Construction Delay Computation Method

CONSTRUCTION DELAY COMPUTATION METHOD

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By Jonathan Jingsheng Shi,1 Member, ASCE, S. O. Cheung,2 and David Arditi,3 Member, ASCE ABSTRACT: Delay is one of the most common problems in the construction industry. This paper presents a method for computing activity delays and assessing their contributions to project delay. The method consists of a set of equations, which can be easily coded into a computer program that allows speedy access to project delay information and activity contributions. The proposed method contrasts the as-planned and as-built schedules. It is not based on critical path analyses; therefore, it does not require the calculation or updating of the critical path, and it is even not necessary to update the as-planned schedule, as required by the traditional delay analysis methods. The results calculated from the proposed method include various variations of activity schedules and their contributions (in days) to the overall project delay. They provide an objective baseline for determining responsibilities of delays. The method can be integrated into any delay analysis system to further improve and automate the construction delay analysis process. Practical examples are used to illustrate the computation mechanism.

BACKGROUND Time is the essence of a construction contract. Typically, a time period is specified as the contract duration. The contractor is obliged under the contract to achieve substantial completion within the specified period. Unfortunately, unexpected events can happen during the life of the construction project and can affect the construction time necessary for the completion of the work. When a contractor fails to complete the project within the contract period, delay becomes the reality of the project. The contractual remedy for the owner is to deduct liquidated damages. Obtaining an extension is the contractual release for the contractor against liquidated damages. Based on the responsibility, delays are generically categorized as excusable compensable, excusable noncompensable, and inexcusable (Kraiem and Diekmann 1987; Arditi and Robinson 1995). In such situations, contract law provides no mechanism for adjustment of the terms of the contract unless specific provisions are included in the contract. The design of a mechanism to deal with such changes and the associated time and cost adjustments for situations where certain events occurred during the course of the construction is therefore an integral part of contract planning. Common delay analysis methods are based on critical path method (CPM) techniques and are performed by contrasting the as-planned and as-built schedules (Kraiem and Diekmann 1987; Trauner 1990). A delay of an activity on the critical path delays the completion of the project. However, the criticality of individual activities in a CPM network changes from day to day due to delays and accelerations in construction (Arditi and Robinson 1995). Therefore, extra effort is required on the part of managers to update the as-planned schedule with daily as-built information (Kallo 1996). Research efforts have contributed to the development of computer-based systems for delay analyses. Alkass et al. (1995) developed a computer-aided construction delay analysis system. Diekmann and Kim (1992) developed an expert sys1 Assoc. Prof., Dept. of Civ. and Arch. Engrg., Illinois Inst. of Technol., 3201 S. Dearborn St., Chicago, IL 60616-3793. 2 Asst. Prof., Dept. of Build. and Constr., City Univ. of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong. 3 Prof., Dept. of Civ. and Arch. Engrg., Illinois Inst. of Technol., 3201 S. Dearborn St., Chicago, IL. Note. Discussion open until July 1, 2001. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on October 20, 1999. This paper is part of the Journal of Construction Engineering and Management, Vol. 127, No. 1, January/February, 2001. 䉷ASCE, ISSN 0733-9634/01/0001-0060–0065/ $8.00 ⫹ $.50 per page. Paper No. 22126.

