Scheduling On A Batch Processing Machine Considering Preventive Maintenance

In the process of semiconductor production,such as oxidation and deposition,silicon chips need to be processed in batches.How to group jobs into batches and how to schedule batches on a batch processing machine need to be jointly optimized.In addition,batch processing equipment is expensive and has a high risk of failure,so preventive maintenance is needed.In this paper,the joint optimization problem of how to group jobs into batches and how to schedule batch production and preventive maintenance on a batch processing machine is discussed.In the first problem,the scheduling of preventive maintenance adopts flexible periodic preventive maintenance strategy.In the second problem,the batch processing machine is subjected to random failure.Mathematical models are established and algorithms are designed to solve these problems.This paper considers the problem of minimizing makespan on a single batch processing machine with preventive maintenance.This problem combines two sub-problems,scheduling on a batch processing machine with jobs' release dates considered and arranging the preventive maintenance activities on a batch processing machine.The preventive maintenance activities are flexible but the maximum continuous working time of the machine,which is allowed,is determined.Firstly,a mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed with the objective of minimizing makespan and the constraints of how to group jobs into batches,how to schedule batches and how to arrange preventive maintenance.Secondly,it is proved that this model can be solved by two-stage method.In the first stage,a batching rule LRD is proposed to group jobs into batches.In the second stage,an improved heuristic is proposed to schedule production and maintenance.Computational results indicate that the two-stage method based on proposed batching rule and improved heuristic is effective.However,the computation time of the improved heuristic is too large.In order to solve this problem,a method combining rules with the genetic algorithm is proposed to solve this model,in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities.The computational results indicate the method is effective under practical problem sizes.In addition,the influences of jobs' parameters on the performance of the method are analyzed,such as the number of jobs,the number of job families,jobs' processing time and jobs' release time.This paper also considers the problem of minimizing makespan on a single batch processing machine with random failure.This problem consists of two subproblems: one is scheduling on a batch processing machine with dynamic arrival of jobs,the other is arranging the preventive maintenance activities on a batch processing machine with random failure.Preventive maintenance can reduce the risk of machine failure and improve the availability of the batch processing machine.To achieve a balance between preventive maintenance and corrective maintenance is the goal of arranging preventive maintenance activities on a batch processing machine with random failure.Firstly,a mathematical model for integrating preventive maintenance into batch processing machine problem is proposed with the objective of minimizing makespan and the constraints of how to group jobs into batches,how to schedule batches and how to arrange preventive maintenance.Secondly,two different genetic algorithms are proposed to solve this model.One is to group jobs into batches first and we will get the processing time and arrival time of batches.Then we will use genetic algorithm to solve the scheduling of batches and preventive maintenance.The other is to directly use genetic algorithm to get the scheduling of jobs and preventive maintenance.We will use batch rule ERD to get the results of grouping of jobs and use scheduling rule ERD to get the sequence of processing of batches.Computational results indicate that the grouping-first genetic algorithm is more effective than the scheduling-first genetic algorithm.In addition,the influences of parameters of jobs and machine failure on the performance of the method are analyzed,such as the number of jobs,jobs' processing time,jobs' release time,proportion parameter of Weibull distribution and shape parameter of Weibull distribution.