Critical Sequences and Resource Links Optimization in Resource-Constrained Project Scheduling

In order to identify critical activities and critical sequences under resource availability constraints, resource dependencies need to be established. By doing this, project managers and practitioners can focus their limited energy on specific activities and paths during the execution of a project schedule, thus guaranteeing that the project gets finished on time and with the available resources. This study proposes various rules to judge the superiority or inferiority of the methods of dependencies’ creation. The total number of critical sequences which is one of these rules, directly influences the degree of difficulty in controlling the whole project — a major concern for project managers. This study classifies activities in a resource-constrained project schedule on the basis of the relationships between activities and develops the basic idea behind the optimization of resource dependencies. Specifically, two mathematical models to minimize the total number of critical sequences and that of resource links through the table translation method are proposed. A computation example shows great improvement in the number of critical sequences, critical activities and resource links and gives effective results while solving the problems in the previous research. Moreover, simulations using J30, J60, and J120 instances by Kolisch highlight the high computing speed when searching for the actual minimum number of critical sequences and resource links thanks to the table translation method.