Research On Performance Modeling Of Production System With Random Properties And Finite Buffer

Production system plays an important role in modern manufacturing industry.Under the deployment of "made in China 2025",the mode of production and industrial form of manufacturing industry have changed.In order to estimate and maintain enterprise’s competitiveness in the industry,performance design and control method of production system become more and more flexible,and more comprehensive performance evaluation indicators are needed to make scientific analysis and reasonable evaluation for the performance of the production system and their abilities to respond to market demand.There are finite buffer and many random characteristics in the practical production system,such as the arrivals of products,setup times,reliability of facilities,service rates of machine in different production stages,which increase the complexity of performance analysis and control.However,the performance analyses in many features and requirements have not been analyzed thoroughly,and the performance measures are relatively homogeneous.Therefore,in this dissertation we build theoretical models,meanwhile,expand the performance measure indicators extensively and provide scientific analysis to study the system performance and optimization control of production system with randomness.This dissertation studies a single machine production system with randomness.There are setup times when the machine begins to produce the certain type of products.In addition,each product type has its own finite buffer,and First Come First Serve scheduling policy is used to coordinate different products.We focus on the flexibility of the machine.In multi-product production system,three typical system configurations are investigated respectively,including multi-product production system with state-dependent setup times,multi-product production system with service rate during setup period and multi-product production system with buffer breakdown.In single-product production system,considering to variable service rate of the machine,the repairable production system with service rate in standby period and in breakdown period are considered separately.The main research results and innovations are as follows:(1)Aiming at the problem of exponential growth of state space caused by one-dimensional Markov model,a finite Quasi-Birth-Death process model is proposed for performance analysis of multi-product system with state-dependent setup times and finite buffer.Firstly,the multi-product production system is decomposed into single-product subsystem model.And define the vacation of the machine which the period that the machine doesn’t process the current product type.Secondly,threeparameters are estimated including the length of the vacation,the probabilities of the machine becomes an idle period or set up for other product types at the end of the service for current product type.The two-dimensional continuous time Markov chain of the system is defined by the number of products in the buffer and the states of the machine.Then,by analyzing the balance equations of the two-dimensional Markov chain,the infinitesimal generator is represented by block triangulation structure,and the finite Quasi-Birth-Death process model of the system is constructed.Finally,the finite Quasi-Birth-Death process model is derived based on matrix geometric method,and the analytic expressions of the variance of output,interval estimation,the availability of steady state,the throughput and the probability that the system satisfies the customer’s order are derived,and the detailed solving steps are given.The proposed finite Quasi-Birth-Death process model can effectively expand the performance measures indicators and improve the shortcoming of the traditional one-dimensional Markov prediction model in dealing with more types of products or lager capacities of buffer with too large state space and complex modeling analysis.It has an extensive foreground of application.(2)Considering that the external production preparations of the setup period are completed without shutdown,a finite Quasi-Birth-Death process model is proposed to analyze the performance of the multi-product production system with service rate during setup period.According to whether the machine needs to be shut down in setup period,the production preparation is divided into internal production preparation and external production preparation.In view of the particularity of the external production preparation,the stochastic characteristic of variable service rate is introduced into the multi-product production system.A finite Quasi-Birth-Death process model of the system is constructed by defining the two-dimensional continuous time Markov chain by the number of products in the buffer and the states of the machine and representing its infinitesimal generator by block triangulation structure.Based on matrix geometric method,the model is solved and the calculation process of the throughput is given.The analytical expression of the throughput is obtained for the simplified two-product case.At the same time,the asymptoteics and monotonicities of the throughput with respect to the system parameters are presented accurately by derivative calculation,which will provide theoretical support for improving production efficiency and reference for optimization control of the system.(3)In view of the reliability of the buffer and the influence to the machine,a discrete-time Markov chain model is proposed for performance analysis of the multi-product production system with buffer breakdown and arbitrary processing time.The steady state probability of each state is obtained by constructing the discrete-timeMarkov chain of the system.Then the states of the system is separated into four cases and the contribution of each state to the production cycle time is calculated according to the type of product being processed,the fault state of the buffer and the number of products in each buffer.The analytical expression of the throughput is developed when the average production cycle time is obtained.And the detailed calculation processes of state transition probability matrix and the throughput for identical Erlang-2 product system are given.The influences of parameters on the throughput and the interaction of parameters are discussed through numerical analysis,which provides theoretical support for enterprises to select parameters in the practical production.(4)In view of the situation that the machine may have service rate in the standby dormancy period,the working vacation strategy is introduced into the single-product production system for the first time.A finite Quasi-Birth-Death process model is proposed for performance analysis of the repairable production system with setup times and working vacation.The three-dimensional continuous time Markov chain is defined by the number of products in the buffer,the states of the machine and the fault state of the machine.And the finite Quasi-Birth-Death process model of the system is constructed by representing the infinitesimal generator of the Markov chain by block triangulation structure.Then the finite Quasi-Birth-Death process model is derived based on matrix geometric method,and the analytical expressions of the throughput,the variance of output,the availability of steady state,interval estimation and the probabilities in steady state are derived.The influences of parameters on performance measures are summarized through the numerical analysis,which provides the theoretical basis for enterprises to improve the production efficiency and increase the system reliability.The proposed finite Quasi-Birth-Death process model is also very instructive for the qualitative research of queuing theory on working vacation.(5)In view of the situation that the machine may have service rate in breakdown period,the working breakdown strategy is introduced into the single-product production system for the first time.A finite Quasi-Birth-Death process model is proposed for performance analysis of the repairable production system with setup times and working breakdown.The finite Quasi-Birth-Death process model of the system is constructed by defining the two-dimensional continuous time Markov chain by the number of products in the buffer and the states of the machine and representing its infinitesimal generator by block triangulation structure.The finite Quasi-BirthDeath process model is derived based on matrix geometric method,and the analytical expressions of the throughput,the availability of steady state,the number of the products waiting for processing in steady state and the probabilities in steady state arederived.Then the influences of parameters on performance measures and the stability of production system with working breakdown are summarized through the numerical analysis,which gives optimization suggestions for the improvement of production system.The proposed finite Quasi-Birth-Death process model is also very instructive for the qualitative research of queuing theory on working breakdown.