Modelling And Optimization Methods Of The Manufacturing System Of Reheating Furnace With Markov Queues

A manufacturing system is a physical organization system which is built to achieve a predetermined manufacturing goal,including production process and logistics process.Production process is that workpieces are processed by the equipment in a particular order.Logistics process is that the objects are operated by equipment to make space transfer in a certain order.The manufacturing system of steel industry has a complicated production process,a large variety of products,and a complex network structure.There are random uncertainties in the production and logistics scheduling process.The dynamics changes generated by randomness need to be considered,when making decisions of production and logistics scheduling process.Based on the manufacturing system of a reheating furnace,this thesis studies the reheating problem of slabs in the production process and the storage problem of slabs in the logistics process,and optimizes the equipment resources allotment in the system.Because the production and logistics process of the system have random characteristics,this thesis establishes a Markov queueing system to study them.Therefore,the research on optimizing the resource allocation of equipments of steel manufacturing system based on modelling Markov queues has great significance for steel industry to save energy and reduce costs.Based on the production process of slab reheating and the logistics process of slab storage in the manufacturing system of reheating furnace,this thesis extracts the production and logistics scheduling problems with random characteristics.The problems are described by queueing models.In the scheduling system of production process of reheating furnace,this thesis considers the congestion condition of reheating slabs and random characteristics of service time of the reheating furnace.Then a queueing model with threshold conversion policy is established to optimize the resource allocation of reheating furnace,and the matrix geometry method is used to solve the problem;For the problem of dynamic resources configuration of reheating furnace,a semi-Markov queueing model is established,and the submodular method is used to prove the theory.The reinforcement learning algorithm is used to solve the problem.In the scheduling system of logistics process of reheating furnace,considering the congestion situation of slabs and random characteristics of arrival slabs,the queueing model with threshold conversion is established to optimize the resource configuration of cranes,and the matrix geometric method is used to solve the problem;Aiming at the problem of resource allocation with time constraints and resource constraints in the process of slab storage,a nonlinear optimization model based on slab storage system is established,which is optimized by convex optimization method.The main contributions of this thesis are summarized as follows:(1)For reheating process of slabs in production scheduling system of reheating furnace,resource allocation problem is refined.The problem is to determine the allocation of reheating furnace in order to minimize the production cost of the reheating process of slabs,considering the slab congestion and the randomness of the reheating time.Unlike the traditional methods that use the exponential distribution to describe the service time,this thesis is based on the fitting historical production data and uses the phase-type(PH)distribution to describe the reheating time of furnaces accurately.The M/PH/C with threshold conversion is built to describe the production process of reheating furnace.Since the reheating time obeys PH distribution,the analytical solution of M/PH/C with threshold conversion model cannot be obtained.The matrix geometry method is designed to solve the problem accurately.The experimental results show that the model and method can effectively determine the number of open reheating furnace.(2)The queueing problem with dynamic resource allocation is extracted from the production scheduling process of reheating furnace.A semi-Markov queueing model is established to reduce the reheating cost of slabs according to situation of arrival market orders.It can determine the number of open reheating furnaces in real time.The submodular theory is used to prove the monotonicity between the optimal number of open reheating furnaces and the amount of slabs.This property is not affected by the arrival process of market order and the distribution of service time of the reheating furnace.The properties provide of optimal solution is a theoretical support for the semi-Markov queueing model.Combined with the reinforcement learning algorithm,the optimal configuration policy of servers is calculated under time infinite dimension.(3)The queueing problem with Markov modulated Poisson process(MMPP)is extracted from the logistics scheduling process of slab storage,and the threshold conversion policy is introduced according to the situation of slab congestion.The main characteristic of this problem is that the slabs with different steel grades arrive at the slab yard with different speeds.The traditional Poisson distribution cannot truly describe the arrival process of slab.Based on the characteristic,MMPP is used to accurately describe the arrival process of slabs,and an MMPP/M/C queueing model with threshold conversion is established.The matrix geometric method is implemented with the MATLAB software,and the optimal configuration policy of cranes is given.The numerical experiments are used to verify the advantages of the queueing model with threshold conversion for modelling and analyzing the process of slab storage.(4)The problem of resource allocation of the logistics scheduling system is extracted from the storage process of slabs.The storage process of slabs is regarded as a queueing system It considers the constraints of waiting time and space capacity.The problem is to establish a nonlinear optimization model with the constraints of logistics time and storage space of slabs.A conversion method is designed,since the nonlinear optimization model of the queueing system is difficult to solve.The nonlinear optimization model is transformed into a convex optimization model,so that the model can be solved in polynomial time.