1、附录附录1:英文文献Line Balancing in the Real WorldAbstract: Line Balancing (LB) is a classic, well-researched Operations Research (OR) optimization problem of significant industrial importance. It is one of those problems where domain expertise does not help very much: whatever the number of years spent sol
2、ving it, one is each time facing an intractable problem with an astronomic number of possible solutions and no real guidance on how to solve it in the best way, unless one postulates that the old way is the best way .Here we explain an apparent paradox: although many algorithms have been proposed in
3、 the past, and despite the problems practical importance, just one commercially available LB software currently appears to be available for application in industries such as automotive. We speculate that this may be due to a misalignment between the academic LB problem addressed by OR, and the actua
4、l problem faced by the industry.Keyword: Line Balancing, Assembly lines, OptimizationLine Balancing in the Real WorldEmanuel FalkenauerOptimal DesignAv. Jeanne 19A bote2, B-1050 Brussels, Belgium+32 (0)2 646 10 741 IntroductionAssembly Line Balancing, or simply Line Balancing (LB), is the problem of
5、 assigning operations to workstations along an assembly line, in such a way that the assignment be optimal in some sense. Ever since Henry Fords introduction of assembly lines, LB has been an optimization problem of significant industrial importance: the efficiency difference between an optimal and
6、a sub-optimal assignment can yield economies (or waste) reaching millions of dollars per year. LB is a classic Operations Research (OR) optimization problem, having been tackled by OR over several decades. Many algorithms have been proposed for the problem. Yet despite the practical importance of th
7、e problem, and the OR efforts that have been made to tackle it, little commercially available software is available to help industry in optimizing their lines. In fact, according to a recent survey by Becker and Scholl (), there appear to be currently just two commercially available packages featuri
8、ng both a state of the art optimization algorithm and a user-friendly interface for data management. Furthermore, one of those packages appears to handle only the “clean” formulation of the problem (Simple Assembly Line Balancing Problem, or SALBP), which leaves only one package available for indust
9、ries such as automotive. This situation appears to be paradoxical, or at least unexpected: given the huge economies LB can generate, one would expect several software packages vying to grab a part of those economies. It appears that the gap between the available OR results and their dissemination in
10、 Todays industry, is probably due to a misalignment between the academic LB problem addressed by most of the OR approaches, and the actual problem being faced by the industry. LB is a difficult optimization problem even its simplest forms are NP-hard see Garry and Johnson, 1979), so the approach tak
11、en by OR has typically been to simplify it, in order to bring it to a level of complexity amenable to OR tools. While this is a perfectly valid approach in general, in the particular case of LB it led some definitions of the problem hat ignore many aspects of the real-world problem. Unfortunately, m
12、any of the aspects that have been left out in the OR approach are in fact crucial to industries such as automotive, in the sense that any solution ignoring (violating) those aspects becomes unusable in the industry.In the sequel, we first briefly recall classic OR definitions of LB, and then review
13、how the actual line balancing problem faced by the industry differs from them, and why a solution to the classic OR problem maybe unusable in some industries.2 OR Definitions of LBThe classic OR definition of the line balancing problem, dubbed SALBP (Simple Assembly Line Balancing Problem) by Becker
14、 and Scholl (), goes as follows. Given a set of tasks of various durations, a set of precedence constraints among the tasks, and a set of workstations, assign each task to exactly one workstation in such a way that no precedence constraint is violated and the assignment is optimal. The optimality cr
15、iterion gives rise to two variants of the problem: either a cycle time is given that cannot be exceeded by the sum of durations of all tasks assigned to any workstation and the number of workstations is to be minimized, or the number of workstations is fixed and the line cycle time, equal to the lar
16、gest sum of durations of task assigned to a workstation, is to be minimized.Although the SALBP only takes into account two constraints (the precedence constraints plus the cycle time, or the precedence constraints plus the number of workstations), it is by far the variant of line balancing that has
17、been the most researched. We have contributed to that effort in Falkenauer and Delchambre (1992), where we proposed a Grouping Genetic Algorithm approach that achieved some of the best performance in the field. The Grouping Genetic Algorithm technique itself was presented in detail in Falkenauer (19
18、98).However well researched, the SALBP is hardly applicable in industry, as we will see shortly. The fact has not escaped the attention of the OR researches, and Becker and Scholl () define many extensions to SALBP, yielding a common denomination GALBP (Generalized Assembly Line Balancing Problem).
19、Each of the extensions reported in their authoritative survey aims to handle an additional difficulty present in real-world line balancing. We have tackled one of those aspects in Falkenauer (1997), also by applying the Grouping Genetic Algorithm.The major problem with most of the approaches reporte
20、d by Becker and Scholl () is that they generalize the simple SALBP in just one or two directions. The real world line balancing, as faced in particular by the automotive industry, requires tackling many of those generalizations simultaneously.3 What Differs in the Real World?Although even the simple
21、 SALBP is NP-hard, it is far from capturing the true complexity of the problem in its real-world incarnations. On the other hand, small instances of the problem, even though they are difficult to solve to optimality, are a tricky target for line balancing software, because small instances of the pro
22、blem can be solved closet optimality by hand. That is however not the case in the automotive and related industries (Bus, truck, aircraft, heavy machinery, etc.), since those industries routinely feature Assembly lines with dozens or hundreds of workstations, and hundreds or thousands of Operations.
