A genetic algorithm for project scheduling in activity networks under resource complementarity

We address the issue of optimal resource allocation, and more specifically, the analysis of complementarity of resources (primary resource or P-resource and resource or S-resource) to activities in a project. The concept of complementarity can be incorporated into the engineering domain as an enhancement of the efficacy of a primary resource (P-resource) by adding to it other supportive resources (S-resources). We developed a Genetic Algorithm capable of determining the ideal mixture of resources allocated to the activities of a project, such that the project is completed with minimal cost. This problem has a circularity issue that greatly increases its complexity. In this paper we present a constructive algorithm to build solutions from a chromosome that will be integrated in a Genetic Algorithm, which we illustrate by application to a small instance of the problem. The Genetic Algorithm is based on a random keys chromosome that is very easy to implement and allows using conventional genetic operators for combinatorial optimization problems. A project is formed by a set of activities. Each activity uses a specific set of resources, and it is also necessary to guarantee that there is no overlap in the time it takes to process activities in the same resource.