U形生产线的分析与优化外文翻译

U形生产线的分析与优化外文翻译 ANALYSIS AND OPTIMIZATION OF A U-SHAPED PRODUCTION LINEKatsuhisa Ohno Koichi NakadeNagoya Institute of TechnologyReceived August 21 1995 Revised January 16 1996Abstract In the just-in-time context parts are often processed by a single-unitproduction and conveyance system called quotzkko-nagash in Japanese withoutconveyors. The U-shaped layout in which each multifunction worker takes charge ofseveral machines has been introduced as an implementation of this concept. Presentlythe layout is gaining an increasing popularity due to the low running cost . In this paper first we deal with the U-shaped production line with a singlemulti-function worker. We derive his waiting time and a cycle time of the line whenprocessing times of items operation times and his walking times between machinesare constants. Then we deal with a U-shaped production line with multiple workers. Wederive the overall cycle time of this line and consider an optimal worker allocationproblem that minimizes the overall cycle time when the number of workers is given. Inparticular it is shown that the U-shaped layout is superior to the linear layout for lineswith one or two workers. We also discuss the case where those processing operationand walking times are stochastic.1. Introduction In a conveyor system for mass production as in the Ford system each stationprocessesjust one item in one cycle time where the cycle time is the time-intervalbetween two successive outputs. The sums of necessary operation and processing timesare intended to be equal among the stations the items are processed synchronouslyamong the stations and there exist no items between adjacent stations. In the just-in-time JIT production system the above concept which is called asingleunit production and conveyance quotikko-nagashiquot in Japanese is applied to aproduction line without conveyors which manufactures different kinds of relativelysmall parts Monden 3 p.107. To achieve this at a low production cost a U-shapedlayout is used with multifunction workers. The U-shaped production line with threeworkers and ten machines is shown in Figure 1. When the entrance and exit of items arenear as shown in Figure 1 we call this layout a U-shaped layout and if the same workerhandles both machines at the entrance and exit in the U-shaped layout then we call thislayout a U-shaped production line. The multifunction worker takes charge of multiple machines and visits each of themounce in one cycle. When he arrives at one of these machines he waits for the end ofprocessing of the preceding item if it is not completed and then operates the items andwalks to the next machine. The operation consists of detaching the processed item fromthe machine putting it on a chute to roll in front of the next machine attaching the newitem to the machine and switching it on. The cycle time of the worker is thetime-interval between his consecutive arrivals at his first machine and consists of thewaiting times for the end of processing operation times and walking times betweenmachines.In the JIT production system two kinds of Kanbans that is a production ordering and awithdrawal Kanbans are used as tools to control production and withdrawal quantitiesineach production line. In the U-shaped line the same worker inputs a new item andoutputs a completed product. Consequently he can observe changes of two kinds ofKanbans and respond to them promptly. Since a new item enters the system only afterone completed product exits the work-in-process in the system is always constant.Further there exist more possible allocations of the workers to machines than in thelinear layout. Therefore when the demand changes we can more appropriatelyreallocate the workers to machines so that the cycle times of workers are balanced. Thatis the U-shaped layout can be more properly adapted to the changes of thecircumstances than the linear layout. In this paper we first consider the U-shaped production line with just onemulti-function worker. We analyze his waiting time and the cycle time. Then weconsider the overall cycle time of the U-shaped line with more than one multi-functionworker which is the maximum of the cycle times of all workers. It is noted that itsreciprocal gives the throughput or the production rate of finished products. Moreoverwe consider an optimal worker