【正文】
ircumstances than the linear layout. In this paper, we first consider the Ushaped production line with just one multifunction worker. We analyze his waiting time and the cycle time. Then we consider the overall cycle time of the Ushaped line with more than one multifunction worker, which is the maximum of the cycle times of all workers. It is noted that its reciprocal gives the throughput, or the production rate of finished products. Moreover, we consider an optimal worker allocation problem that minimizes the overall cycle time. In Section 2, we explain the Ushaped production line with a single worker, and analyze his waiting time and the cycle time of this line, when the operation, walking and processing times are constants. We show that the nth cycle time bees constant for n 2, and that after several cycles the worker waits for the pletion of processing of at most one specified machine. Recently, Miltenberg and Wijngaard [2] considered the line balancing problem of the Ushaped line with constant operation times, no waiting times and no walking times. They discussed the optimal machine allocation problem to workers (which they called stations)under the constraints on the orders of machines in which the items are processed, like the assembly line balancing problems (Baybars [I], for example). In the Ushaped line, however, the walking times should be taken into account to derive the exact cycle time. In addition, it is possible for the worker to wait for the end of processing at a machine for an allocation,because the time interval from departure to next arrival of the worker at the machine may exceed the processing time at the machine. Therefore, the problem which they discussed does not represent the real features of the Ushaped line. In Section 3, we consider a production line with I workers and K machines, and derive the overall cycle time of this line under a given allocation of workers to machines. Then we discuss the optimal worker allocation problem that minimizes the overall cycle time of this line. It is shown that the problem can be formulated into a binatorial optimization problem. We examine the optimal worker allocation problem with one or two workers in a production line with K machines placed at the same distance. This will reveal advantages of the Ushaped layout over the linear layout. We can further reduce an overall cycle time by admitting what Toyota calls mutual relief movement ([3], ). This means that a worker who has finished his own operations in one cycle helps another adjacent worker. This, however, is not taken into account in this paper, because the problem bees more plicated. If multiple kinds of items are processed in this line, the processing times and operation times are not constant. In addition, the operation and walking times of the worker may fluctua