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11. Advanced Scheduling Techniques
11.1 Use of Advanced Scheduling Techniques
Construction project scheduling is a topic that has received extensive research over a number of decades. The previous chapter described the fundamental scheduling techniques widely used and supported by numerous commercial scheduling systems. A variety of special techniques have also been developed to address specific circumstances or problems. With the availability of more powerful computers and software, the use of advanced scheduling techniques is becoming easier and of greater relevance to practice. In this chapter, we survey some of the techniques that can be employed in this regard. These techniques address some important practical problems, such as:
• scheduling in the face of uncertain estimates on activity durations,
• integrated planning of scheduling and resource allocation,
• scheduling in unstructured or poorly formulated circumstances.
A final section in the chapter describes some possible improvements in the project scheduling process. In Chapter 14, we consider issues of computer based implementation of scheduling procedures, particularly in the context of integrating scheduling with other project management procedures.
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11.2 Scheduling with Uncertain Durations
Section 10.3 described the application of critical path scheduling for the situation in which activity durations are fixed and known. Unfortunately, activity durations are estimates of the actual time required, and there is liable to be a significant amount of uncertainty associated with the actual durations. During the preliminary planning stages for a project, the uncertainty in activity durations is particularly large since the scope and obstacles to the project are still undefined. Activities that are outside of the control of the owner are likely to be more uncertain. For example, the time required to gain regulatory approval for projects may vary tremendously. Other external events such as adverse weather, trench collapses, or labor strikes make duration estimates particularly uncertain.
Two simple approaches to dealing with the uncertainty in activity durations warrant some discussion before introducing more formal scheduling procedures to deal with uncertainty. First, the uncertainty in activity durations may simply be ignored and scheduling done using the expected or most likely time duration for each activity. Since only one duration estimate needs to be made for each activity, this approach reduces the required work in setting up the original schedule. Formal methods of introducing uncertainty into the scheduling process require more work and assumptions. While this simple approach might be defended, it has two drawbacks. First, the use of expected activity durations typically results in overly optimistic schedules for completion; a numerical example of this optimism appears below. Second, the use of single activity durations often produces a rigid, inflexible mindset on the part of schedulers. As field managers appreciate, activity durations vary considerable and can be influenced by good leadership and close attention. As a result, field managers may loose confidence in the realism of a schedule based upon fixed activity durations. Clearly, the use of fixed activity durations in setting up a schedule makes a continual process of monitoring and updating the schedule in light of actual experience imperative. Otherwise, the project schedule is rapidly outdated.
A second simple approach to incorporation uncertainty also deserves mention. Many managers recognize that the use of expected durations may result in overly optimistic schedules, so they include a contingency allowance in their estimate of activity durations. For example, an activity with an expected duration of two days might be scheduled for a period of 2.2 days, including a ten percent contingency. Systematic application of this contingency would result in a ten percent increase in the expected time to complete the project. While the use of this rule-of-thumb or heuristic contingency factor can result in more accurate schedules, it is likely that formal scheduling methods that incorporate uncertainty more formally are useful as a means of obtaining greater accuracy or in understanding the effects of activity delays.
The most common formal approach to incorporate uncertainty in the scheduling process is to apply the critical path scheduling process (as described in Section 10.3) and then analyze the results from a probabilistic perspective. This process is usually referred to as the PERT scheduling or evaluation method. [1] As noted earlier, the duration of the critical path represents the minimum time required to complete the project. Using expected activity durations and critical path scheduling, a critical path of activities can be identified. This critical path is then used to analyze the duration of the project incorporating the uncertainty of the activity durations along the critical path. The expected project duration is equal to the sum of the expected durations of the activities along the critical path. Assuming that activity durations are independent random variables, the variance or variation in the duration of this critical path is calculated as the sum of the variances along the critical path. With the mean and variance of the identified critical path known, the distribution of activity durations can also be computed.
The mean and variance for each activity duration are typically computed from estimates of "optimistic" (ai,j), "most likely" (mi,j), and "pessimistic" (bi,j) activity durations using the formulas:
(11.1)

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