A Mathematical Model for HVLV Systems Scheduling and Optimization With Periodic Preventive Maintenance Using (max, +) Algebra

Abstract The High-Variety, Low-Volume (HVLV) scheduling problem is one of the most arduous combinatorial optimization problems. This paper considers an interesting formulation of the HVLV scheduling problem using (max, +) algebra while periodic Preventive Maintenance (PM) is considered. Maintenance is time based since activities are periodically fixed: maintenance is required after a periodic time interval (all periods are equals on each machine). In this paper, the maintenance tasks of machines are controllable.The jobs and the maintenance operations are scheduled simultaneously. Also, the maintenance operations are scheduled between each other, so that a regular criterion is optimized. To generate feasible schedules, constrained decision variables are incorporated into the (max, +) model. The validity of the proposed approach is illustrated by simulation examples.

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