Exact resolution for the unrelated parallel machine scheduling problem with flexible maintenance and human operators planning

This study addresses a novel parallel machine scheduling problem where machines undergo periodic, flexible maintenance needing human operators. Operators differ in competence and availability, affecting maintenance execution and planning feasibility. We focus on optimizing a weighted objective function encompassing both production and maintenance. Indeed, we aim to minimize the sum of production tardiness and the maintenance earliness-tardiness. To tackle this problem, we introduce two mathematical models: one based on Mixed-Integer Linear Programming (MILP) and the other on Constraint Programming (CP). Both models are solved using IBM ILOG Cplex 22.1, demonstrating the effectiveness of the CP modelling in managing this complex scheduling problem.