Project Crashing Optimization Strategy with Risk Consideration

Read this article. The study develops a comprehensive evaluation strategy for project management. Section 2.1, Schedule Method-CPM/PERT, suggests that CPM does not consider risk or uncertainty. What would you add to a sensitivity analysis such that it could address risks or uncertainties?

Background

Schedule Method-CPM/PERT

The traditional critical path method (CPM) has been widely used in the construction industry for schedule analysis and project planning since the 1950s. The critical path represents the longest and most inflexible chain of activities in the overall project. The total float time for activities located in the critical path is zero. A project may contain several important critical paths. The backwardness of any activity in critical paths affects the completion of the entire project after a project starts. Hulett stated that CPM is a traditional and widely accepted approach for scheduling, and it is essential for developing the logic of a project and managing daily project tasks. However, CPM does not consider risk or uncertainty. CPM scheduling is accurate only when every activity begins as planned and consumes the same amount of time as estimated. Managers understand that projects do not always go according to plan and therefore require frequent status reviews. Given that projects generally do not proceed as planned, CPM can only serve as the beginning of project schedule management. Project managers should understand key reservations about standard CPM and should know how to perform a schedule risk analysis to obtain information that is crucial to project success before they embark on projects.

The program evaluation and review technique (PERT) in conjunction with CPM was developed in the late 1950s. Network planning technology using classical CPM/PERT as the core has been widely applied in project management. PERT uses a three-point estimate (optimistic, most likely, and pessimistic estimates) of activity duration to represent the lack of certainty in duration estimates.

(1) Optimistic time $\left(\mathrm{t}_{0}\right)$ : refers to the minimum possible time required to accomplish a task under the assumption that everything proceeds better than is normally expected.

(2) Pessimistic time $\left(t_{p}\right)$ : refers to the maximum possible time required to accomplish a task under the assumption that everything goes wrong.

(3) Most likely time $\left(\mathrm{t}_{\mathrm{m}}\right)$ : refers to the estimated time required to accomplish a task under the assumption that everything proceeds normally. This duration is more likely to occur than the others.

The completion time for project is expressed in formulas (1) and (2). The completion time (T) for project is the maximum of all the completed paths, that is, the completion time of the critical path. The formula is shown below, where P(j) refers to the set of all jobs on path j, refers to the average time (or mean time) of activity i on path j, and refers to the completion time of path j.

$\mathrm{T}=\max \left(\mathrm{T}_{\mathrm{j}}\right)$ (1)

$\mathrm{T}_{\mathrm{j}}=\sum_{\mathrm{i} \in \mathrm{p}(\mathrm{j})} t_{i}$ , where $\mathrm{i}=1,2,3, \ldots, \mathrm{n} \mathrm{j}=1,2,3, \ldots, \mathrm{m}$ (2)

However, PERT might underestimate the schedule risk because it ignores important risks at the merge points applied to the path when multiple paths and merge points exist. Omid et al. stated that PERT considers only one critical path, and it does not consider paths close to the critical one. Nearly all schedules for actual projects possess multiple paths. Thus, the Monte Carlo simulation method is applied in this study to overcome the shortcomings of PERT, because it can correctly compute risks at the merge points and represent the duration with a realistic probability distribution. This method is a preferred and reliable solution.