1、外文原文：http:/ AND OPTIMIZATION OF A U-SHAPED PRODUCTION LINE Katsuhisa Ohno Koichi Nakade Nagoya Institute of Technology (Received August 21, 1995； Revised January 16, 1996) Abstract In the just-in-time context, parts are often processed by a single-unit production and conveyance system (
2、called "zkko-nagash? in Japanese) without conveyors. The U-shaped layout, in which each multifunction worker takes charge of several machines, has been introduced as an implementation of this concept. Presently the layout is gaining an increasing popularity due to the low running cost . In this
3、 paper, first we deal with the U-shaped production line with a single multi-function worker. We derive his waiting time and a cycle time of the line when processing times of items, operation times, and his walking times between machines are constants. Then we deal with a U-shaped production line wit
4、h multiple workers. We derive the overall cycle time of this line, and consider an optimal worker allocation problem that minimizes the overall cycle time when the number of workers is given. In particular, it is shown that the U-shaped layout is superior to the linear layout for lines with one or t
5、wo workers. We also discuss the case where those processing, operation and walking times are stochastic. 1. Introduction In a conveyor system for mass production as in the Ford system, each station processesjust one item in one cycle time, where the cycle time is the time-interval betw
6、een two successive outputs. The sums of necessary operation and processing times are intended to be equal among the stations, the items are processed synchronously among the stations, and there exist no items between adjacent stations. In the just-in-time (JIT) production system, the above concept,
7、which is called a singleunit production and conveyance ("ikko-nagashi," in Japanese), is applied to a production line without conveyors which manufactures different kinds of relatively small parts (Monden 3, p.107). To achieve this at a low production cost, a U-shaped layout is used with m
8、ultifunction workers. The U-shaped production line with three workers and ten machines is shown in Figure 1. When the entrance and exit of items are near as shown in Figure 1, we call this layout a U-shaped layout, and if the same worker handles both machines at the entrance and exit in the U-shaped
9、 layout then we call this layout a U-shaped production line. The multifunction worker takes charge of multiple machines, and visits each of the mounce in one cycle. When he arrives at one of these machines, he waits for the end of processing of the preceding item if it is not completed, and then ope
10、rates the items and walks to the next machine. The operation consists of detaching the processed item from the machine, putting it on a chute to roll in front of the next machine, attaching the new item to the machine, and switching it on. The cycle time of the worker is the time-interval between hi
11、s consecutive arrivals at his first machine, and consists of the waiting times for the end of processing, operation times and walking times between machines. In the JIT production system, two kinds of Kanbans, that is, a production ordering and a withdrawal Kanbans are used as tools to control produ
12、ction and withdrawal quantities ineach production line. In the U-shaped line, the same worker inputs a new item and outputs a completed product. Consequently, he can observe changes of two kinds of Kanbans and respond to them promptly. Since a new item enters the system only after one completed prod
13、uct exits, the work-in-process in the system is always constant. Further, there exist more possible allocations of the workers to machines than in the linear layout. Therefore, when the demand changes we can more appropriately reallocate the workers to machines so that the cycle times of workers are
14、 balanced. That is, the U-shaped layout can be more properly adapted to the changes of the circumstances than the linear layout. In this paper, we first consider the U-shaped production line with just one multi-function worker. We analyze his waiting time and the cycle time. Then we co
15、nsider the overall cycle time of the U-shaped line with more than one multi-function 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 p
16、roblem that minimizes the overall cycle time. In Section 2, we explain the U-shaped 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 n-th cycle time becomes constant fo
17、r n > 2, and that after several cycles the worker waits for the completion of processing of at most one specified machine. Recently, Miltenberg and Wijngaard 2 considered the line balancing problem of the U-shaped line with constant operation times, no waiting times and no walking t
18、imes. 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 U-shaped line, however, the walking times sh
19、ould 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 mac
20、hine. Therefore, the problem which they discussed does not represent the real features of the U-shaped 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
21、optimal worker allocation problem that minimizes the overall cycle time of this line. It is shown that the problem can be formulated into a combinatorial optimization problem. We examine the optimal worker allocation problem with one or two workers in a production line with K machines placed at the
22、same distance. This will reveal advantages of the U-shaped layout over the linear layout. We can further reduce an overall cycle time by admitting what Toyota calls mutual relief movement (3, p.114). This means that a worker who has finished his own operations in one cycle helps another adjace
23、nt worker. This, however, is not taken into account in this paper, because the problem becomes more complicated. 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 fluc
24、tuate because of his weariness and learning effect. In Section 4, we deal with the case where the processes of operation, walking and processing times are stochastic. In particular, we discuss the case where the sequences of random variables in these processes are independent and identically distrib
25、uted and there is a bottleneck machine such that the sum of processing and operation times of this machine is larger than that of any other machine with probability one. It can be shown that the worker waits for the completion of processing at the bottleneck machine in all cycles. 2. Cycle and Waiti
26、ng Times of a Multi-Function Worker In this section we consider the U-shaped production line with a single multi-function worker, which is shown in Figure 2. The worker handles machines 1 through K. The facility has enough raw material in front of machine 1. The material is processed at machines 1,2
27、,. . . , K, sequentially, and departs from the system as a finished product. Let K = l,. . . , K.When the worker arrives at machine k K, if the processing of the preceding item is completed, then he removes it from machine k, sends it to machine k + 1, attaches the present item to machine k and swit
28、ches it on. After the operation at machine k, he walks to machine k + 1. If the preceding item is still in process at his arrival, then he waits for the end of the processing before the operation. It is assumed as an initial condition that at time 0, there is one item on each machine, which has been already processed at this machine. That is, in the first cycle the worker operates without waiting at all machines. In this and next sections, we
