Hierarchical control of production and maintenance rates in manufacturing systems

Abstract

SOMMAIRELes systèmes de production sont en général constitués de plusieurs machines interconnectées qui produisent simultanément plusieurs types de pièces. Ces machines sont sujettes à des pannes et réparations aléatoires. La dynamique des pannes de ces machines dépend de leurs âges et leur disponibilité dépend des stratégies de maintenance adoptées. Dans ce contexte, le problème de planification de la production et de la maintenance de ces types de systèmes de production peut être formulé comme un HIERARCHICAL CONTROL OF PRODUCTION AND MAINTENANCE RATES IN MANUFACTURING SYSTEMS JEAN-PIERRE KENNE EL-KÉBIR BOUKAS ABSTRACTThis paper deals with the production and preventive maintenance planning control problem for a multi-machine flexible manufacturing system (FMS). A two-level hierarchical control model is developed according to the discrepancy between the time scale of the discounting cost event and the one of the machines states process. The proposed model extends the classical singular perturbation approach by considering age dependent machines failure rates and controlling both production and preventive maintenance rates. We replace the stochastic optimal control problem by a deterministic control problem called limiting control problem. With this approach, we compute an age dependent near-optimal control policy of the stochastic initial control problem from the optimal solution of the equivalent limiting control problem. A numerical example is used to illustrate the procedure and to show the reduction of the control problem size.

Optimal safety stocks and preventive maintenance periods in unreliable manufacturing systems

“…It is assumed in Salameh and Ghattas (2001) that extra capacity is maintained to buffer against uncertainties of the production processes and that there is no possible breakdown of the machine before the preventive maintenance date. Without the assumption made by Salameh and Ghattas (2001) on the machine dynamics, the stochastic optimal control theory is used in Boukas et al (1995), Kenne (2000, 2005), Kenne and Gharbi (1999) and in Kenne and Boukas (2003) to define an machine age dependent production and preventive maintenance policies. Such policies are based on non homogeneous Markov models, and hence are restricted to exponential distributions describing operational and down times of the involved machines.…”

Maintenance scheduling and production control of multiple-machine manufacturing systems

“…In this paper, we will first define the structure of the optimal control policies, both for identical and for non-identical machine manufacturing systems. Based on such structures, we will then extend the production and maintenance rates control model presented in Kenne and Boukas (2003) in order to determine the control policy in a more general case including non-identical machine manufacturing systems. The resulting structure is described through a set of parameters we call input factors.…”

Age-dependent production and replacement strategies in failure-prone manufacturing systems

“…The value function ( , , ) defined in equation (18) represents the value of the total cost function described by equation (16), and provides the viscosity solution that satisfies the HJB equations (also called optimality conditions). These conditions are necessary and sufficient for an optimum.…”

“…This policy shows that the value function (. ) given by equation (18) satisfies the set of partial differential equations known as the Hamilton-Jacobi-Bellman equations (HJB). In Appendix 2, we develop the derivation of the HJB equations.…”