An Integrated Efficiency-Risk Approach in Sustainable Project Control

Goldratt introduced the new approach for project management after 40 years' experience by publishing his best trade experiments called the "critical chain". The critical chain methodology is based on the deep knowledge of human nature and the reaction of individuals in the project management framework. According to this method, critical chain management completes projects faster than the CPM technique. Critical chain management defines and explains the communication among activity periods, independence relations, and required resources and how to access resources during the project. According to the CCM method, "time and its risks" are the most important items among the main principles of project management. The consumed budget of the project increases as time passes. However, we may have to interfere in the project scope to accomplish the project on the predefined time schedule. In this method, the problems, such as estimated extra confidence time for each activity to prevent undesirable events, student syndrome of working at the last minute, and performing different tasks at the same time (simultaneous activities), are solved; therefore, the project is completed sooner with using this technique.

According to the CCM, all problems resulted from the "confidence time" that we assign to consider and prevent unpredictable events. This reserved time should not be applied to the project if no unpredictable factor is caused. Clearly, the manner of considering and implementing the confidence coefficient is not satisfactory, and we should seek better ways to protect the system against unpredictable events. Unpredictable events have probability and statistical properties and should be treated with regard to statistical principles. However, statistical rules are only valid and reliable when the sample space is large enough. Therefore, allocating the confidence coefficient for one activity to keep the activity statistically safe cannot even be theoretically expected. The main constraint of the system, which prevents its immediate completion, is a critical path of the system. Therefore, this path should be protected against external events. With regard to the above-mentioned materials, we conclude that considering one confidence time (buffer) at the end of the project to face unpredictable events is better than allocating a reserved time to each activity. One of the main challenges of the CCM is the adequate sizing and management of the buffers. Focusing on the buffer time at the end of the project has two positive properties.

If we want to save the project completion time by monitoring individual operations one by one, reservation time should be allocated to each activity in which this time is added to the project when it is not necessary. Reservation time can be considered for the entire project as a buffer, which can be equal to the second root of the sum of squares of the activities' reservation time that reduces the project's duration (the project buffer is considered practically equal to half of the total time of the activity reservation).

The concentration of reservation time in the project uses the central limit theorem. Each reservation time uses a different sample distribution (high skewedness), the concentration of which leads to the normal distribution that prevents the prolongation of time.

In the CCM method, buffer sizing and buffer management (BM) are the most important work steps for controlling and planning the project, and they are explained in this section. A buffer is an instrument of the critical chain project control system that resists against the lack of determination of the project environment and absorbs it. Therefore, a buffer is an important section. Three types of buffers are available in a project: the project buffer, which is added at the end of the critical chain to protect the entire project from delay; the feeding buffer, which is added to the non-critical activities feeding into the critical chain to prevent non-critical activities from delaying critical ones; and the resource buffer, which is a flag to alert which resources have been planned in the critical chain and which ones have been used in the previous critical chain activities.

If the buffer size selected is smaller than the required size, the project will not be completed in the expected time. If the feeding buffer is small, project scheduling will be disturbed and the implementation of the project will be delayed. However, if the buffer size selected is larger than the required size, the project implementation duration will be longer. The buffer is usually obtained by adopting three methods (i.e., cut and paste, root square error, and Monte Carlo simulation). The calculation method is shown in Equation (1):

$B_{C-P}=0.5 \times \sum_{i=1}^{N}\left(T_{p}-T_{m}\right)$

$B_{r s e}=\sqrt{\sum_{i=1}^{N}\left(T_{p}-T_{m}\right)^{2}}$

$B_{m c s}=B P D_{\% 90}-B P D_{d}$

$where$

$B_{C-P}=Buffer \, calculated \, from \, cut-past \, method$

$B_{r s e}=Buffer \, calculated \, from \, root \, square \, error \,  method$

$B_{m c s}=Buffer \,  calculated \, from \,  monte  \, carlo  \, simulation$                                                          (1)

$N= quantity  \, of \,  activity$

$T_{p}= pessimestic  \, duration \,  of \,  activity$

$T_{m}= most  \, likely  \, duration \,  of \,  activity$

$B P D_{d}= deterministic  \, Baseline  \, Plan  \, Duration  \, of  \, project$

$B P D_{\% 90}= Baseline  \, Plan  \, Duration  \, of  \, project  \, with  \, a  \, probability  \, of  \, 90 \%$

$T_{m}= most  \, likely \,  duration \,  of \,  activity$

$T_{m}= most  \, likely  \, duration  \, of  \, activity$

$B P D_{d}= deterministic  \, Baseline  \, Plan  \, Duration  \, of  \, project$

$B P D_{\% 90}= Baseline  \, Plan  \, Duration  \, of  \, project  \, with  \, a  \, probability  \, of  \, 90 \%$

According to CCM, the project control is conducted using BM so that the buffers are divided into three equal parts, with each part accounting for 33% of the total buffer. The first part is green, the second is yellow, and the third is red. In each moment, no activity is necessary in the green part. The problem should be evaluated and corrective activities should be considered in the yellow part. Practice is required in the red part. In practice programs, the methods used for the immediate completion of unfinished activities in the chain, or those used to increase the speed of future activities in the chain, should be predicted. Project control is conducted, as shown in Figure 1, to evaluate the rate of using a buffer proportional to the project development.

Figure 1. Project control charts based on project progress and the buffer usage percentage.