are assigned based on actual start and finish dates in which delay informati on is embedded. †¢ Started-without-delay activity. For un-delayed started activities, start dates are assigned based on actual start dates; finish dates are determined based on actual start dates plus consumed activity duration with remaining duration (asplanned duration minus consumed duration). †¢ Started-with-delay activity.For those delayed but started activities, start dates are assigned based on actual start dates; finish dates are determined using actual start dates plus the consumed activity duration, delayed duration and remaining duration. †¢ Un-started activity. For activities not yet started, their start and finish dates are determined by their predecessors by considering predetermined logic relationships with the asplanned duration. 4. 4. Approach for determining analysis timing For solving the limitations of existing windows-based delay analysis methods in window determination depicted in 388 J. -B. Yang, C. -K.Kao / International Journal of Project Mana gement 30 (2012) 385–397 Preparing the as-planned schedule Identifying delay attributes and determining analysis periods Updating schedule-related information Performing CPM calculation Analyzing the difference between updated and baseline schedules A period with out delay A period with delay Analyzing delay impact day-by-day Identifying the number of critical activity No shortening performance NO Project schedule shortening? YES Calculating the performance of schedule shortening NO Concurrent delay? YES Allocating liability of concurrent delay NO NO Delay on CP?YES Two or more delays? YES Cumulating schedule variance Identified delay impact Identified schedule shortening performance Calculating delay liability Final period? YES Summarizing analysis results NO Fig. 1. Delay analysis processes for EDAM. Section 3. 3, the proposed method has an approach to determine the timing for delay analysis. This approach considers the following two situations when determining analysis tim ing. †¢ No delay occurred. In this situation, the time frame without a delay event is designated as a single analysis period. Therefore, all activities have actual durations that are the ame as planned durations. Moreover, if an activity's duration is shorter than the planned duration, the performance of project acceleration is considered. †¢ Delay occurred. To accurately calculate delay effects on a construction project, the minimum time frame, i. e. , a day or a week depending on the contract, should be considered. J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 389 4. 5. Algorithms for liability identification and calculation The EDAM method calculates projected project total duration (Duribase) using Eq. 1) among each analysis period, in which Duriact1 is the actual consumed duration of the previous ? analysis period; Duriremained is the remaining duration for all unfinished activities considering logic relationships in th e asplanned schedule. Moreover, the EDAM method uses Eqs. (2) and (3) to determine the impacted project duration while considering the liabilities for the owner (Duriown ) and contractor (Duricon). In those two equations, anticipated total project duration (Duribase) is calculated by Eq. (1); DuriNE, DuriENand DuriEC represent the impact from an NE delay, an EN delay and an EC delay, respectively.Based on calculation results by Eqs. (2) and (3), the extended duration considering the liabilities of the owner and contractor are determined. Therefore, in each delay analysis period, delay liability for the owner (Dutyiown ) and contractor (Dutyicon) is calculated using an apportioned duration minus the original anticipated project completion duration, as in Eqs. (4) and (5). After determining the delay liability in each analysis period, the EDAM method summarizes project delay liability for each contract party (Duty ownfor the owner and Duty con for the contractor) from all analyzed per iods using Eqs. 6) and (7). act Duribase = Duri? 1 + Duriremained first condition is that only one delay event occurred in a time frame; the second condition is two or more delay events occurred concurrently. In the first condition, an activity with zero or negative remaining total float is responsible for the project delay; otherwise, the analyzed activity only consumes its usable float. In the second condition, if multiple delays occurred in an analyzed time frame, a further consideration for allocating delay liability is required. Thus, the EDAM method uses Eqs. 9) and (10) to allocate liability for a concurrent delay. The approach of allocating delay liability uses the ratio of a concurrent delay's delay value to the total delay values on the critical path. Although the calculation results may be some whole days with a decimal, considering the right ratio of delay liability on the critical path, the proposed method does not round up the analytical results. PSTjcon = Durjplanned ? Durjact ? TFjremained 0 CDown = ? i=1 n ?8? 