Integrated maintenance planning and production scheduling with Markovian deteriorating machine conditions

Abstract

In many industries, production capacity diminishes as machine conditions deteriorate. Maintenance operations improve machine conditions, but also occupy potential production time, possibly delaying the customer orders. Therefore, one challenge is to determine the joint maintenance and production schedule to minimize the combined costs of maintenance and lost production over the long term. In this paper, we address the problem of integrated maintenance and production scheduling in a deteriorating multi-machine production system over multiple periods. Assuming that at the beginning of each period the demand becomes known and machine conditions are observable, we formulate a Markov decision process model to determine the maintenance plan and develop sufficient conditions guaranteeing its monotonicity in both machine condition and demand. We then formulate an integer programming model to find the maintenance and the production schedule in each period. Our computational results show that exploiting online condition monitoring information in maintenance and production decisions leads to 21% cost savings on average compared to a greedy heuristic and that the benefit of incorporating long-term information in making short-term decisions is highest in industries with medium failure rates.

Keywords:

• maintenance planning
• maintenance scheduling
• scheduling
• flow shop scheduling
• optimization
• operations management

Notes

1 Comprehensive reviews of both literatures addressing the relationship between maintenance and production are provided by (Aramon Bajestani (2014), Chapter 2).

2 If machine is maintained at time period () and is the start-time of maintenance operation, it means that and . In case , then ).

3 The number of time periods , , equals 6, 14, 42 and 180 for discount factors of 0.2, 0.5, 0.8 and 0.95, respectively.

4 Because of the high computational time to find , there are no results for the case where the number of customer orders is generated from and the discount factor is 0.95. Therefore, the mean and the standard deviation for in Table 3 and Figure 5 are calculated over the demand situation of .

5 See (Aramon Bajestani (2014), Chapter 6) for more details.