tem named SuperChange to advise inexperienced site engineers about the legal consequences of construction disputes so as to reduce potential claims. Yates (1993) presented a construction decision support system for delay analysis with the capability of determining possible causes for project delays, and suggesting alternative courses of action to prevent further delays. A multimedia system for construction delay management is discussed by Abudayyeh (1997). Delay analysis should provide information to enable the parties to implement the relevant contract provisions. In this respect, delay analysis should pinpoint the extension allowable in accordance with the contract. Where appropriate, it should assist in the apportionment of responsibility among the parties involved in the delay. The ascertainment of the period of project delay serves as baseline information for the apportionment of responsibility, which may be a highly complex operation in cases with concurrent causes. A medium size project may consist of hundreds of activities, many of which may be constructed at different times than originally planned. Some activities may be delayed, and such delays may partially or fully or may not be translated into project delay. There is no question that project delay is fully caused by delays of individual activities. However, which activities contribute to project delay and what is the magnitude of their contribution? Such information provides the baseline for investigating the causes and assigning responsibilities for project delays. This paper presents a method for computing such information. The method can be easily coded into a computer program so that the detailed delay information of a project becomes readily available to the manager. PROJECT DELAY COMPUTATION METHOD This section will first examine the occurrence of construction delay, then present a method for computing activity delays. It will then offer a method for computing the contributions of activity delays to project delay. Finally, an example is presented to illustrate the computation mechanism. Occurrence of Construction Delay A project consists of collections of activities. An activity’s completion may be delayed due to a delayed start or extended activity duration. While an activity’s start may be delayed due to certain reasons, its duration may be extended due to some other reasons. An activity’s delayed completion may cause delays in the succeeding activities, which in turn can cause a delay in the project completion. Schematically, a cause-effect relationship of project delay can be shown as in Fig. 1. Delays can occur in any and all activities, and these delays

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FIG. 1.

Cause-Effect Relationship of Construction Delays

can concurrently or simultaneously cause delays in the project completion. In other words, a project delay is the accumulated effect of the delays in individual activities. Activity Variation Analysis The as-built schedule of an activity may be different from its as-planned schedule. The magnitude of the differences can be evaluated by calculating the variations between the as-built and the as-planned schedules. The as-planned schedule may be a CPM schedule or any schedule that has been accepted by both the owner and the contractor. It can also be an original plan or an updated plan, depending upon which level of delay the user intends to determine VS = actual start time ⫺ planned start time

(1)

VF = actual finish time ⫺ planned finish time

(2)

VD = actual duration ⫺ planned duration

(3)

where VS and VF measure the variation in the start and finish times, respectively; and VD denotes the variation in the activity duration comparing the as-built with the as-planned schedules. A negative value of VS or VF indicates that the activity is ahead of the as-planned schedule. A negative value of VD means the activity’s actual duration is less than the as-planned duration. In any CPM network, the following relationships hold: actual finish time = actual start time ⫹ actual duration

(4)

planned finish time = planned start time ⫹ planned duration

(5)

can be expanded to other relationships. In the as-built schedule, the time when all activities immediately preceding an activity are actually completed is defined as the could start time of that activity [(7)]. The time difference between the could start time and the planned start time is the variation caused by the variation in the completion of one or more preceding activities. VSP is named to measure the variation in the start time caused by the preceding activities could start time = max{actual㛭finish㛭times㛭of㛭preceding㛭activities} (7) VSP = could start time ⫺ planned start time

VSP can take a positive or negative value, depending on whether the preceding activities are completed behind or ahead of schedule, respectively. The actual start time of the activity may take place any time after the could start time. Any variation that occurs after the could start time is caused by reasons associated with the running of the activity itself. It is termed variation in the start time due to causes associated with the activity itself (VSS), and is expressed in (9). Note that, since it is physically impossible for an activity to start before the preceding activities are completed, the value of VSS is always 0 or positive, indicating an on-time or delayed start compared with the could start time. The total variation in the start time (VS) of an activity is expressed in (10), and is the sum of the two components VSP [(8)] and VSS [(9)]. Eq. (10) corresponds exactly to the relationship in (1) VSS = actual start time ⫺ could start time

(9)

VS = VSP ⫹ VSS

(10)

Eq. (2) can be rewritten using (1), (3), (4), and (5) as VF = VS ⫹ VD

(6)