1 DuriCP ? j=1 m A n B A CDEN + CDEC = ? BDuriEN ? i i @ i=1 DurjCP C C A ?9? ?1? ?2? ?3? ?4? ?5? 0 n B + ? BDuriEC ? i=1 1 DuriCP C C m A ? DurjCP j=1 A A Duriown = Duribase + DuriEN + DuriEC Duricon = Duribase + DuriNE Dutyown i Duriown ? Duribase 0 n n B CDcon = ? CDNE = ? BDuriNE ? i @ i=1 i=1 m 1 DuriCP C C: A ? DurjCP ? 10? = j=1 Dutycon = Duricon ? Duribase i n Dutyown = ? Dutyown i i=1 ?6? Dutycon = ? Dutycon i i=1 n ?7? For the apportionment of concurrent delay liability, several studies (Kraiem and Diekmann, 1987; Arditi and Robinson, 1995) have proposed varied rules. Ibbs et al. (2010) proposed that a recent trend in concurrent delays is to advocate an equitable apportionment (i. e. eaning apportionment of days and/or dollars). This fair apportionment has been described as â€Å"fail rule† or â€Å"comparative negligence† (Ibbs et al. , 2010). The proposed method for apportionment of concurrent delays supports th e fail apportionment. 5. Hypothetical Case Study Hypothetical case studies have been widely used for similar studies in literature (i. e. , Hegazy and Zhang, 2005; de la Garza et al. , 2007; Sakka and El-Sayegh, 2007; Nguyen and Ibbs, 2008; Ibbs et al. , 2010), therefore, this study uses hypothetical projects to demonstrate the capabilities of proposed EDAM method.Furthermore, for comparing the results by other windows-based methods and the proposed method, a hypothetical case used in literature is examined in this study. In addition to considering the impacts of delay events, the EDAM method uses Eq. (8) to determine the performance of project acceleration by a contractor in an analyzed period when no delay exists and the value calculated by Eq. (5) is negative. In Eq. (8), TFjremained is the remaining total float for the analyzed activity. As projects are typically managed by a contractor not an owner, the EDAM method does not calculate the project acceleration performance from an owner.To determine the effect of delay event(s) on total project duration, two conditions must be considered independently. The 390 J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 Table 1 Information of as-planned and as-built schedules for test case. Act. As-planned information Duration (day) 1 2 3 4 5 6 7 8 9 10 7 5 7 9 6 4 3 9 5 3 Predecessor Start day 1 1 8 6 6 15 15 12 19 21 Finish day 7 5 14 14 11 18 17 20 23 23 As-built information Duration (day) 11 10 12 9 15 6 5 11 12 5 Actual start day 1 1 12 11 11 24 20 26 30 37 Actual finish day 11 10 23 19 25 29 24 36 41 41 5. 1.Case description This study applies the EDAM method and four other windows-based methods to a modified test case (Fig. 2), originally developed by Kraiem and Diekmann (1987) and examined by Alkass et al. (1996) and Kao and Yang (2009). This test case has ten activities and an original total duration of 23 days. Based on critical path calculation, the test case has two critical paths, namely the paths of activities 1 > 3 > 6 > 9 and 2 > 5 > 8 > 10. The project was finally completed in 41 days, with 18 days of delays. Table 1 shows the planned and actual activity information for duration, start date, finish date and logical relationships.Table 2 shows delay events, classified as NE, EN and EC delays affecting all activities. To explain the effects of all delay events on each activity, the as-planned and as-built schedules are organized as Fig. 3 and adopted for delay analysis. 5. 2. Summary analytical procedures According to the processes shown in Fig. 1, this study performed delay analysis for the test case. For each delay analysis scenario in Fig. 4, Eqs. (1) to (3) are used to determine anticipated project duration, the impacted duration considering one delay caused by the owner or contractor, respectively.Consequently, the EDAM method employs Eqs. (4) and (5) to calculate the delay liability allocated to the owner or contractor, respectivel y. While all 34 delay periods were complete, Eqs. (6) and (7) are used to summarize all delay liability allocated to the owner or contractor, respectively. 5. 