Joint optimization of lot sizing and condition-based maintenance for a production system using the proportional hazards model

Abstract

This paper optimizes economic production quantity (EPQ) and condition-based maintenance (CBM) simultaneously for a production system subject to aging and deterioration. Different from previous models jointly determining EPQ and CBM, the proposed model is developed based on the proportional hazards model with a continuous-state covariate process, and on a CBM policy with multiple maintenance actions and dynamic control limits. Taking advantage of the opportunity of the downtime when a production run completes, condition monitoring is performed to reveal the system deterioration and then a suitable action is selected from preventive replacement, preventive repair, and no maintenance. Random failures during a production phase can be fixed by corrective replacement, corrective repair, or minimal repair. Considering that in many practical situations condition monitoring cannot be conducted at failure, corrective maintenance actions are determined based on (1) the system age at failure and the deterioration at the beginning of the production run (Scenario 1); or (2) both the system age and deterioration at the beginning of the production run (Scenario 2). The objective is to jointly optimize the production lot size and the CBM policy by minimizing the long-run average cost rate. The optimization problem is solved based on the policy-iteration algorithm in the semi-Markov decision process (SMDP) framework. A numerical example is provided to illustrate the proposed approach. The results show that Scenario 1 produces a more cost-effective but more complex maintenance strategy than Scenario 2 does.