MILP formulations for single- and multi-mode resource-constrained project scheduling problems

This work presents new mixed-integer linear programming models for the deterministic single- and multi-mode resource constrained project scheduling problem with renewable and non-renewable resources. The modeling approach relies on the Resource-Task Network (RTN) representation, a network representation technique used in process scheduling problems, based on continuous time models. First, we propose new RTN-based network representation methods, and then we efficiently transform them into mathematical formulations including a set of constraints describing precedence relations and different types of resources. Finally, the applicability of the proposed formulations is illustrated using several example problems under the most commonly addressed objective, the makespan minimization.

► New network representation and MILP models for the single- and multi-mode RCPSP.
► The MILP models are based on the Resource-Task Network representation.
► Both renewable and non-renewable resources are modeled.
► Application on several example problems under the objective of makespan minimization.