Research Of Markov Queuing Model In Flow Shop Scheduling Problem

With the rapid development of science,technology and the popularity of intelligent manufacturing in twenty-first Century,How to improve the utilization of resources and enhance the adaptability to the environment of enterprises.As the core of intelligent manufacturing,job shop scheduling has attracted the attention of scholars in various fields.A fast and efficient scheduling method can improve the efficiency of manufacturing system.The development of manufacturing will be intelligence,high efficiency and globalization.In order to maximize the resources utilization and deal with the unexpected random events,this paper constructs a queuing model of two kinds of job shop scheduling.In this paper,the Markov queuing model with different processing capability is firstly established to selectively optimize the different types of machines,and the M/M/2 and M/M/3 queuing models was simulated respectively;Secondly,the queue length of the flow shop with buffer is longer,and the integrated priority queuing rule was proposed;Finally,this paper set the machine in busy and idle time(the productivity of busy machine reached the maximum,idle machine reached the minimum)and workpiece priority to establish Markov queuing model of production,according to the arrival number of the workpiece to adjust the upper and lower limits of machine productivity and the priority of various types of work,so as to optimize the production cost.The main research contents are:(1)Aiming at the problem of low machine utilization and the too long average waiting time of the work piece in the processing model of machine shop scheduling with unequal machine capability.This paper do experiment on Markov’s M/M/2 and M/M/3 queuing model of unequal processing ability with the help of matlab signal simulation module.The experimental results show that the utilization rate of each machine is improved,and the stronger of the machine processing ability,the faster the machine performance;At the same time,the average waiting time of the work piece is decreased,and the stronger of the machine processing capacity,the more the average waiting time is reduced.The queuing rules of Markov S queuing model with different processing capacities are optimized,and an integrated priority queuing model is proposed,the integrated priority queuing model achieves the optimal number of jobs in the unit time and does not reduce the quality of the work piece.(2)In this paper,we proposed an integrated priority queuing model based on the rule of first come first service and the short job priority service,and the simulation experiment of the integrated priority queuing model was done in Matlab platform.The experimental results show that with the increase of machine numbers,the three kinds of queuing strategy(first come first serve,short job first serve,integrated priority service)workpiece waiting time and queue length were decreased,and the first service queuing strategy decreased most quickly,then integrated priority processing strategy.Under the same number of machines,the short service time priority strategy and the integrated priority service strategy can reduce the waiting time of the work piece,which can process more jobs in the same time.With the increase of machine numbers,the integrated priority service strategy of each production performance gradually rising and closely near to the short service time priority strategy,and integrated priority service strategy considering both the job arrival time,the situation that the first workpiece always waiting will not appear in the integrated priority service strategy.(3)In order to solve the problems of high queuing cost and high production cost in the scheduling problem,this paper puts forward Markov’s queuing production model,and a differential evolution algorithm based on production cost is designed.The birth and death process of Markov process derived from the related parameters of queue length,unit time job arrival frequency,rejection rate after work piece arrival,calculation formula of production intensity.The related parameters and the formulas of the system were brought into differential evolution algorithm and genetic algorithm and did simulation experiments,which showed that the differential evolution algorithm can quickly converge to the optimal value.Based on the analysis of the experimental data,the production cost can be reduced by adjusting the priority,the basic productivity and the supplementary productivity under different system parameters.