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.

Towards a tropical automaton product minimizing global completion times

“…Here, the decision-making is meant to be multivariate, it implies information about the availability of resources/devices, about the customers (e.g., their order of arrival), the maintenance plans, and the operational conditions (e.g., delays in service), to define an appropriate exploitation of the operational capacity of the system. It is typical in sectors as diverse as transportation (Kammoun et al 2010), manufacturing production (Aguilar 2001;Nasri et al 2012;Ponnambalam et al 2010), energy (Aguilar 1998), etc. This problem has been widely studied through formal and approximate approaches.…”