By T. Aized

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M Mi-1 Bi-1 Mi Bi Mi+1 ... M Bn Fig. 3. The flexible manufacturing cell line The parts enter the first machine and they are processed and transported to the succeeding components, until they finally leave the system. The machines produce at different rates, fail, and are repaired randomly, thus causing changes in the flow of parts. The changes propagate to neighboring machines and may render them starved or blocked. Buffers of finite capacity are inserted in order to reduce these effects. The operation of the production line is ruled by the following: a) The line consists of N+1 buffers.

We notice that once a piece is blocked from cell entry, the conveyor does not stop service; instead it proceeds with its operation to the other pieces waiting for transport. At the system level, we assume that the cells are functionally equivalent, so that each cell can provide the necessary processing for a piece. Hence, one cell is sufficient to maintain production (at a reduced throughput). We say that the manufacturing system is available (or, operational) if the conveyor and at least one of the cells are available.

Although the buffer Bi has enough parts for the transient period T1i, because machine Mi+1 produces faster than Mi (see Fig. ), or the delay time T1i is too long, finally Bi becomes empty. Discrete event models for flexible manufacturing cells T2i Pi+1-1 2 ... 1 23 Pi+1 Mi+1 starved 1 ... Ni Mi t TA T1i T’1i Fig. 2. Buffer - empty event The situation depicted in Fig. 2. is encountered when: (pri < pri+1)  [pri+1 (Ti1 - T2i) > BL(i)] (14) The inter-departure interval of Mi+1 just before the occurrence of the empty buffer event satisfies the following: 0  Ti'1  1 1  pri pri 1 (15) Pi+1 - Ni = BL(i) + 1 (16) Pi+1 = 1 + (TA - t - T2i).

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