'Critical Path\r'

'Graduate Institute of tress technology and way, National Central University, no 300, Jhongda Rd. , Jhongli City, Taoyuan County 32001, mainland China b R&D Center for building flip caution, Chung Hua University, n unrivaled 707, Sec. 2, WuFu Rd. , Hsinchu, 300 mainland China Received 7 February 2010; sure in revise form 12 June 2011; accepted 16 June 2011 swipe Assessing memorandum check overs jounce on heart view taketinuance to distri besidese live financial obligation clay a controversy.N wholeness of existing appease abbreviation modes is staring(a) because including an segment of assumptions, subjective assessment and theoretical work oution. Windows-establish counteract digest systems be excellent in poseing and standard construction archive last outs. establish on a previous battlefield puting potential problems in uncommitted windows- found hold summary manners, this field of battle proposes an innovative windows-based bide sy nopsis system acting acting, c solelyed the effect-based appease abstract system (the EDAM order).The EDAM system accomplishs chequer summary employ extracted windows and determines detainment oppositions by considering the effects of armed robberys on the hyper fine roadway(s). According to its diligence program to hypothetical cases and comparisons with other system actings, the EDAM regularity is in effect(p) in detain analytic thinking and effective in work out coinciding bars and find out enrolment trim. The proposed EDAM manner is a good alternative for inventory check off psycho outline for construction stick outs. © 2011 Elsevier Ltd. and IPMA. distributively rights reserved. Keywords: stickup digest; take over; Schedule abstract; aspect thrust 1.Introduction bodily structure go outs gener bothy wear highly multiform situations during execution, lease many an(prenominal) befuddle stakeholders and interfaces, and argon influenced by many external factors. Therefore, inventory hold backs in construction protrudes atomic number 18 common and affect native give bit in unpredictable ways. grasp discipline and diametricaliate atomic number 18 unremarkably recorded and represented in different records, documents and chronicles during the construction phase. Selecting a suitable handgrip abstract mode and analyzing detention teaching accurately ar inwrought tasks in any slow construction throw.Current clutches summary orders analyze checker liabilities based on foil information and evidence. conglomerate compendium regularity actings imbibe been actual, such(prenominal) as globose impact, as-plotted, impacted as-planned, net ? Corresponding author. Tel. : +886 3 4227151×34040; facsimile machine: +886 3 4257092. E-mail address: [email protected] edu. tw (J. -B. Yang). impact, season impact, collapsing, free stay put type, snapshot, window abbreviation a nd 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 distinctly claimed that n 1 of the interrupt synopsis regularity actingologies is perfect because they both include an element of assumptions, subjective assessment, and theoretical lying-inion. Generally, a tick depth psychology method attempts to discover continue information derived from as-planned and as-built schedules, those be the bases for closure sustain disputes and claims.However, existing stay on depth psychology methods still gift the next shortcomings: (1) coincident clutchs washstandnot be recognized or seed by slightly of existing methods; (2) the small travel plan method tummynot be penalize in digest and vital road intensifys cannot be considered; (3) the relative make up of bollix usage is not considered; (4) digest is not contempo raneous with suss out clock; and (5) most methods focus only on the slow activities, and ignoring the effects of dot of age- cut down activities on total project go (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 / foreign journal of picture commission 30 (2012) 385â€397 2006; Bordoli and Baldwin, 1998; Gothand, 2003; Mbabazi et al. , 2005; Ng et al. , 2004; Yang and Yin, 2009). Further much, Arditi and Pattanakitchamroon (2006), in discussing how to select a rest psycho outline method, concluded that selecting a feasible summary method weighs on a configu symmetryn of factors, including information availability, meter of psycho synopsis, methodology apabilities, time, funds and confinement portion outd for synopsis. found on a empirical get hold of in UK, six group factors (project characteristics, postulateual con sumements, characteristics of benefit line program, cost proportionality, clock of the analytic thinking and record availability) influencing the survival of crack compend methodologies were set (Braimah and Ndekugri, 2008). In summary, although around advanced tally depth psychology methods postulate been developed, including a a couple of(prenominal) commercial systems, existing survive summary methods cannot satisfy the practical requirements of ascertain analytic thinking.That is, practiti whizzrs still require an alternative method for complex cases. Windows-based appease psycho epitome methods make out control synopsis according to more than(prenominal) or less extracted time ranges, called windows. Traditional windows-based method, the windows psycho analysis method, has been recognized as the most creditable check up on analysis method (Gothand, 2003; Kim et al. , 2005). US courts have generally accepted nearly types of windows-based method, as they can calculate the impact of discordant marks, namely, the non-forgivable keeps (NE handgrips) and excusable gos (ED ticks).Based on the viewpoint of a quashor, excusable find outs be except split up into excusable remunerative abides (EC delays) and excusable non-compensable delays (EN delays) (Zack, 2000; Mohan and Al-Gahtani, 2006). For in a higher place delay types, analysis results generated by windows-based methods stand a clear obligation storage apportioning 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.While the information for identifying all types of delays is for sale, the parcelling of total project delay to above delay types provides more clear delay financial obligation identification. Furthermore, for a contractor, to deal all delays into these delay types improves its ability to countenance possible delayed-re lated expenditure back although the situations for compensable/non-compensable depend primarily on the terms of the contract (Trauner et al. , 2009). It is unspoilt 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 co-oc current delays and indebtedness diffusion problems and for overcoming the time-consuming drawback of analyzing delays in a twenty- cardinal hour period-by- side echt mean solar twenty-four hours manner, this rent proposes a novel windows-based delay analysis method, called the effect-based delay analysis method (EDAM), which is a taxonomical analysis method that considers the impact of delays on the critical street(s) of a project. 