allocation problem that minimizes the overall ycletime. In Section 2 we explain the U-shaped production line with a single worker c andanalyze his waiting time and the cycle time of this line when the operation walkingand processing times are constants. We show that the n-th cycle time becomes constantfor n gt 2 and that after several cycles the worker waits for the completion of processingof at most one specified machine. Recently Miltenberg and Wijngaard 2 considered the line balancing problem oftheU-shaped line with constant operation times no waiting times and no walking times.They discussed the optimal machine allocation problem to workers which they calledstationsunder the constraints on the orders of machines in which the items areprocessed like the assembly line balancing problems Baybars I for example. In theU-shaped line however the walking times should be taken into account to derive theexact cycle time. In addition it is possible for the worker to wait for the end ofprocessing at a machine for an allocationbecause the time interval from departure tonext arrival of the worker at the machine may exceed the processing time at themachine. Therefore the problem which they discussed does not represent the realfeatures of the U-shaped line. In Section 3 we consider a production line with Iworkers and K machines and derive the overall cycle time of this line under a givenallocation of workers to machines. Then we discuss the optimal worker allocationproblem that minimizes the overall cycle time of this line. It is shown that the problemcan be formulated into a combinatorial optimization problem. We examine the optimalworker allocation problem with one or two workers in a production line with Kmachines placed at the same distance. This will reveal advantages of the U-shapedlayout over the linear layout. We can further reduce an overall cycle time by admitting what Toyota calls mutualrelief movement 3 p.114. This means that a worker who has finished his ownoperations in one cycle helps another adjacent worker. This however is not taken intoaccount in this paper because the problem becomes more complicated. If multiple kinds of items are processed in this line the processing times andoperation times are not constant. In addition the operation and walking times of theworker may fluctuate because of his weariness and learning effect. In Section 4 wedeal with the case where the processes of operation walking and processing times arestochastic. In particular we discuss the case where the sequences of random variablesin these processes are independent and identically distributed and there is a bottleneckmachine such that the sum of processing and operation times of this machine is largerthan that of any other machine with probability one. It can be shown that the workerwaits for the completion of processing at the bottleneck machine in all cycles.2. Cycle and Waiting Times of a Multi-Function WorkerIn this section we consider the U-shaped production line with a single multi-functionworker which is shown in Figure 2. The worker handles machines 1 through K. Thefacility has enough raw material in front of machine 1. The material is processed atmachines 12. . . 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 thepreceding item is completed then he removes it from machine k sends it to machine k 1 attaches the present item to machine k and switches it on. After the operation atmachine k he walks to machine k 1. If the preceding item is still in process at hisarrival 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 eachmachine which has been already processed at this machine. That is in the first cyclethe worker operates without waiting at all machines. In this and next sections weassume that the processing operation and walking times are constants at each machine.This assumption is satisfied when one kind of products are produced and the worker iswell experienced in the operation. We use the following notations: for k?K and n?Z l 2 . . .ik: the processing time at machine ksk: the operation time of the worker at machine krk: the walking time from machine k to machine k l K to l if k KWkn: the waiting time of the worker at machine k in the n-th cycleCn: the n-th cycle timea ? b maxa b a ?b mina b a max0a .Figure 3 illustrates the behavior of the worker and the above defined variables. Theinitial