Simulation Based Construction Project Schedule Optimization: An Overview on the State-of-the-Art

2. Background

A project scheduling problem can either be defined as a network of activities connected by their respective precedence constraints, or by a network of milestones connected by activities. The first notation with activities as nodes will be used throughout this chapter. Generally each node is associated with a list of resource requirements and a duration value. A node’s incoming arrows define its precedence constraints. To illustrate example problems throughout this chapter the scheme shown in Figure 1 is used. Each of the boxes defines one activity, which are labeled by capital letters. The width of each box is scaled according to the activity’s duration. While in complex problems activities can use multiple types and numbers of resources, the illustrative problems only use a single resource per activity which is indicated by a different hatching for each resource. The arrow from A to B implies that A has to be executed prior to B. In order to illustrate solution schedules the Gantt chart scheme of Figure 2 is used. The horizontal axis defines the time line of the resulting schedule. The boxes are aligned according to their respective execution times. The right hand side extension of boxes, such as for activity E in Figure 2 illustrates the float time of the activity, which will be described in more detail in Section 4.1. Figure 3 illustrates the usage of the resources over time. Again each box corresponds to an activity and the vertical sections correspond to the different resource types.

Figure 1.

Problem notation for resource constrained project scheduling problems. Each rectangle is an activity, arrows indicate precedence constraints, and hatching corresponds to used resources