Joint optimization of lot-sizing and maintenance policy for a partially observable two-unit system

In this paper, we present a new model to find the jointly optimal economic manufacturing quantity (EMQ) and preventive maintenance (PM) policy for a complex production facility. Unlike the previous joint models which dealt with EMQ and maintenance policy considering a single unit production facility and traditional maintenance approaches, we consider a production facility which consists of two modules with economic dependence. The more expensive module (unit 1) is subject to condition monitoring (CM), and only the age information of the second module (unit 2) is available, which follows a general distribution. The deterioration process of unit 1 is modeled as a continuous time hidden-Markov process. CM data is available at the end of each production run, and it provides only partial information about the hidden state of unit 1. The failure state of unit 1 is observable at any time. The objective is to develop a jointly optimal lot sizing and maintenance policy for a two-unit production facility using multivariate Bayesian control approach by minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Also, a formula for the mean residual life (MRL) of the production facility is derived, which is an important statistic for practical applications. A practical example of the wind turbine CM and maintenance is provided and a comparison with other policies shows an outstanding performance of the new model and the control policy proposed in this paper.