Integrated Optimization Of Production Control And Canpacity Planning Under Uncertainties

For a manufacturing system,its capacity planning problem and production control problem are usually solved separately.However,production capacity cannot exert its maximum productivity without employing optimal production control;and optimal production control may not satisfy the demand without sufficient production capacity.Specially,in order to make the manufacturing system exert the maximum production performance with minimum investment on devices under uncertainties,e.g.,random machine failure and uncertain process route,it is more important to jointly optimize capacity planning and production control to resist the negative effects of uncertain factors.Therefore,in this paper,we study the Integrated Production Control and Capacity Planning(IPCCP)problem under uncertainties for four types typical manufacturing systems.1.The IPCCP problem of single-product-type,multi-parallel-machine and multi-stage serial production line with random machine failureThe objective of the IPCCP problem for a single-product-type,multi-parallel-machine and multi-stage serial production line with random machine failure is to minimize the investment on machines while keeping the average production cost below a desired level.Moreover,the key point for evaluating the average production cost is also the calculation of the steady-state probability distribution of the state variables.Firstly,we start with single-stage and multi-parallel-machine manufacturing system,and develop the method of calculating its steady state probability distribution.Based on the steady state probability distribution of single-stage and multi-parallel-machine manufacturing system,we propose a method of calculating the steady state probability distribution of a two-stage and multi-parallel-machine system by using a decomposition-based method.Furthermore,the method of calculating the probability distribution of a two-stage and multi-parallel-machine system is extended to a multi-stage production line.Thus,the average production cost of multi-stage production line can also be acquired.Finally,we employ a gradient-based algorithm to optimize the production control parameters and an integer programming technique to optimize the production capacity.Numerical experiments are conducted to verify the correctness of the method of evaluating steady-state probability distribution,and indicate that the solution of PI-PCCP has better performance.2.The IPCCP problem of multi-product-type,multi-parallel-machine and multi-stage manufacturing system with random machine failureThe objective of the IPCCP problem for a multi-product-type,multi-parallel-machine and multi-stage manufacturing system with random machine failure is to minimize the investment on machines while keeping the average production cost below a desired level.Moreover,the key point for evaluating the average production cost is also the calculation of the steady-state probability distribution of the state variables.Because the two-product-type,multi-parallel-machine and single-stage manufacturing system where no demand backlog is allowed can be considered as a building-block of a multi-product-type,multi-parallel-machine and multi-stage manufacturing system,we firstly analyze its steady state probability distribution under the prioritized hedging point policy.Although the shape of the domains of the work-in-process(WIP)levels influences the steady state probability balance equations,we still have developed a unified form of the marginal probability balance equations for all the possible shapes of WIP domains,which can be used to calculate the marginal probability distribution for each product type for the two-product-type and multi-parallel-machine system.Furthermore,we extend this analysis method to the multiple-product-type,multi-parallel-machine,and single-stage system.Based on the decomposition method of a production line,we can calculate the marginal probability distribution of a multiple-product-type,multi-parallel-machine,and multi-stage system and its average production cost.Finally,we employ a gradient-based algorithm to optimize the production control parameters and an integer programming technique to optimize the production capacity.Numerical experiments are conducted to verify the correctness of the method of evaluating steady-state probability distribution,and indicate that the solution of the IPCCP problem has better performance.3.The IPCCP problem of multi-stage assembly system with random machine failureThe objective of the IPCCP problem for a multi-stage assembly system with random machine failure is to minimize its investment on machines while keeping the average production cost below a desired level.Moreover,the key point for evaluating the average production cost is also the calculation of steady-state probability distribution of the state variables.Firstly,we analyze the approximate control policy of the multi-stage assembly system to determine state distribution domain.Furthermore,the probability balance equations of all the states in the state distribution domain are constructed.Then,we propose a method to obtain the marginal probability distribution of the multi-stage assembly system.Thus,the average production cost can be obtained.Because the optimal control policy parameter is impacted by production capacity,we employ the mixed integer programming technique to obtain the optimal machine number.Numerical experiments are conducted to verify the correctness of the method of evaluating steady-state probability distribution,and indicate that the solution of the IPCCP problem has better performance.4.The IPCCP problem of semiconductor manufacturing system with uncertain wafer lots transfer probabilityFor a semiconductor manufacturing system,wafer lots transfer probability(WLTP)is introduced to capture the flowing rate of wafer lots among production tools,which is uncertain due to various wafer types and quantities.We study a new production capacity planning problem for wafer fabrication systems with uncertain WLTP.Based on an open queueing network model,the average work-in-process(WIP)level of the system is evaluated.Because of the uncertain WLTP,the average WIP level fluctuates significantly and sometimes exceeds its desired upper bound.Therefore,we develop a robust production capacity planning model with two layers: the bottom layer is for finding the maximum WIP fluctuation under a given vehicle quantity,and the upper layer is for determining the vehicle quantities to minimize the WIP fluctuation and the probability of the average WIP exceeding its upper bound.A method based on the monotonicity of the objective functions is developed to solve such a bi-objective optimization problem.Numerical experiments indicate that the solution of robust capacity planning has stronger robustness against uncertain WLTP.The main contributions of this research include:(1)An IPCCP model is proposed for a single-product-type,multi-parallel-machine and multi-stage serial production line.In order to evaluate the average production cost,we developed a new decomposition-based method for such a system based on the method of calculating its steady state probability distribution.(2)An IPCCP model is proposed for a multi-product-type,multi-parallel-machine and multi-stage manufacturing system.Firstly,we develop an uniform steady state marginal probability distribution of the two-product-type,multi-parallel-machine and one-stage manufacturing system,and extend this marginal probability distribution to a multi-product-type,multi-parallel-machine and multi-stage manufacturing system so as to evaluate its production cost;(3)An IPCCP model is proposed for a multi-stage assembly system.By aggregating the state space,we propose a concept of generalized two-dimensional state space.Furthermore,the method of calculating marginal steady state probability distribution of the multi-stage assembly system is proposed based on the concept of generalized two-dimensional state space,which can be used to evaluate the production cost.(4)For a semiconductor manufacturing system,we propose the uncertain WLTP to describe the change of the wafer processing routes,also develop the robust capacity planning model based on open queuing network so as to optimize the vehicle quantities.The mathematical model,analysis method and algorithm are developed for the IPCCP problems of four typical manufacturing systems,which are helpful for them to achieve their best production performance at a minimum investment on machines,and to resist the negative impact of uncertainties.The results of this research provide a good guidance to reducing the investment on machines and decreasing the production cost for real-world manufacturing systems.