condition implies thatConsider the n-th cycle time for n gt 2. If the worker does not wait at any machinethen thecycle time is simply the sum of all operation and walking times. Since oneitem is processed and operated at each machine in one cycle the cycle time must begreater than or equal to the maximum of the sums of the processing and operationtimes among all the machines. If the worker starts from the machine with themaximum sum then the cycle time will be equal to the maximum of the maximumsum and the sum of all operation and walking times. That is the cycle time will begiven byand then the total waiting time of the worker in one cycle is given byIn the following we derive the n-th waiting time at machine k for all k E K and n E-Eand show that 2 and 3 hold in the n-th cycle for all n ?2. In the n - l-th cyclewhere n gt 2 when the worker finishes the operation at machine k and starts walkingto machine k 1 machine k begins the processing of the n - l-th item. When hereturns to machine k in the n-th cycle if the machine completes the n - l-thprocessing then he begins the operation for the n-th item without waiting. If the n -l-th item is still in process at his return then he waits for its completion. Figure 3shows that the time from the n - l-th departure to the n-th arrival of the worker atmachine k is given bySince the waiting time at machine k is the time difference between the processing timeand the interarrival time it holds that for n ?2翻 译:题目:U 形生产线的分析与优化摘要: 在准时制中，零件往往由一个单一生产 和运送系统(在日本称为quotikko-nagashi”)进行处理，却没有运输。每名配套的工 作者负责几个机器的 U 型布局，体现了作为这个概念的实施。这种布局目前赢得 的增长声望归功于低运行费用.。在本文中，我们首先处理一个单一的多功能工人的 U 型生产线。我们汲取她的等待时间，产品生产时间，操作时间，在机器之间走动 的时间为常量，然后，我们处理有一个有很多工人的 U 形生产线。我们得出这系 列的整体周期时间，并考虑在工人人数确定时使加工周期最小的工人分配问题。最 佳的工作分配问题职工人数时，最大限度地减少整体周期时间。特别是，它表明， U 形布局，是优于线与一个或两个工人的线性布局。我们还讨论了加工，操作以及 走路的时间是随机的情况。介绍 在大规模生产的福特系统的运输系统中， 每个站 点流程的输送系统在一个周期的时间只有一种物品， 这里的周期时间为两个时间连 续输出之间的间隔。 在不同站点之间操作时间加工时间的总和都应该趋于相等这些 物品是在站点中同步处理的 且相邻站之间不存在物品。 在准时制(JIT)生产系统， 上述的概念，被称为单机生产和输送(在日本称为“IKKO-nagashi，) ”，被应用到 没有运输带的生产线中，那种输送带是用来生产多种相对较小的产品的(Modem3，第 107 页) 。为了低生产成本实现这个，一个 U 形布局使用多功能工人。三个工人和 10 台机器的 U 形生产线如图 1 所示。当物品的入口和出口相近如图 1 所示，我们称此布局的一个 U 形布局，如果同一个的工人在 U 形布局的入口和出口操作两台机器，那么我们称这种布局的 U 形生产线。 多功能职工负责多台机器，且在一个周期中会检查每一台机器。当他到达其中一台机器如果生产没完成，他将等待物品的最后加工。然后操作物品走到下一个机器。分离的操作包括从机器上分离物品，将它们放置在一个降落伞滚下到一个机器的前端连接新的项目机器和切换。周期时间是职工连续到达他的第一个机器的时间间隔，由过程结束的等待时间，操作时间和在机器减走动的时间构成。 在准时制生产系统中两种看板就是一个生产排序看板和取货看板，被用作工具的数量控制每个生产线的生产和撤销。在 U 形线，同一个工人投入一个新项目，并输出一个完整的产品。因此，他可以观察到两种看板的变化，迅速作出反应。从新项目进入系统，只有在一个产品生产完成，否则在系统的工作进程中始终不变。进一步说，相比现行生产布局，U型布局，机器可能分配到更多的工人。因此，当需求变化时，我们可以更适当地重新分配工人到机器，从而工人的周期时间是平衡的。也就是说，U 型布局可以比线性布局更适应情况的变化。 在本文中我们首先考虑只一个多功能工人 U 形生产线。我们分析他的等待时间和周期时间。然后我们考虑有超过一个多功能工人的 U 形线的周期时间这是最大的包括所有工人的周期时间。它指出其相互给予的生产量，或完成后的成品率。此外我们寻求一个最优的职工分配问题 最大限度地减少整体周期时间。 第 2 章中，我们解释一个工人的 U 形生产线，并分析他等待时间和周期时间，这条线的操作时间，步行时间和处理时间是常数。我们证明了 n 个周期的时间成为常数 ngt 2 时，几个周期后，工人等待一个加工完成 的时间不超过一个机器。 最近Miltenberg 和 Wijngaard2的基础上考虑了在作业时间不变的前提下生产线平衡问题 没有等待的时间以及没有步行时间。他们讨论了在约束条件下工作的工人(他们成为站点)操作的生产物品的机器的机械优化配置问题，像装配线平衡问题BaybarsI例如。在 u 形线然而步行时间应该在获得精确的周期时间是被考虑。此外工人可能在一个分配的机器等待过程结束因为工人从离开到到达下一个机器的时间间隔可能超过在这台机器的处理时间。因此他们讨论的问题不代表真正的特点的 u 形线。在第三章中我们考虑一个生产线有 I 个工人和 K 机器并推导出在特定的机器配置工人时整个周期时间。然后讨论了最优的工人分配问题是周期时间最小。 结果表明问题是可以制定成一个组合优化问题。我们检测有一个或两个工人在一条生产线上和 K 机器放置在同样距离的优化职工分配问题。这将揭示 u 形的优点超过线性布局。图 1.U 形生产线我们可以进一步降低整体周期时间通过接纳丰田所谓的相互救济运动(3，第 114 页) 。这意味着，一个完成自己一个周期里的业务工人，帮助相邻的另一工人。然而，这不考虑在这章，因为这个问题变得更加复杂。 如果多种物品在一个生产线中加工，处理时间和操作时间不固定。此外，工人的操作和步行时间波动，因为他的厌战情绪和学习效果。第 4 章中，我们处理操作过程中的情况，步行和处理时间是随机的。特别是，我们讨论在这些过程中的随机变量序列独立同分布，且有一个瓶颈机器的操作时间和加工时间的和等是大于任何其他机的概率的情况。它可以表明，工人等待瓶颈机器的处理完成出现在所有周期。2.一个多功能的工人的 周期和等待时间 在本节中，我们考虑用一个单一的多功能 U 形生产线工人， 在图 2 所示。工人处理 1-K的机器。在机器 1 之前有足够的原料材料。材料 J 按顺序从 12， 。 。 ，K 加工，并离 。开系统后成为一个成品。让 k 1， 。 。 ，K。当工人到达机器 k?K 时，如果处理前 。面的项完成，然后他从机器 K 删除它，把它发送到机 K1，附加现在的项目到机器 K 和切换。在机器 K 的运作后，他走到机器 K1。如果在他的到来时机器还在运作，那么他就等待知道处理结束。 假定初始条件时间 0 时，每台机器上有一个项目，已经机器上处理。也就是说，在第一个周期的工人无需等待机器就可以进行操作。在这章以及接下来的章节中，我们假设，每一台机器的加工，操作和步行的时间是常数。这个假设在是当一种产品被生产以及工人很有经验的时候可以被满足的。我们用下面的符号: ?K 和的 E?Z 1，2， 。 。IK:在 。机 K 的处理时间，SK:在机 K 工人的工作时间，RK:步行时间从机器 K 到机器 K1(K 到l，如果 k K) K(n) ，W :工人第 n 周期在机器 K 等待时间，图 2.U 型生产线与一个工人C(n) 个周期的时间， :na 3 显示了工人的行为和上述定义的变? b maxa b a ? b mina b a max0a.图 量。 初始条件意味着考虑第 n 个周期的时间为 n?2。如果工人在任何一台机器不等待，然后周期时间仅仅是所有操作和步行时间的总和。由于一个项目在每一个周期的每一台机器上被处理和运行，周期时间必须大于或等于在所有的机器加工和操作时间的总和。如果工人从的最大总和的机器开始，那么周期时间等于最大总和当中的最大值，而这个总和等于操作时间和行走时间的和。也就是说，周期时间就可以得出了然后在一个周期内工人的总等待时间为.