This research presents a Resource-constrained Critical Path Method (RCPM) technique that capitalizes on and improves the existing Critical Path Method (CPM) and Resource-Constrained Scheduling (RCS) techniques. A traditional CPM schedule is not realistic since it assumes unlimited resources, some of which are highly limited in practice. Although traditional RCS techniques can consider resource limitations, they do not provide correct floats and the critical path as the CPM does. The difference between the theoretical remaining total float and the real remaining total float is referred to as "Phantom Float" in this study. Another disadvantage of the traditional RCS techniques is that work sequence in the schedule could be considerably changed with a schedule update resulting in high costs to reorganize it. These problems are caused by the fact that, in addition to technological relationships, a resource-constrained schedule contains resource dependencies between activities that are neglected in traditional RCS techniques. This study proposes a step-by-step RCPM algorithm to consider those resource-constrained relationships. Hence, the method can identify real floats and correct critical paths, considering both technological and resource-dependent relationships. RCPM also provides a certain level of stability with a schedule update due to the newly identified resource relationships. Based on the RCPM algorithm, a prototype RCPM system has been developed using Visual C++, Visual Basic, and Ra (Primavera Project Planner API). The system is integrated with P3, so that it reads project information directly from a P3 project, performs necessary RCPM procedures, and updates the P3 project to contain identified resource relationships. To make the system more practical, functions to handle multiple project calendars and progressed schedules have been included as well. / Ph. D.

On a regular basis, project managers concentrate their efforts on critical and near-critical activities. However, the concepts of total float and critical path lose their significance after applying resource-constrained scheduling (RCS) methodologies. RCS techniques solve the resource conflicts but create phantom float in the schedules (i.e., a float that does not exist). RCS techniques overlook the resources relationships between activities that compete for the same but unavailable resources. Therefore, each time an activity uses this apparent float (phantom float), there is a resource violation in the schedule. Due to the projects' size and complexity, schedulers use scheduling software such as Primavera P6 to fix the resource conflicts of a schedule. The software correctly determines the activities' earliest dates that satisfy the resource limitations, but they calculate total float based on a "Time Context" ignoring the presence of resource constraints. Thus, the results show incorrect total float values and a broken critical path. The lack of a continuous critical path makes impossible the anticipation of the impact of a delaying event in the project completion time. Several algorithms have been developed to address the shortcomings of RCS methods. These RCS related algorithms were developed with the aim of providing project managers a tool to correctly schedule and identify critical activities with respect to time and resource allocation and correctly calculate the total float of each activity under resource constraints. In this regard, the Resource-Constrained Critical Path Method (RCPM) is an algorithm that correctly calculates the floats of activities and identifies a continuous critical path in resource-constrained schedules. Regardless of the RCPM provides more reliable float values than traditional RCS-related algorithms, there are some shortcomings that must be addressed to enhance its capability. This study addresses the existing shortcomings of RCPM to make it more practical for real construction projects. / Doctor of Philosophy / One of the challenges of resource allocation is resource availability because oftentimes, the resource demand exceeds the supply. When resources are over-allocated, activities are delayed until resources become available. Due to the projects' size and complexity, schedulers use available software to solve the resource conflicts of a schedule. After testing Primavera P6 versions and MS Project v2016, both software create phantom float in a resource-constrained schedule. This is, the RCS calculations suggest that activities have float, but this float might not exist at all. Resource-Constrained Scheduling (RCS) techniques mitigate a resource supply-demand problem but fail to identify a project critical path. The methods do not consider the resource-activity dependencies that arise when activities are delayed due to resource limits. As a result, the critical path is broken, and all the activities must be considered as critical. To provide correct float values and a continuous critical path, the Resource-Constrained Critical Path (RCPM) was introduced by Kim and de la Garza in 2003. Regardless of the RCPM provides more reliable float values than traditional RCS-related algorithms, there are some shortcomings that must be addressed to enhance its capability. This study addresses the existing shortcomings of RCPM to make it more practical for real construction projects.