研究生产商采用MTS、MTO混合作业的方式为不同客户提供产品和服务的策略。计划利用一组可灵活控制的动态设备处理那些不同需求的MTS和MTO生产业务，为此，我们开发了一个多服务台的排队模型，利用拟生灭过程和相位型分布得到了MTS、MTO排队系统平衡条件和稳态概率矩阵几何解。通过求解分块矩阵方程组，给出了系统队列长度、平均等待队长、顾客服务水平等绩效测度指标。建立了系统运作成本最优化的数学模型，采用搜索算法，确定了关键参数的边界值，找到了混合系统运作的最优策略。数值模拟和系统绩效比较分析结果显示：（1）动态切换策略能够更快速的帮助MTS恢复目标库存量，控制系统缺货风险，降低库存持有成本；（2）找到了满足顾客服务水平的最少的设备配置数量和库存成本最低的生产切换时间，且动态系统的平均队列长度低于静态系统；（3）混合运作策略减少了约2/3的静态系统平均队列长度，企业在队列长度减小的窗口期内可以接受更多订单和缩短MTO订单交货时间。
Research manufacturing enterprises adopt the way of hybrid MTS-MTO to provide products and service of strategies for different customers. In this paper, we aim to use a set flexible controllable dynamic equipments to process the different needs of MTS and MTO production projects. Therefore, a multi-server queuing model is developed, where a subset of the servers or machines is dynamically switched between MTS and MTO production via a congestion-based switching policy. Using the quasi-birth-death process and the phase-type distribution, MTS-MTO queuing system equilibrium conditions and the steady-state probability matrix geometric solutions are obtained. By solving partitioned matrix equations, the system queue length, average waiting for captain, customer service levels and other performance indicators are given. Furthermore a system operating costs optimization mathematical model is established. Using simulation search algorithm, the key parameters of the system boundary value are determined and the optimal policy of hybrid system operation is found. The numerical simulation and performance comparison and analysis results show:(1) Dynamic switching policy can more quickly help the MTS to recover the target inventory, control the risk of shortage and reduce the inventory holding cost. When the shortage rate reaches 1.1% of MTS dynamic system, the static system safety inventory level must increase from 26 to 160 to satisfy the demand and increase the static inventory pressure. (2)The the minimum number of the equipment configuration or lowest cost of inventory of production switching time are found to satisfy the customer service level, and it is found that the dynamic system of the average queue length is less than that of the static system. Even holding less finished goods inventory, the shortage rate of MTS in dynamic system (0.3%) is lower than that of the static system (0.9-4.8%). (3) Extracting from the MTS to the advantage of extra capacity is not enough to make up for the replacement cost, caused by the switch system and single equipment of switch system become the substitute method of the hybrid system, the inventory operation policy to design that dynamic system to control the static system of three key performance indicators:average level of inventory, shortage rate of MTS and queue length of MTS and MTO to achieve optimum operation. (4)When the maximum intensity 3.8 of system average arrival rate, system service level 0.95, policy of hybrid operation reduce 2/3 average queue length of the static system, firm can accept more orders and shorten MTO order delivery time during of the queue length decreases.
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