Study On Continuous Modeling And Optimization For Re-entrant Manufacturing System

The re-entrant manufacturing system is a multi-stage kind of manufacturing system in which the job routing is such that a part may returns to the same work station for one or more times. Different from the general manufacturing system's rework, this kind of re-entrant is the requirement of product processing technology, and the quantity of the re-entrant parts and its frequency are much higher. So the parts in different stage should compete for the same equipment, which increases the fluctuations of processing load and the difficulty to forecast the parts'arrival time.The typical example of re-entrant system is the semiconductor manufacturing system, while Mini-Fab model is the most commonly used study case.Firstly, the semiconductor manufacturing process is introduced to specify the features of re-entrant system. Then the traditional modeling methods for re-entrant system are enumerated as well as their disadvantages and difficulty during the modeling. Because the continuous model runs much more quickly and the time for calculation is not affected by the scale of the system, continuous modeling method is much superior to traditional methods when applying to re-entrant system. But most of the researches in this field are focus on large-scale re-entrant system with single production.Secondly, a generic continuous model of single-product re-entrant manufacturing systems is elaborated, which is solved by finite difference method. By comparing with ExtendSim simulation model, this paper proves that the generic continuous model does not suit for the small-scale re-entrant system. So a concept called re-entrant factor is introduced to revise the model, in which the influences of degree of re-entrant are considered. Based on the revised continuous model, the variation of production's throughput and WIP are studied under different influx, and the reverse throughput at the discontinuity point is explained.Thirdly, based on the revised continuous model, the demand control problem is proposed, in which the optimized influx is obtain to minimize the difference between outflux and demand. This model is a nonlinear optimization with a constraint condition in the form of PDE. To solve it, adjoint method is used to calculate the gradient of the cost function, and nonlinear conjugate gradient method is applied to work out the optimized results. Besides, the optimized influxs for staircase demand, linear demand and periodic demand are analyzed, through which the lead time for changing the influx and its fluctuation are studied.Finally, the single-product continuous model is extended to a continuous model for multi-product re-entrant manufacturing systems in which the product priority is considered. The model's validation is proved by the same method as the single-product model. Based on the multi-product continuous model, how the influx of product with different priority impact on the throughput of all products in the system is studied.