REVERSIBILITY AND DEPENDENCE IN A U-SHAPED PRODUCTION LINE

We deal with a U-shaped production line with multiple machines and a m ultifunction worker. The worker visits machines in a cyclic fashion an d operates an item on each machine. The operation consists of detachin g the processed item from the machine, sending it to the next machine, putting the new item on the machine and switching it on. Walking time s of the worker and processing and operation times are i.i.d. random v ariables for each machine. We show that the sum of the first n cycle t imes is stochastically the same as that in the reversed system where m achines are arranged in the reversed order. We give examples where the distributions of waiting and cycle times depend on the machines, call ed starting ones, where the worker begins operation at time 0. A suffi cient condition is derived under which the limiting expected waiting a nd cycle times do not depend on the starting machines.