Modelling and scheduling of an asynchronous cyclic production line with multiple parts
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Modelling and scheduling of an asynchronous cyclic production line with multiple parts B Tan and S Karabati* KocË University, Istanbul In this study, we model and analyse a production line with asynchronous part transfers, processing time variability, and cyclic scheduling in the same framework. We consider a production line with multiple parts and ®nite interstation buffers. The line produces a batch of n jobs repetitively using the same order of jobs in every batch. The processing time of a job on a station is a random variable and is assumed to have a phase-type distribution. Parts are transferred between the stations in an asynchronous manner. We ®rst present a continuous time Markov chain model to analyse the performance of this system for a given sequence. A state-space representation of the model and the associated rate matrix are generated automatically. The steady state probabilities of the Markov chain are determined by using a recursive method that exploits the special structure of the rate matrix. The cycle time, the production rate, and the expected Work-In-Progress (WIP) inventory are used as the main performance measures. We then present an approximate procedure to determine the cyclic sequence that minimises the cycle time. We then investigate the effects of operating decisions, system structure, processing time variability, and their interaction in the same framework. Numerical results for the performance evaluation and scheduling of cyclic production lines are also presented. Keywords: cyclic scheduling; stochastic scheduling; asynchronous production lines; Markov chain; manufacturing systems
Introduction The success of a manufacturing process is largely determined by its ability to support the manufacturing task, which is formulated with the objective of meeting the requirements of the marketplace. The demand of the marketplace for more ¯exibility has changed manufacturing practices. The emphasis of JIT on increasing delivery speed and reliability, and reducing setup times has paved the way for the development of new design and operational policies for the management of manufacturing systems. The production line concept has been re-de®ned to better support the manufacturing task under increasing product variety and decreasing volumes. The simultaneous manufacturing of a mix of products has become a primary objective in the management of medium to high volume production lines. In this paper, we consider an asynchronous production line which is operated under a cyclic scheduling policy. Cyclic scheduling policies have proved to be very effective in repetitive manufacturing environments within the JIT context.1 In this approach, the minimal product set, that is, the smallest product set having the same product mix ratio with the forecasted demand for various items, or a multiple of it, is cyclically produced. Therefore, for an effective implementation of the cyclic *Correspondence: Dr S Ka
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