Eq. (6) means that the variation of an activity’s completion is composed of two portions—variation in start time and variation in activity duration. The variation in start time can be caused either by the variation in the completion of the immediately preceding activities or by reasons associated with the activity itself, or both. Logical relationships constrain the order that activities are to be constructed. There are many relationships, such as finish to start, start to start, and finish to finish. However, the most common relationship is finish to start, in which an activity cannot start until its preceding activities are completed. A finish-to-start relationship is used for developing the method to be discussed in the following sections, although the method

(8)

The following example illustrates the concepts generated so far. Assume all activities immediately preceding activity X were completed on day 14 so that activity X could start on day 14. Activity X was originally scheduled to start on day 8, but it actually started on day 19. Therefore, the delayed completion of preceding activities caused activity X’s start to be delayed by six days (VSP = 14 ⫺ 8). Because activity X did not start until day 19, a delay of five days (VSS = 19 ⫺ 14) was caused by events associated with the activity itself. These events may include one or more of the following: (1) lack of resources; (2) management decisions, including the owner’s and the contractor’s; (3) adverse weather conditions; and (4) changed site conditions. It is therefore possible to describe the variation in the finish

JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / JANUARY/FEBRUARY 2001 / 61


time of an activity (VF ) by using the relationships in (6) and (10). The result is presented in (11)


VF = VSP ⫹ VSS ⫹ VD

(11)

Eq. (11) shows that the variation in an activity’s completion time is composed of three portions—variation in the start time of the activity due to variation in the completion of immediately preceding activities (VSP), variation in the start time of the activity due to reasons associated with the activity itself (VSS), and variation in the activity duration (VD), again caused by events associated with the activity itself. VSP can be traced back to preceding activities in the project. Both VSS and VD are incurred at the current activity and are defined as the activity variation VA = VSS ⫹ VD

(12)

In the delayed activity, VA contributes the extra time (in addition to the planned activity duration) needed to complete the activity; in an accelerated activity, VA represents the time by which the planned activity duration has been reduced to speed up the activity, all irrespective of the preceding activities. Contribution of Activity Variation to Project Delay The variation in the project duration equals the difference between the actual completion time and the planned completion time VP = actual completion time ⫺ planned completion time

(13)

The presented method has the flexibility to evaluate both accelerated and delayed situations. Although a negative variation in project duration occurs sometimes, a delayed situation represents a more common scenario in the construction industry. For illustrative purposes, the following analysis will address project delay. Variation in an activity’s completion may or may not contribute to project delay, based on the nature and magnitude of the floats. It may affect the project in the following three ways: (1) It does not affect any other activity, addressed as the use of free float in the literature (Arditi and Robinson 1995); (2) it affects the succeeding activities but not the project; and (3) it contributes to the variation in the project duration. Such a contribution can be either independent from or concurrent with other activities. To quantitatively evaluate the effect of activity variation on project delay, the following two factors are defined: PDAC, measuring the project delay due to accumulated activity variations contributed by this and all its preceding activities; and PDA, measuring the project delay contributed only by this activity. The PDAC and PDA values provide the baseline information for delay analysis. The remainder of the section describes how to compute the two values for all activities in a project. A project delay is fully realized on the terminal activities. The proposed computation mechanism starts from the terminal activities and continues backward through all intermediate activities in the project. The computation of PDAC and PDA values for an activity requires that all of its immediately succeeding activities have been computed.

PDAC = actual finish time of the terminal activity ⫺ planned project completion time

where PDAC denotes the delay realized through the terminal activity, including the effects of all activities logically preceding the terminal activity. If PDAC is less than 0, then no delay has been incurred. Fig. 2 illustrates the last four activities of a project. The actual project completion time is day 40 (activity Y), and the planned project completion time is day 38 (activity Z). Therefore, the project delay is two days. The PDAC values are 1, 0, 2, and 1 for activities W, X, Y, and Z, respectively. In other words, activity Y and its preceding activities caused a two-day delay. Similarly, activities W and Z caused a one-day delay. Activity X did not cause any project delay, although its completion is delayed by two days. The contribution of a terminal activity to the project delay can be calculated by (15) PDA = min{VA, PDAC}

