Theoretical Results on Single Machine Scheduling to Minimize the Number of Tardy Jobs with Periodic Maintenance

In the last two decades, maintenance as an essential method to prevent machine breakdown has achieved undoubted importance in process industries and manufacturing systems. With ever increasing high-quality products demand, the number of tool change or machine maintenance become quite remarkable. Besides, industry 4.0 supports manufacturing enterprises to explore more efficient and intelligent scheduling modes. Machine periodic maintenance has a significant impact on the scheduling of many manufacturing companies, it therefore has become one of the factors they must consider. Despite this, theoretical analysis for the machine scheduling problem with periodic maintenance has not received considerable critical attention in previous studies. Motivated by scheduling practice, this work revisits a single machine scheduling problem with periodic maintenance to minimize the number of tardy jobs. First, a polynomial-time solvable case is identified. Then we propose a dynamic programming algorithm to solve the general case. At last, the non-approximability is proven.