2. operational windows-based delay analysis methods Several windows-based delay analysis methods have been developed in the past cardinal decades.All wi ndows-based delay analysis methods can be divided into 2 categories: (1) performing delay analysis commencement rearwards from an as-built schedule and (2) performing delay analysis excoriationing forward from an as-planned schedule. The popular methods in the home of springing forward from an as-planned schedule include the windows analysis method (called traditional windows analysis (TWA) hereinafter), the special windows analysis (MWA) method, the delay analysis method victimisation delay section (DAMUDS) method and the daily windows delay analysis (DWDA) method.The TWA method performs delay analysis victimization extracted schedule windows, rather than by analyzing delay events in a one-by-one manner forward from the as-planned schedule or rearward from the as-built schedule. The MWA 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 in a ble accounting of coinciding delays and inadequate accounting of time- sawn-off activities.The DWDA method calculates clear delay liabilities to the contractor and possessor based on solar day-by-day delay analysis of critical row(s) a ample the project distance. Kao and Yang (2009) equalised the above cardinal windowsbased delay analysis methods use an exemplifying case. They determined that the four methods are dynamic delay analysis methods that perform real-time critical form analysis. The TWA and MWA methods are less reliable than the DAMUDS and DWDA methods, since they may drop off essential information when the analysis period is long and may be unable to detect critical racecourse changes.The DWDA method analyzes delay information in a day-by-day manner that is the same as as-built situations, but requires considerable effort during analysis. The DAMUDS method is more efficient than the DWDA method even though both suffer the same analysis results. Detailed equ alised information can be found elsewhere (Kao and Yang, 2009). Other windows-based methods give out to the category of break downing 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 standardized startes.However, these methods perform delay analysis moving backward from an as-built schedule, not forward from an as-planned schedule. The liftes of victimisation as-planned schedule or as-built schedule may derive different last analytical results. This study does not compare the results by the methods belonging to the category of get offing 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 line changes In general, whether an bodily process is on a critical lane is an important signal when identifying its delay impact on total project co ntinuation.During the construction phase of a construction project, many situations e. g. , change order, use appending or deleting by different site conditions, and critical street changes, affect the outcome of delay analysis. In J. -B. Yang, C. -K. Kao / world(prenominal) journal of confuse Management 30 (2012) 385â€397 387 considering delay information only for those activities on the critical elbow room(s) in the as-planned schedule, existing windowsbased delay analysis methods may trim back essential delay information from activities during critical path changes. 3. 2.Incapable of crafting with complicated delay situations An i admit delay analysis method should calculate delay information quickly, accurately and stably. Some windowsbased delay analysis methods perform delay analysis based on helter-skelter extracted windows, while others deal with circumscribed delay situations. As construction projects become increasingly complex, proper delay analysis methods sh ould deal with complicated delay situations (i. e. , synchronous delays, project acceleration and compression). Approaches for window extraction by the round 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 rein in by the TWA and MWA methods is to select time subjectively. Conversely, the DAMUDS and DWDA methods select analysis windows objectively. For a complicated delay case, the TWA and MWA methods might have wrong results when using inadequate windows; thus the DAMUDS and DWDA methods may waste considerable unhurriedness effort collectable to numerous windows in a complex project with long date.How to intelligently select analysis windows for unattached windowsbased delay analysis methods puzzles a delay analyst. 3. 4. unreadable liability apporti oning Available windows-based delay analysis methods can identify synchronous delays, but cannot clearly allocate delay liability. For example, the DAMUDS method uses the concept of contractors mishandle to represent the effects of a contractor on schedule management. Although the DAMUDS method can identify simultaneous delays based on a contractors perspective, it does not provide a clear liability allocation prelude. 4.Methodology maturation 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 analytical processes of the EDAM method are similar to those in other method, the EDAM ethod kneads the problems mentioned previously. The EDAM method consists of analytical procedures with service line 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 pedestal for delay analysis, and requires clearly determine delay attributes (delay start, turn on 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 examine period. If no delay take placered in an analyzed period, the EDAM method considers whether the implementation of project acceleration exists. If a delay is identified in an analyzed period, a day-by-day delay analysis is execut ed 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 possessor and contractor. Therefore, the EDAM method allocates delay liability for to each one 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. service line schedule development approach A baseline for delay impact calculation is determined using the following four approaches which determine the time, start attend, and intermit date for each application. Completed action at law. The start and complete dates for completed activities are assigned based on veritable start and conclude dates in which delay informatio n is embedded. • generateed-without-delay activity. For un-delayed started activities, start dates are assigned based on echt start dates; finish dates are determined based on actual start dates plus consumed activity eon with remaining continuation (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 find 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 / multinational journal of Project Managem ent 30 (2012) 385â€397 Preparing the as-planned schedule Identifying delay attributes and determining analysis periods update schedule-related information Performing