(15)

Recall that VA indicates the variation in the completion time of an activity caused by events associated with the activity itself. Eq. (15) means that a terminal activity’s contribution to the project delay should not exceed either the variation in the activity’s completion time (VA) caused by the activity itself or the total accumulated delay (PDAC). The PDAC and PDA values of the four terminal activities of the example problem are computed and are summarized in Table 1. It is interesting to note that activity W’s start is delayed by one day due to the delayed completion of its preceding activities and the activity duration is extended by one day. However, the total accumulated delay (PDAC) for activity W is one day. This scenario happens because activity W has a one-day float in the original schedule. Intermediate Activities After all terminal activities have been computed, the computation continues backward to intermediate activities. If activity j is the activity immediately succeeding activity i, the logic diagram can be illustrated in Fig. 3. The backward mechanism assumes that PDAC and PDA values for all activities (including activity j ) immediately succeeding activity i have been computed. The variation in the start time of activity j may be affected by the variation in the actual completion time of activity i. The magnitude of this variation (VSPij ) can be calculated by (16)

FIG. 2. As-Planned versus As-Built Schedules of Last Four Activities TABLE 1.

Terminal Activities Terminal activities are the last activities that do not have succeeding activities in the network. The variation in the completion time of the terminal activities may contribute to the project delay. Such a contribution combines with the contributions of other preceding activities accumulated through the logical sequence of the network

(14)

Summary Results

Activity (1)

VSP (2)

VA (3)

PDAC (4)

PDA (5)

W X Y Z

1 1 0 1

1 1 3 0

1 0 2 1

1 0 2 0



FIG. 3.

Intermediate Activities


VSPij = actual finishi ⫺ planned start j

(16)

Because of the logical constraint, activity j can start only after activity i is complete. If the actual finish time of activity i occurs later than the as-planned start time of activity j, then activity i causes a delay in the start of activity j. Otherwise, activity i does not cause any delay in the start of activity j; instead, it accelerates the project. A delayed start may not be fully transferred into project delay if the activity has unused float. The magnitude of the variation (PDACij ) that is transferred into project delay from activity i through activity j can be computed from (17) PDACij = min{VSPij , PDACj }

(17)

where PDACj = accumulated delay at activity j; and PDACij denotes the delay to be transferred from activity i to activity j. Activity i may be immediately succeeded by multiple activities. The cumulative contribution to project delay identified at activity i is the maximum of the PDACij values, i.e., the delay to be transferred from activity i to each of the succeeding activities PDAC = max{PDACij }; j

FIG. 4.

TABLE 2.

As-Planned versus As-Built Programs

Summary Results of Delay Computation

Variations between As-Planned and As-Built Schedules

Variation due to Various Reasons

Activity (1)

VS (2)

VF (3)

VD (4)

VSP (5)

VSS (6)

VA (7)

H G F E D C B A

3 2 1 1 ⫺1 0 0 1

4 2 2 1 0 1 ⫺1 3

1 0 1 0 1 1 ⫺1 2

1 2 1 1 ⫺1 ⫺1 0 0

2 0 0 0 0 1 0 1

3 0 1 0 1 2 ⫺1 3

Contribution to Project Delay PDAC PDA (8) (9) 3 2 2 1 0 1 ⫺1 1

3 0 1 0 0 1 ⫺1 1

j 僆 (immediately succeeding activities) (18)

VA in (13) stands for the variation in the completion of the activity due to reasons associated with the activity itself. The contribution of the activity to the project delay should not be greater than VA. Moreover, an activity’s contribution to the project delay should not exceed the accumulated delay PDAC. Mathematically, an activity’s contribution to the project delay (PDA) can be computed by (19) PDA = min{VA, PDAC}

(19)

