Multi-project scheduling problem under shared multi-skill resource constraints

In this paper, we address a multi-project scheduling and multi-skilled employees assignment problem with hard and soft constraints. The goal is to assign employees to project tasks in a way that minimizes the total weighted tardiness and the undesirable goal deviations. Employees are assigned to projects with fixed percentages of time, and they must complete all projects within the desired time horizon. Each project is broken down into a set of preemptive tasks with release and due dates, without explicit precedence constraints. Each task must be performed by a single employee owning several skills and an efficiency level per skill, i.e., the processing time of the task may be reduced according to the efficiency level of the employee assigned to this task. As specified later, the studied problem comes from an industrial case in an IT company. All the constraints and the goal to achieve have been discussed with the projects managers. For this problem, we present a mixed-integer goal programming (MIGP) formulation to produce an optimal schedule. Furthermore, a local search algorithm and a tabu search algorithm are proposed to tackle large-scale instances. We compare the performance of the heuristic algorithms against the corresponding MIGP formulation with simulated instances derived from real-world instances got from the partner company.