An Algebraic Max-plus Model for Hvlv Systems Scheduling and Optimization with Repetitive and Flexible Periodic Preventive Maintenance: Just-in-time Production

Most production scheduling problems, including High-Variety, Low-Volume (HVLV) scheduling problems assume that machines are continuously available. However, in most actual situations, machines become unavailable during certain periods when preventive maintenance (PM) is scheduled. In this paper, a HVLV scheduling problem is proposed while considering machines availability constraints. Each machine is subject to PM while maintaining flexibility in the start time of maintenance activities during the planning period. In this paper, two situations are investigated. First, the maintenance tasks are periodically scheduled: maintenance is required after a periodic time (all periods are equals on each machine). Second, time intervals between two consecutive maintenance activities are not equals (flexible periodic maintenance). However, time intervals are known in advance. Consequently, the maintenance operations are controllable. The jobs and the maintenance activities are scheduled simultaneously. Also, the maintenance tasks are scheduled between them, such that a regular criterion is optimized. In order to illustrate the performance of the proposed methodology, a simulation example is given.