Mixed-integer/linear and constraint programming approaches for activity scheduling in a nuclear research facility

This paper presents the results of a research project aiming to optimise the scheduling of activities within a research laboratory of the ‘Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA)’. To tackle this problem, we decompose every activity into a set of elementary tasks to apply standard scheduling methods. We model the problem as an extended version of the Multi-Skill Project Scheduling Problem (MSPSP). As a first approach, we propose a Multi-Skill Project Scheduling Problem with penalty for preemption, along with its mixed-integer/linear programming (MILP) formulation, where the preemption is allowed applying a penalty every time an activity is interrupted. However, the previous approach does not take into account all safety constraints at the facility, and a more accurate variant of the problem is needed. We propose then to integrate the concept of partial preemption to the MSPSP. This concept, that has not been yet studied in the scientific literature, implies that only a subset of resources is released during preemption periods. The resulting MSPSP with partial preemption (MSPSP-PP) is modelled using two methodologies: MILP and constraint programming. Regarding the industrial need of having good solutions in a short time, we also present a greedy algorithm for the MSPSP-PP.