Математическое моделирование процессов выполнения пакетов заданий в конвейерных системах с промежуточными буферами ограниченных размеров

Modern methods of process planning in conveyor systems with buffers of a certain size between processing devices allow optimizing schedules for single tasks or fixed task packages with a limited number of them and a limited number of devices. The use of mathematical models of the processes of performing single tasks (task packages) used by these methods in optimizing the composition of packages and schedules for their execution in systems with an arbitrary number of packages and devices is impossible. At the same time, mathematical models of the processes of executing task packages in conveyor systems in the presence of buffers of limited sizes between devices are the basis for the development of methods for optimizing their (package) compositions and schedules for the implementation of actions with them on the devices of conveyor systems. In this regard, the article develops mathematical models of multi-stage processes of performing an arbitrary number of task packages in conveyor systems in the presence of intermediate buffers of limited sizes for two and three devices, as well as for an arbitrary number of devices. The use of these models makes it possible to determine the time points of the start of the execution of task packages on the devices of conveyor systems, taking into account the limited size of intermediate buffers, as well as the duration of time intervals for the use of these resources and the efficiency of their use over time. An algorithm has also been developed for mathematical modeling of the processes of executing task packages in conveyor systems in the presence of intermediate buffers of limited size, which calculates the time characteristics of these processes based on a given order of implementation of actions with task packages on the devices of conveyor systems. An application has been developed that implements synthesized mathematical models of the processes of executing task packages in conveyor systems with intermediate buffers of limited sizes and an appropriate method for modeling these processes. Versatile testing of the developed application has shown that the obtained mathematical models and the modeling method adequately describe the course of multi-stage processes of task packages in pipeline systems, set using different values of their (processes) parameters.Современные методы планирования процессов в конвейерных системах с буферами определенного размера между обрабатывающими приборами позволяют оптимизировать расписания выполнения единичных заданий либо фиксированных пакетов заданий при их ограниченном количестве и ограниченном количестве приборов. Применение математических моделей процессов выполнения единичных заданий (пакетов заданий), используемых этими методами, при оптимизации составов пакетов и расписаний их выполнения в системах с произвольным количеством пакетов и приборов является невозможным. В то же время математические модели процессов выполнения пакетов заданий в конвейерных системах при наличии буферов ограниченных размеров между приборами являются основой для разработки методов оптимизации их (пакетов) составов и расписаний реализации действий с ними на приборах конвейерных систем. В связи с этим в статье разработаны математические модели многостадийных процессов выполнения произвольного количества пакетов заданий в конвейерных системах при наличии промежуточных буферов ограниченных размеров для двух и трех приборов, а также для произвольного количества приборов. Использование этих моделей позволяет определять моменты времени начала выполнения пакетов заданий на приборах конвейерных систем с учетом ограниченных размеров промежуточных буферов, а также длительности интервалов времени использования этих ресурсов и эффективность их использования в течение времени. Также разработан алгоритм математического моделирования процессов выполнения пакетов заданий в конвейерных системах при наличии промежуточных буферов ограниченных размеров, осуществляющий на основе заданного порядка реализации действий с пакетами заданий на приборах конвейерных систем вычисление временных характеристик этих процессов. Осуществлена разработка приложения, реализующего синтезированные математические модели процессов выполнения пакетов заданий в конвейерных системах с промежуточными буферами ограниченных размеров и соответствующий метод моделирования этих процессов. Разностороннее тестирование разработанного приложения показало, что полученные математические модели и метод моделирования адекватно описывают ход многостадийных процессов выполнения пакетов заданий в конвейерных системах, задаваемый с использованием различных значений их (процессов) параметров

Development and Simulation Assessment of Semiconductor Production System Enhancements for Fast Cycle Times

Long cycle times in semiconductor manufacturing represent an increasing challenge for the industry and lead to a growing need of break-through approaches to reduce it. Small lot sizes and the conversion of batch processes to mini-batch or single-wafer processes are widely regarded as a promising means for a step-wise cycle time reduction. Our analysis with discrete-event simulation and queueing theory shows that small lot size and the replacement of batch tools with mini-batch or single wafer tools are beneficial but lot size reduction lacks persuasive effectiveness if reduced by more than half. Because the results are not completely convincing, we develop a new semiconductor tool type that further reduces cycle time by lot streaming leveraging the lot size reduction efforts. We show that this combined approach can lead to a cycle time reduction of more than 80%

Considering stockers in reentrant hybrid flow shop scheduling with limited buffer capacity

Diversification of products has increased the involvement of reentrant manufacturing processes, in which a job returns multiple times to a machine at the preceding workflow stage to continue the manufacturing process. Reentrant flow shop manufacturing can substantially improve manufacturing efficiency when scheduled properly. In practice, advanced manufacturing companies (e.g., semiconductor foundries) have introduced automated material handling system (AMHS), including stockers that serve as centralized inventory buffer space for temporarily storing the inventories owing to limited buffer capacity of each machine. However, no previous studies on reentrant flow shop scheduling have considered the impact of limited buffer capacity or stockers on scheduling efficiency. Consequently, this study investigated the application of stockers in solving the reentrant hybrid flow shop scheduling problem with limited buffer capacity. With the objective of optimizing the makespan and mean flowtime of a schedule, this problem is NP-hard because it generalizes the flow shop problem. Therefore, this study developed a hybrid harmony search and genetic algorithm (HHSGA) for the problem, in which limited buffer capacity and stockers cause solution decoding to be non-trivial. Experimental comparison on scheduling problems with different numbers of jobs showed that the HHSGA performed better than conventional algorithms. Moreover, among three manufacturing conditions (i.e., with buffers and stockers, with buffers only, and with stockers only), the results indicated that the condition using inventory buffers and stockers was more beneficial