When a noncritical activity is delayed and becomes critical, only a portion of the activity delay is converted into project delay. In reality, an activity may be delayed by various parties. This leads to the scenario that multiple parties may have caused concurrent delays, but their total effect on the project delay is less than their sum. For example, the owner and contractor caused a two-day and a five-day delay, respectively, but the project was delayed only three days. What is a fair apportionment of the three-day delay between the owner and the contractor remains a disputable issue. Relevant discussions can be found in Kraiem and Diekmann (1987) and Trauner (1990). Illustration of Computation Mechanism An example project is presented to demonstrate the computation mechanism. The as-planned schedule is from the early schedule of network calculations. Its logic-linked bar charts are plotted in Fig. 4 for the as-planned and as-built schedules with planned early start times, planned early finish times, logical sequences, and actual start and finish times for all activities in the project. A logic-linked bar chart is equivalent to a time-scaled, activity-on-arrow network diagram. Readers preferring network diagrams can easily convert Fig. 4 into an activity-on-arrow network diagram and perform relevant anal-

yses on start times, finish times, and floats. The as-planned critical path is B-C-E-F-G, with a duration of 16 days. The actual critical path changed a few times during the course of construction. Step 1: Compute Activity Variations between As-Planned and As-Built Schedules. Using (1)–(3), the VS (variation in activity start), VF (variation in activity finish), and VD (variation in activity duration) are computed for each activity, and the results are listed in columns 2–4 of Table 2. Activities are listed in column 1 in reverse chronological order to reflect the backward computation algorithm. The as-planned and as-built completion times of the project are day 16 and day 19, respectively. Therefore, the variation in the project duration is VP = 19 ⫺ 16 = three days (delay)

(20)

Step 2: Compute Activity Variations Based on Causes. The variation in an activity’s start caused by the variation in the completion of its immediately preceding activities is computed using (8). The results are presented in column 5 of Table 2. For instance, the could start time of activity D is day 2 (its preceding activity B is completed on day 1). The planned start time is day 3. Therefore, VSPD = 2 ⫺ 3 = ⫺1, indicating an acceleration of a day. The variation in an activity’s start caused by events associated with the activity itself (VSS) is computed using (9). The results are presented in column 6 of Table 2. For example, although activity C could start on day 2, it did not start until day 3. This one-day delayed start in activity C is due to reasons associated with the activity itself. The total activity variation caused fully by reasons associated with the activity itself (excluding the effect of preceding activities) is computed using (12) and is presented in column




FIG. 5.

Delay Information of Activity C

7 of Table 2. The value of an entry in column 7 equals the sum of the respective values in columns 4 and 6. Step 3: Compute Activity Contributions to Project Delay. The computation starts from the terminal activities G and H in the project. Their PDAC values are computed using (14); i.e., PDACG = 18 ⫺ 16 = two days; PDACH = 19 ⫺ 16 = three days. PDA values are computed from (15); i.e., PDAG = min{0, 2} = 0 day; PDAH = min{3, 3} = three days. In other words, activities G and H have contributed zero and three days, respectively, to the project delay. The PDAC values of intermediate activities are computed using (16)–(19). Activity F, for instance, has one succeeding activity, G. VSPFG = actual finishF (15) ⫺ planned startG (14) ⫹ 1 (due to time period) = 2. PDACF = PDACFG = min{VSPFG (2), PDACG (2)} = 2. The PDA value of activity F is computed using (19); PDAF = min{VAF (1), PDACF (1)} = 1. In summary, activity F’s contribution to the project delay is one day. The contributions of all other activities are presented in column 9 of Table 2. The various delay information of activity C is highlighted in Fig. 5 for better comprehension of the results in Table 2. Activity C’s preceding activity B was completed one day ahead of schedule; i.e., VSP = ⫺1, indicating that activity C could start one day earlier. However, activity C did not start earlier, but on schedule; i.e., VSS = 1, indicating that activity C’s start was delayed one day due to reasons relevant to the activity itself. Overall, activity C has a total delay of two days (one-day delayed start and one-day extended duration). It contributed one day to the project delay, as shown in Fig. 5. Table 2 indicates that four activities have contributed to the project delay. Specifically, H contributes three days; F, C, and TABLE 3. Activity (1)