3. Final results Based on the test case consisting of original as-planned and as-built schedules, delay events and related responsibilities, delay analysis was performed using the EDAM method and four other windows-based methods, i. e. the TWA/MWA, DAMDUS and DWDA methods.Table 3 lists identification results for different delays, and the timings of the critical path changes. Table 4 summarizes analysis results. Compared to actual delay information (Tables 3 and 4), the DAMUDS, DWDA and EDAM methods accurately calculated the values for the NE, EN, EC and concurrent delays. The TWA and MWA methods do not calculate the concurrent delay, and calculate the NE delay incorrectly. The information for NE, EN and EC shown in 0 0 0 0 0 Start 0 0 0 0 0 7 1 0 5 2 0 7 7 5 5 7 7 5 11 5 5 7 3 0 9 4 6 6 5 0 14 14 14 20 11 11 – – 1 2 2 3 4 5 6 8Tables 2, 3 and 4 confirms that the proposed method can accurately identify those delay information that DAMUDS, DWDA and EDAM methods do. In addition to its calculation accuracy, the EDAM method identifies right critical path changes and has adequate analysis scenarios to perform delay analysis efficiently. That is, the EDAM method yields an accurate calculation result with economic analysis times. 6. Discussion 6. 1. Efficiency for delay analysis To compare the efficiency of the EDAM method to that of the other four windows-based methods, all studied methods use the same test case. Fig. shows the analysis periods used by all methods. The TWA and MWA methods employed the start and finish dates of key delay events as the timing for extracting analysis periods; the DAMUDS method determined the timings of delay sections from the start, change and finish dates of any delay event, while the DWDA method analyzed delays on a day-by-day basis. Detailed parameters for the fou r methods can be found elsewhere (Kao and Yang, 2009). Notably, the current state of the art in delay analysis through discussed methods is performing delay analyses by the schedule analysts manually, because only a few of methods are computerized.Therefore, this study concerns the efficiency of studied methods by the number of analysis times (analysis runs), rather than the computing times (total duration). 14 14 14 20 11 11 4 6 0 3 7 6 9 8 0 18 18 17 23 20 20 20 20 3 10 0 23 23 18 18 5 9 0 23 23 23 23 ES LS 0 End 0 Duration Activity TF 23 23 EF LF Legend Fig. 2. Precedence diagram for test case. J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 Table 2 Delay information for test case. Act.NE delay Duration (day) 1 2 3 4 5 6 7 8 9 10 Sum 3 1 3 – 1 – 1 – 3 – 12 Start day 1 3 12 – 13 – 22 – 32 – – Finish day 3 3 14 – 13 – 22 – 34 – – EN delay Duration (day) 1 3 – – 5 – – 1 2 2 14 Start day 7 4 – – 19 – – 30 35 37 – Finish day 7 6 – – 23 – – 30 36 38 – EC delay Duration (day) – 1 2 – 3 2 1 1 2 – 12 Start day – 7 15 – 14 24 23 33 39 – – Finish day – 7 16 – 16 25 23 33 40 – – 391 Total delay 4 5 5 – 9 2 2 2 7 2 38 Based on the analysis periods shown in Fig. 4 and Table 4, the number of analysis times for the TWA/MWA, DAMUDS, DWDA and EDAM methods are 17, 20, 41 and 34, respectively.Notably, one analysis time means to perform one analysis scenario. The DWDA and EDAM methods have the same accuracy level; however, the EDAM method is more efficient than the DWDA method. In the test case, the EDAM method saves 17% in the number of analysis times than the DWDA method. For complicated construction projects the number of activity and the complexity of d elay events are increased, the numbers of analysis times by those methods are increased consequently; therefore, the EDAM method is a more efficient calculation approach than four other windows-based methods. 6. 2.Ability to identify critical path changes Delay claim in the construction industry usually considers delays on the critical path(s); therefore, identifying critical path changes is essential for allocating delay liability. The as-built schedule in Fig. 3 shows real situations of critical path changes while delays appear on the critical paths. Table 3 shows the real timing of critical path changes and the analysis results from different delay analysis methods. In summary, eight critical path changes occurred in the test case. The DWDA and EDAM methods correctly reflected the real situations.Furthermore, the EDAM method calculated the delay impacts on total project duration by only considering the delay on the critical path correctly. Detailed information concerning liabilit y allocation is discussed in Section 6. 4. 6. 3. Ability to deal with concurrent delays and project acceleration To identify the appearances of a concurrent delay and project acceleration, the EDAM method uses a minimum cycle time, one day, as its analysis period. For example, one concurrent delay (one day) appears on day 14 in the test case. The EDAM method accurately identifies this concurrent delay shown in Table 3.If the analysis period exceeds the duration of the concurrent delay, the concurrent delay would not be detected. Notably, in an as-built schedule, the situations of project delay and project acceleration do not occur concurrently. Project acceleration means shortening the duration of activity on original critical path(s), by which a project is