Single-machine Scheduling with Periodic Maintenance and both Preemptive and Non-preemptive jobs in Remanufacturing System

This paper considers a single-machine scheduling with preventive periodic maintenance activities in remanufacturing system. Although the scheduling problem with maintenance has attracted researchers’ attention, most of past studies consider only non-preemptive jobs. In fact, there exist both preemptive and non-preemptive jobs due to their different processing technic in remanufacturing workshop. Our objective is to find a schedule to minimize the makespan and subject to periodic maintenance and non-preemptive jobs. In this paper, an algorithm(we denote it as LPT-LS algorithm)is proposed. Its steps are as follows: 1) Firstly, scheduled the non-preemptive jobs in machine by the LPT(the Longest Processing Time)rule; 2)Then, scheduled the preemptive jobs into the machine’s remaining time by the LS (the List Scheduling)rule. And more importantly we discuss the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the preemptive jobs(We denoted it as 2 S ): 1) When 2 S is longer than the remaining time of the machine after assigned the non-preemptive jobs by the LPT rule, it is equal to 1; 2) When 2 S falls in between the remaining time of the machine by the Biographies: Liu Biyu(1981-), Female, doctoral student, [email protected]; Chen Weida(1965-), male, doctor, professor, [email protected]. 2 LPT rule and the OPT rule, it is less than 2; 3) When 2 S is less than the remaining time of the machine by the OPT rule, it is less than 2.