Pii: S0893-9659(97)00124-9

Keywords--Manufactur ing system, Steady state distribution, Preconditioner conjugate gradient method. 1. I N T R O D U C T I O N In this paper, we s tudy a two-station manufacturing system. The system consists of two reliable machines (one in each station) producing one type of product. Each product has to go through the manufacturing processes in the two stations before it is finished. The processing t imes for one unit of product in the first and second machines are exponentially distributed with parameters 1/#1 and 1/#2, respectively. We assume the first machine has infinite supply of raw material. A buffer B1 of size bl is placed between the two machines to store the products which are finished by the first machine and waiting for further operations by the second machine. Finished products are put in a buffer B2 of maximum size b2. The interarrival t ime of a demand is assumed to be exponentially distributed with parameter 1/A. Finite backlog is allowed in the system. The maximum allowable backlog of product is m. When the inventory level of the finished product is m , any arrival demand will be rejected. Hedge point policy is employed as the inventory control in both buffers B1 and B2. I t is well known tha t the hedging point policy is optimal for one machine (one station) manufacturing systems in some simple situations; see [1], for instance. When the optimal policy is a zero-inventory policy (i.e., the hedging point is zero), then the policy matches with the just-in-time (JIT) policy. The J IT policies have been strongly favored in reallife production systems for process discipline reasons even when they are not optimal. By using the J I T policy, the Toyota company can manage to reduce work-in-process and cycle time. We focus ourselves in hedging point policies for our manufacturing systems. Usually, proper positive inventory level is maintained to hedge against the uncertainties in supply and demand. The hedging point policy is characterized by an integer number h. The machine keeps on producing Research supported by HKRGC, Grant CUHK 489/95E, and by the Hong Kong Croucher Foundation. Typeset by AA/~S-TEX