completed earlier than planned completion date. While the duration of critical-path activities is shortened, two situations occur. One is the shortened activity is still on critical path; the other is the activity is changed from a critical activity into a no-critical activity.The former one does not cause different analysis result. The latter one might result in different results and is discussed in this study. In Fig. 5, the test case with five activities has one critical path, namely the path of activities 2 > 4 > 5. Finally, this case was completed in 14 days with three days acceleration. In the as-built schedule (the bottom part in Fig. 5), it is clear that, activity 2 shortened one day and activity 4 shortened three days. Fig. 5 shows the complete analyses, in which five analytical scenarios were performed. Notably, according to the algorithm shown in Eq. 8), the performance of project acceleration is caused by activity 2 with 1 day (5-4-0) and activity 4 with 2 days (9-6-1), which are calculated during analytical scenario 1 (day 1–4) and 3 (day 8–10), respectively. 6. 4. Liability allocation approach The EDAM method has an approach that allocates delay liability based on the ratio of an analyzed concurrent delay event to the total delay values on the critical path. As the information shown in Table 4, the DAMUDS and DWDA methods can identify concurrent delays, but cannot clearly allocate delay liability.Those two methods provide the same concurrent delay value of 1 day, that is, the analysis period. In the test case, one concurrent delay appears on day 14, in which activity 3 encounters an NE delay while activity 5 has an EC delay. According the allocation approach (described by Eqs. (9) and (10)), the duration of activities 3 and 5 should be calculated. Notably, the duration of an activity on the critical path just considers the conditions up to the analysis period. Therefore, 392 NO. Duration 1 7 3 7 6 4 9 5 2 5 4 9 5 6 7 3 8 9 10 3 Path 1( 1 3 6 9) Path 2( 2 4 7) Path 3( 2 5 8 10) Critical Path NO. 1 3 6 9 2 4 5 7 8 10 2 3 4 5 6 7 8 9 As-planned shedule 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 J. -B. Yan g, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 CP 1 CP 2 Act. Dur. 1 2 3 4 5 6 7 8 11 NE NE NE EN 12 6 12 10 NE EN EN EN EC 9 15 5 11 5 Note delay project completion Path 1( 1 3 6 9) Path 2( 2 4 7) Path 3( 2 5 8 10) 9 As-built schedule 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 concurrent delay NE NE NE EC EC EC EC NE NE NE EN EN EC EC NE EC EC EC EN EN EN EN EN NE EC EN EC EN ENFig. 3. As-planned and as-built schedule with delay liability. J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 EDAM Analysis TWA/MWA Period DAMUDS DWDA NO. Duration 1 11 3 12 6 6 9 12 2 10 4 9 5 15 7 5 8 11 10 5 Path 1( 1 3 6 9) Path 2( 2 4 7) Path 3( 2 5 8 10) 1 2 1 3 4 1 2 1 2 3 4 1 2 3 4 NE NE NE 5 2 3 5 5 6 7 3 4 6 7 8 6 7 8 EN 22 9 10 11 12 13 14 15 16 17 18 19 20 21 23 5 6 7 8 9 10 11 7 8 9 10 11 12 6 13 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2 9 30 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 NE NE NE EC EC EC EC 4 5 24 12 14 31 31 25 26 27 28 29 30 31 32 33 34 13 14 15 16 17 17 18 19 20 15 16 32 33 34 35 36 37 38 39 40 41 32 33 34 35 36 37 38 39 40 41 42 NE NE NE EN EN NE EN EN EN EC NE EC EC EC EN EN EN EN EN NE EC EN EC EN EN EC EC Fig. 4. Analysis period partition by EDAM and other methods. 393 394 J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 Table 3 Analysis results by EDAM and other windows-based methods.Type NE delay S/N 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3 4 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Timing in day 1 2 3 12 13 4 6 19 20 21 22 23 30 37 38 7 15 16 33 14 1 2 3 5 6 12 14 19 21 23 36 37 38 40 Actually occurred Y Y Y N Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N N Y Y Y N Y N N Y Y N Y Total 4 EDAM Y Y Y N Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N N Y Y Y N Y N N Y Y N Y TWA/MWA Y Y Y Y Y Y N Y Y Y Y Y Y Y Y Y Y Y Y N N N Y N Y N Y N N Y Y N Y Y DAMUDS Y Y Y N Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y N Y N N Y Y N N Y N Y N Y Y DWDA Y Y Y N Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N N Y Y Y N Y N N Y Y N YEN delay 9 EC delay 4 Concurrent delay Critical path change 1 8 activity 3 takes 3 days on the critical path while activity 5 takes 4 days on the critical path. The values of delay liabilities for activity 3 (NE delay, attributed to the contractor) and activity 5 3 (EC delay, attributed to the owner) are 0. 43 (1 ? 3 + 4 = 0:43) 4 and 0. 57 (1 ? 