We address the Unrelated Parallel Machine Scheduling Problem (UPMSP), where machines are subject to unavailability periods due to maintenance interventions. Two conflicting objectives are considered: the first focuses on production and maintenance tardiness, while the second aims to minimize energy consumption. This problem was previously studied in [15], where it was formulated as a Mixed-Integer Linear Programming (MILP) model and solved using an enhanced Multi-Objective Simulated Annealing algorithm based on a population of solutions (POP-MOSA).In this work, we aim to improve the performance of POP-MOSA by integrating reinforcement learning techniques, specifically the Q-learning algorithm. The resulting approach, referred to as Q-MOSA, leverages Q-learning to adaptively select the most appropriate local search strategy at each iteration.Q-MOSA introduces several novel contributions. First, at the end of the learning phase, the Q-table is generated using a compact design that reduces its size while preserving decision quality. Second, given the conflicting nature of minimizing both tardiness and energy consumption, a more flexible learning mechanism is required. This motivates the adoption of a multi-reward reinforcement learning strategy, which offers a more effective alternative to traditional single-reward schemes.Q-MOSA is evaluated using small-scale benchmark instances, and its performance is compared against the exact Pareto front obtained in [15].

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.

The objective of this study is to address a scheduling issue arising in production workshops, specifically dealing with unrelated parallel machine scheduling integrating flexible and periodic maintenance interventions. Machines, while operational, consume varying amounts of energy based on their state: idle states consume less energy than active ones. Additionally, energy consumption is influenced by both the production job and the specific machine.Our goal is to minimize two functions: the first pertains to reducing production and maintenance earliness/tardiness, while the second focuses on minimizing energy consumption. To address this problem, a Mixed Integer Linear Program (MILP) is proposed. The ϵ—constrained method is employed for computing the Pareto front, and further adaptation involves applying the Multi-Objective Simulated Annealing algorithm (MOSA) to handle instances of substantial size.The proposed MILP model demonstrates the ability to accurately determine the Pareto front for up to 30 production jobs and 2 machines on literature benchmarks within a timeframe of less than 1 hour. Moreover, the computed metrics proves the effectiveness of the proposed MOSA.

This work concerns the consideration of human resource constraints in the single machine scheduling problem of both production and flexible periodic maintenance activities. We assume that a maintenance activity requires the intervention of a human resource to be treated. These human resources are characterized by a competence level and availabilities considered as strong constraints allowing or not the maintenance activities' planning. To solve this NP-hard scheduling problem, we propose a guided local search metaheuristic that embeds a post-optimization process in order to minimize both production and maintenance delays. We implemented and experimented the proposed method on two series of benchmarks. The first one focuses on small size instances. The results show that the quality of the solutions obtained by the proposed method compared to an exact one is good, and even it reaches the optimal solution in some cases. In the second one, we applied the method on large instances to show its advantages and efficiency.

In this paper, we study a new scheduling problem that considers both production and flexible preventive maintenance on a single machine where the human resource constraints (the availability and the competence) are taken into account. The objective function involves both the tardiness and the earliness resulting from production and maintenance tasks. We propose a mathematical formulation of the studied problem that is expressed in the constraint programming (CP) paradigm as a set of linear constraints. This CP modeling had been implemented in ILOG OPL language and the exact method Cplex is applied on it to compute the optimal solutions of relatively small instances of the problem. Further, a heuristic algorithm is provided to deal with lager instances of the problem. Computational experiments demonstrate that the proposed heuristic performs well and is able to find good solutions to instances up to 700 jobs in a reasonable CPU time.

This research focuses on the problem of scheduling jobs on a single machine that requires flexible maintenance under human resource constraints. A fuzzy genetic algorithm that integrates production, maintenance, human resource availability and competence constraints is developed. This algorithm uses fuzzy logic to deal with uncertainties. Experiments show that the consideration of human resource constraints and uncertainties in the integrated and proactive scheduling allows proposing more realistic and applicable solutions.