Mathematical modeling and genetic alghorithm approach for variable density resource constrained project scheduling

The use of project scheduling approaches for production planning is often used in make-to-order (MTO) or engineer-to-order (ETO) systems because the product is complex and highly customized. In these systems, each stage of production has its own complexities and features. Therefore, in general, all activities of production can be considered as stages of a project. In this type of production, simple finish-start precedence relationships do not accurately represent the actual production process; so overlap between activities must be allowed to minimize the production time and cost. In this study, a mathematical model is developed to balance the resource usage and minimize the production time by using a variable intensity formulation and four different precedence relationships. In this model, all project activities are carried out according to the variable intensity formula. This means that the percentage of an activity completed in a given time period depends on the amount of resource allocation required at that time. This model belongs to the class of NP hard (non-deterministic polynomial) problems, therefore, a genetic algorithm is proposed to calculate suitable solutions in the aforementioned problem. A novel chromosome structure is proposed for this genetic algorithm, and a three-level combinatorial searchis applied to adjust the parameters of the genetic algorithm. The solution obtained by the mathematical model and the genetic algorithm are same for small problems but for medium and large datasets only the genetic algorithm provides sub_optimal solutions.