3 + 4 = 0:43), respectively. Notably, the analytical result is a decimal fraction day because only one-day concurrent delay exists in the test case.In the situation where the NE delay to activity 3 and the EC delay to activity 5 on day 14 were extended to ten days, respectively. Namely, the duration for the concurrent delay is from 1 day changed to 10 days due to the NE delay to activity 3 and the EC delay to activity 5 has been extended to 12 days, respectively. Based on the proposed approach, the values of delay liabilities for activity 3 (NE delay) and activity 5 (EC delay) are 4. 8 (10 ? 2 12 13 = 4:8) and 5. 2 (10 ? 12 13 13 = 5:2), respectively. + + In practice, schedule delays or time extension claims usually result in cost reimbursement or liquidated damage calculations, the analytical results can service as an accurate tool in such calculations. The analytical results based on the proposed transparent calculation approach will provide a better alternative than conventional method that usually employs a half-and-half approach. 6. 5.Comparison to other windows-based delay analysis methods Based on above discussions and the information shown in Table 4, this study summarizes the differences between the proposed method and the discussed windows-based delay analysis methods, organized as follows. Table 4 Analysis results by EDAM and other windows-based methods. Attributes NE delay (in day) EN delay (in day) EC delay (in day) Concurrent delay (in day) Critical path change (in times) Analysis period (in times) Actual EDAM 4 9 4 1 8 TWA/ DAMUDS DWDA MWA 4 9 4 1 7 20 4 9 4 1 8 41 4 5 9 9 4 4 1 (0. 3 for NE; 0 0. 57 for EC) 8 7 34 17 J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 As-Planned schedule Act. No. Duration TF 1 7 3 7 1 2 5 0 4 7 0 5 3 0 Path 1( 1 3) Path 2( 2 4 5) Analysis Period: day 1- 4 Act. No. Duration TF 1 7 2 3 7 2 2 4 0 4 9 0 5 3 0 Path 1( 1 3) Path 2( 2 4 5) Analysis Period: day 5-7 Act. No. Duration TF 1 7 2 3 7 2 2 4 4 9 0 5 3 0 Path 1( 1 3) Path 2( 2 4 5) Analysis Period: day 8-10 Act. No. Duration TF 1 7 3 7 0 2 4 4 6 1 5 3 1 Path 1( 1 3) Path 2( 2 4 5) Analysis Period: day 1-13 Act. No. Duration TF 1 7 3 7 0 2 4 4 6 5 3 1 Path 1( 1 3) Path 2( 2 4 5) Analysis Period: day 14 Act. No. Duration TF 1 7 3 7 0 2 4 4 6 5 3 Path 1( 1 3) Path 2( 2 4 5) 395 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Critical path NW1 1 2 3 4 5 6 10 11 12 13 14 15 16 17 18 19 20 21 22 One day is shortened f or project duration One day is shortened for Activity 2 7 8 9 Critical path 1 2 3 4 5 NW2 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 One day is shortened for project duration One day is shortened for Activity 2Critical path 1 2 3 4 5 6 NW3 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Three days are shortened for project duration One day is shortened for Activity 2 7 8 Three days are shortened for Activity 4 Critical path NW4 10 11 12 13 14 15 16 17 18 19 20 21 22 Three days are shortened for project duration Three days are shortened for Activity 4 Critical path NW5 10 11 12 13 14 15 16 17 18 19 20 21 22 Three days are shortened for project duration One day is shortened for Activity 2 7 8 9 Three days are shortened for Activity 4 Critical path 1 2 3 4 5 6 7 8 9 One day is shortened for Activity 2 2 3 4 5 6 Fig. 5. Project acceleration detected by EDAM. †¢ Comparing to the TWA/MWA method, the EDAM method can deal with the EC, EN, NE and concurrent delays more accurate. †¢ Co mparing to the TWA/MWA and DAMUSD methods, the EDAM method can perform delay analysis considering critical path changes more correct. †¢ Comparing to the DWDA method, the EDAM method can perform delay analysis more efficient. †¢ Comparing to the TWA/MWA, DAMUSD and DWDA methods, the EDAM method can allocate delay liability more accurate, and provide a function of detecting project acceleration. 396 J. -B.Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 6. 6. Advantages and limitations This study proposes a novel delay analysis method for resolving the problems associated with existing windows-based delay analysis methods. The EDAM method has the following advantages compared to existing windows-based delay analysis methods. †¢ It has a systematic window extraction method for performing delay analysis stably and efficiently. †¢ It adopts a process-based analysis approach to identify critical path changes, concurrent delays an d project acceleration. It develops a clear liability distribution approach for apportioning concurrent delays. Although the EDAM method has been tested using hypothetical cases, some limitations exist in applying to solve schedule delay problems in construction projects. The limitations are organized as follows. †¢ The classification of EC, EN, NE and concurrent delays must be identified before employing the developed EDAM method. †¢ The EDAM method does not discuss float ownership. That is, the one uses the float first who owns the ownership. †¢ Construction projects usually encounter complex delay situations.This study just examines the capabilities of the EDAM method using two hypothetical cases that simulate the identified problems. Therefore, the EDAM method might be unable to resolve the complex delay situations that are not identified in this study. 