*3.1. Sample Network*

To analytically assess and compare these techniques, a sample network is introduced. Since a real project network cannot be introduced in this paper, the problems which were identified in the middle of analyzing real big complex projects having up to 5000 activities were dealt through the sample network. A sample network was used for simplification and the instinctive understanding; The schedule is as revealed in Figure 1. It is made of activities A, B, C, D, E, F, and G. Its total project duration is 40 days. Its critical activities are A, B, C, D, and G. Activities E and F have 5 days of float.

**Figure 1.** As-planned schedule of a sample project.

The project started as planned, but in the middle of the progress, three delayed events happened. "Delay event 1" was affected by the owner delaying the authorization on the shop drawing for "activity E". It hindered the start of "activity E" for 10 days from the 11th to the 20th date. Furthermore, the contractor had a labor problem ("delay event 2"), which hindered the start of activity C for 5 days from the 16th to the 20th date. In the progress, the contractor completed "activity F" 3 days earlier than planned. After the finish of activity F, the owner ordered a change ("delay event 3"), which happened for 5 days from the 38th day to the 42nd day, impacting the start of "activity G". Figure 2 revealed the as-built schedule. The project was 7 days late, as it turned out.

**Figure 2.** As-built schedule of a sample project.

#### *3.2. Inserting a Single Delay Event*

To quantify the impact of a single delay event, several researchers and delay analysts argue that it should be put into an as-planned schedule without any other delay events [20]. There are always a lot of delays in real projects. Therefore, inserting all delay events into an as-planned schedule chronologically and analyzing the impact of each delay event sequentially is difficult and time-intensive. For simplicity and convenience, this simplified approach is utilized in practice.

The delay event or the fragnet is connected to logically relevant predecessors and successors when only a single fragnet is inserted into an as-planned schedule. At each evaluation, the impact of each delay event is calculated. The effect of all delay events can be analyzed by repeating this process. The total estimated delay of a project is obtained by adding all delay effects together. The ratio of owner- and contractor-caused delay can be calculated. This approach assumes that the estimated total delay should be equal to the actual delay of the project. Therefore, the summation of the owner-responsible delay is evaluated by multiplying the ratio of owner-caused delay to the actual delay of the project. The contractor-caused delay is also calculated through the same process.

The general process for determining the impact of a delay is as follows: Firstly, only "delay event 1" is added to the as-planned schedule. Figure 3 shows the outcome. It takes 45 days to complete the job. The completion of the project is delayed as much as 5 days. The owner is responsible for the delay, which is classified as the "excusable and compensable (EC)" delay.

**Figure 3.** Impacted as-planned schedule by delay event 1 (owner-caused delay).

Next, as shown in Figure 4, "delay event 2" alone is added. Its total project duration becomes 45 days. Its estimated completion date is delayed 5 days. It is analyzed that "delay event 2" has 5 days of impact. The contractor is liable for the delay, which is classified as "non-excusable and non-compensable (NN)".

**Figure 4.** Impacted as-planned schedule by delay event 2 (contractor-caused delay).

"Activity F" was completed 3 days earlier than as-planned. However, it is not reflected in IAP; only delayed events are added to the as-planned schedule. As shown in Figure 5, the IAP schedule by only "delay event 3", its total project duration is 40 days. There is no delay because there is no change in the project duration according to the analysis.

In this analysis, (owner-caused) delay event 1 and (contractor-caused) delay event 2 have 5 days of impact respectively when a single delay event is inserted without any other delay events. All of the delays are added up to 10 days. Owner-responsible delay (EC) is calculated by multiplying actual delay by owner-caused delays divided by the sum of all delays caused by the owner and contractors. The same method is used to compute the contractor-responsible delay (NN).

Owner-responsible delay (EC) = 7 × 5/10 = 3.5 days (1)

Contractor-responsible delay (NN) = 7 × 5/10 = 3.5 days (2)

This approach is simple and easy to implement but may have some problems. This approach would count the impact of each delay event. As a result, it cannot reflect concurrent delays. This approach would also fail to account for the cumulated impact of previous delay events or any changes. As a result, this approach assumes that the sum of all delays is equal to actual delay of the project and that there is no acceleration.

**Figure 5.** Impacted as-planned schedule by delay event 3 (owner-caused delay).