Cause Analysis of Delays

Contribution to Extended duration project delay and reasons (2) (3)

H

3

F C

1 1

A

1

B

⫺1

1: increased scope

Delayed start due to self reason (4)

2: late delivery of materials 1: adverse weather 0 1: lower productivity 1: contractor’s decision 2: adverse weather 1: late possession of the site ⫺1: higher produc- 0 tivity

A contribute one day each. B has a one-day negative contribution to the project delay; i.e., it helps the project to be ahead of schedule by one day. The sum of the contributions of the five activities (A, B, C, F, and H) is greater than the project delay (three days) because of the existence of concurrent delays, where multiple activities are delayed simultaneously during the construction process. Step 4: Cause Analysis. After the contributions of individual activities to project delay are established, causes of delays can be investigated for individual activities that indeed impact the project delay. For instance, the completion of activity H is delayed by four days, three days of which are due to causes associated with the activity itself and one day is due to the delayed completion of its preceding activity E. The three-day self-caused delay in activity H is further traced down to a one-day delay due to an extended duration (VDH = one day) and a two-day delay due to a delayed start (VSSH = two days). All of this information can be directly retrieved from Table 2. Next, site records are needed to identify the causes of the delays in question. It should be mentioned that this paper does not intend to tackle this issue, which has been discussed in many references (Kraiem and Diekmann 1987; Trauner 1990; Arditi and Robinson 1995). This example illustrates how the computed results can be used to investigate delays. According to site records, the one-day extension of the duration of activity H is due to the changed scope of the work, for which the owner is responsible. The two-day delayed part of activity H is due to the late delivery of a material supplier. Similarly, causes for delays in the other activities can be retrieved from the site records as illustrated in Table 3. With such information, it becomes possible to identify responsibilities for individual delays. It should be mentioned that concurrent delays make assigning of responsibility very complicated. The example project has a total delay of three days. According to the computation, activity H has contributed three days to the project delay. In fact, even if activity H were not delayed, the project would still be delayed for two days due to the delayed completion of activity G. In other words, it would be impossible to eradicate the project delay by eliminating only the delays of some activities if concurrent delays have occurred in parallel activities. CONCLUSION AND DISCUSSION This paper presented a method for computing the contribution of activity variations to project delay. The method con-




sists of a set of equations, which can be easily coded into a computer program so that the project delay information and the contributions of individual activities are easily obtainable. The method is also applicable to any intermediate construction stage for evaluating in-progress project delay. It is not unusual for parties involved in a construction claim to argue about which party is responsible for an activity delay before they agree on the contribution of the delay to the total project delay. In the example project, activity A was delayed by three days, but it contributed only one day to the project delay. Therefore, the problem was to apportion the responsibility for the delay of one day rather than a delay of three days. An activity’s contribution to project delay provides a quantitative baseline for evaluating the impact of a delay. Traditional critical-path based methods require frequent (e.g., daily) updates of the as-built and as-planned schedules in order to keep track of the critical paths that may change daily. Such updating involves a tremendous effort for site management. The method presented in this paper is not based on the criticality of activities. The as-planned schedule provides a basis of comparison for evaluating the variation in the project duration, and does not need to be updated. Construction delay analysis represents a very complex task. It requires extensive project information and knowledge in determining the responsibility of a delay. The method presented in this paper provides an objective baseline for such a task. The method can be integrated into any system for improving and automating construction delay analysis. The computation method is developed based on the simple finish-to-start relationship. Therefore, it is not applicable to other relationships such as start-to-start relationships and finish-to-finish relationships in the current form. However, the equations can be expanded to these relationships as necessary.

APPENDIX.

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