7. Conclusions While schedule delays occur frequently during construction projects, identifying the liability of contract parties accurately has received considerable attention. Although many methods have been developed for analyzing and measuring construction schedule delays, no one method is acceptable for all project participants and suitable for all delay situations.An ideal delay analysis method must calculate delay information stably, accurately and efficiently. Some existing windows-based delay analysis methods perform delay analysis based on an arbitrary window extraction; some deal with limited delay situations. This study presents the EDAM method, a novel delay analysis method that has a systematic window extraction method for performing delay analysis stably, and adopts a process-based analysis approach to resolve concurrent delays and liability distribution problems accurately. Additionally, the EDAM method performs delay analysis efficiently in a test case.The EDAM method is a good alternative for resolving analysis problems associated with schedule delays in construction project s. The construction industry requires continual improvements to delay analysis methodology due to industry complexity. Based on research results, this study provides following suggestions for further study. †¢ Evaluating the performance of the existing windows-based methods (including the EDAM method) for diverse and real cases can improve the acceptance of all windows-based methods in the construction industry.However, illustrative cases, covering all delay situations or real delay cases are hard to retrieve because the cases in the court have limited and simplified information, and information from the arbitration cases is not disclosed. How to develop a protocol for collecting such cases is essential for further development and evaluation. †¢ Most available delay analysis methods are not implemented in popular project management systems (such as Microsoft Project and Oracle Primavera P6) or supported by those systems, thus posing a barrier to apply these methods for sol ving real delay problems.Although capable of providing a basic function for delay analysis, a few systems only perform simple schedule comparisons. For example, the Claim Digger function embedded in Oracle Primavera P6 can be used monthly to compare different schedule variances in start date, finish date and activity duration. According to the systematic approach provided by this research, developing easy-to-use systems embedded in, based on or supported by available commercial project management systems will enhance the application of delay analysis methods. The methods for delay analysis can be divided into four categories: forecasting, real-time, after-delay-occurred and after-project-completion (Arditi and Pattanakitchamroon, 2006). Most of methods belong to the after-projectcompletion category; by those methods some essential documents and evidences may be lost. Developing a method that belongs to forecasting or real-time category can resolve this problem. Furthermore, systems dynamics approach has been recognized and proven to be helpful for dispute resolution (Weil and Rayford, 1990; Cooper and Lee, 2009).It would be another good alternative method for schedule delay analysis for construction projects. †¢ The proposed method for allocating delay liability provides a better alternative with transparent calculation approach than conventional method that usually employs a half-and-half approach. However, if construction contracts have a clear delay liability allocation clause that employ the proposed method or conventional half-and-half approach, the dispute for delay liability allocation will be diminished.How to draft a suitable clause that provides a clear delay liability allocation approach and fair rights and obligations in a contract can be studied carefully. Acknowledgements The authors would like to thank the National Science Council, Taiwan, ROC, for financially supporting this research under Contract No. NSC96-2221-E-216-027-MY2. The authors are also thankful to the reviewers for their valuable suggestions and comments. J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385–397 397 References Alkass, S. , Mazerolle, M. , Harris, F. , 1996. Construction delay analysis techniques.Construction Management and Economics. 14 (5), 375–394. Arditi, D. , Pattanakitchamroon, T. , 2006. 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