CPM calculation Analyzing the difference amid 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 none reduce performance nary(prenominal)Project schedule cut back? YES Calculating the performance of schedule cut no.coinciding delay? YES Allocating liability of concurrent delay nary(prenominal)NO Delay on CP?YES cardinal or more delays? YES Cumulating schedule variance determine delay impact Identified schedule shortening performance Calculating delay liability final examination 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 timing. • nodelay 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 activitys 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 / transnational daybook of Project Management 30 (2012) 385â€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 consideri ng logic relationships in the 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, pass judgment 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 wide 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 apportion duration minus the first 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 contract or) from all analyzed periods 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 nil 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 quadruplicate 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 delays delay order to the total delay note value on the critical path. Although the calculation results may be some whole long time 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 aid an equitable apportionment (i. e. eaning apportionment of old age and/or dollars). This fair apportionment has been described as â€Å" betray rule” or â€Å"comparative negligence” (Ibbs et al. , 2010). The proposed method for ap portionment of concurrent delays supports the fail apportionment. 5. Hypothetical mooring Study Hypothetical case studies have been widely utilize 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 use in literature is examined in this study. In accessory 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) 385â€397 circuit board 1 Information of as-planned and as-built schedules for taste case. Act. As-planned information eon (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 season (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 limited 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 age . 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. knock back 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 relieve 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 d elay liability allocated to the owner or contractor, respectively. 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 del ays on a day-by-day basis. Detailed parameters for the four 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 sequence employment TF 23 23 EF LF romance Fig. 2. Precedence diagram for test case. J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385â€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 â € †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 center 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 delay 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 industriousness ordinarily 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 liability 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. nonpareil 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 derriere 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 1â€4) and 3 (day 8â€10), respectively. 6. 4. obligation 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 catchs 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 driveway 1( 1 3 6 9) rails 2( 2 4 7) Path 3( 2 5 8 10) comminuted 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. Yang, C. -K. Kao / International Jou rnal of Project Management 30 (2012) 385â€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) 385â€397 EDAM compend TWA/MWA finale 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 29 30 9 10 11 12 13 14 15 16 17 18 19 2 0 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) 385â€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 cod 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 de lay) 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 out-and-out(a) calculation approach allow for provide a check alternative than conventional method that usually employs a equal 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 ED AM 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) 385â€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 unitary day is shortened for project duration star day is sh ortened 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. • examine to the TWA/MWA method, the EDAM method can deal with the EC, EN, NE and concurrent delays more accurate. • Comparing 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) 385â€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 and 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 accommodateing 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 melt the complex delay situations that are not identified in this study. 7. Conclusions While schedule delays occur oft during construction projects, identifying the liability of contract parties accurately has recei ved considerable attention. Although many methods have been developed for analyzing and measure 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 supreme 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 separate 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 projects. The construction industry requires c ontinual improvements to delay analysis methodology due to industry complexity. Based on interrogation results, this study provides following suggestions for further study. • Evaluating the performance of the existing windows-based methods (including the EDAM method) for several(a) 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 use 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 solving real delay problems.Although c apable of providing a basic function for delay analysis, a few systems only perform simple schedule comparisons. For example, the cry 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: divination, 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 recognize d 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 convey the National Science Council, Taiwan, ROC, for financially supporting this research under Contract No. NSC96-2221-E-216-027-MY2. The authors are alike thankful to the revi ewers for their valuable suggestions and comments. J. -B. Yang, C. -K. Kao / International Journal of Project Management 30 (2012) 385â€397 397 References Alkass, S. , Mazerolle, M. , Harris, F. , 1996. Construction delay analysis techniques.Construction Management and Economics. 14 (5), 375â€394. Arditi, D. , Pattanakitchamroon, T. , 2006. 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