23、 Those industries are therefore the prime targets for line balancing software.Unfortunately, those same industries also need to take into account many of the GALBP extensions at the same time, which may explain why, despite the impressive OR Work done on line balancing; only one commercially availab
24、le software seems tube currently available for those industries.We identify below some of the additional difficulties (with respect to SALBP) that must be tackled in a line balancing tool, in order to be applicable in those industries.3.1 Do Not Balance but Re-balance Many of the OR approaches impli
25、citly assume that the problem to be solved involves a new, yet-to-be-built assembly line, possibly housed in a new, yet-to-be-built factory. To our opinion, this is the gravest oversimplification of the classic OR approach, for in practice, this is hardly ever the case. The vast majority of real-wor
26、ld line balancing tasks involve existing lines, housed in existing factories infect, the target line typically needs tube rebalanced rather than balanced, the need arising from changes in the product or the mix of models being assembled in the line, the assembly technology, the available workforce,
27、or the production targets. This has some far-reaching implications, outlined below.3.2 Workstations Have IdentitiesAs pointed out above, the vast majority of real-world line balancing tasks involves existing lines housed in existing factories. In practice, this seemingly “uninteresting” observation
28、has one far-reaching consequence, namely that each workstation in the line does have its own identity. This identity is not due to any “incapacity of abstraction” on part of the process engineers, but rather to the fact that the workstations are indeed not identical: each has its own space constrain
29、ts (e.g. a workstation below a low ceiling cannot elevate the car above the operators heads), its own heavy equipment that cannot be moved spare huge costs, its own capacity of certain supplies (e.g. compressed air), its own restrictions on the operations that can be carried out there (e.g. do not p
30、lace welding operations just beside the painting shop), etc.3.3 Cannot Eliminate Workstations Since workstations do have their identity (as observed above), it becomes obvious that a real-world LB tool cannot aim at eliminating workstations. Indeed, unless the eliminated workstations were all in the
31、 front of the line or its tail, their elimination would create gaping holes in the line, by virtue of the other workstations retaining of their identities, including their geographical positions in the workshop. Also, it softens the case that many workstations that could possibly be eliminated by th
32、e algorithm are in fact necessary because of zoning constraints.4 ConclusionsThe conclusions inspection 3 stems from our extensive contacts with automotive and related industries, and reflects their true needs. Other “exotic” constraints may apply in any given real-world assembly line, but line bala
33、ncing tool for those industries must be able to handle at least those aspects of the problem. This is very far from the “clean” academic SALBP, as well as most GALBP extensions reported by Becker and Scholl (). In fact, such a tool must simultaneously solve several-hard problems: Find a feasible def
34、ined replacement for all undefined (ANY) ergonomic constraints on workstations, i.e. One compatible with the ergonomic constraints and precedence constraints defined on operations, as well as zoning constraints and possible drifting operations Solve the within-workstation scheduling problem on all w
35、orkstations, for all products being assembled on the line Assign the operations to workstations to achieve the best average balance, while keeping the peak times at a manageable level. Clearly, the real-world line balancing problem described above is extremely difficult to solve. This is compounded
36、byte size of the problem encountered in the target industries, which routinely feature assembly lines with dozens or hundreds of workstations with multiple operators, and hundreds or thousands of operations.Weve identified a number of aspects of the line balancing problem that are vital in industrie
37、s such as automotive, yet that have been either neglected in the OR work on the problem, or handled separately from each other. According to our experience, a line balancing to applicable in those industries must be able to handle all of them simultaneously. That gives rise to an extremely complex o
38、ptimization problem. The complexity of the problem, and the need to solve it quickly, may explain why there appears to be just one commercially available software for solving it, namely outline by Optimal Design. More information on Outline, including its rich graphic user interface, is available at
39、 . References 1 Becker C. and Scholl, A. () A survey on problems and methods in generalized assemblyline balancing, European Journal of Operations Research, in press. Available online at :10.1016/j.ejor.07.023. Journal article. 2 Falkenauer, E. and Delchambre, A. (1992) Genetic Algorithm for Bin Pac
40、king and Line Balancing, Proceedings of the 1992 IEEE International Conference on Robotics and Automation, May10-15, 1992, Nice, France. IEEE Computer Society Press, Los Alamitos, CA. Pp. 1186-1192. Conference proceedings. 3 Falkenauer, E. (1997) A Grouping Genetic Algorithm for Line Balancing with
41、Resource Dependent Task Times, Proceedings of the Fourth International Conference on Neural Information Processing (ICONIP97), University of Otego, Dunedin, New Zealand, November 24-28, 1997. Pp. 464-468. Conference proceedings. 4 Falkenauer, E. (1998) Genetic Algorithms and Grouping Problems, John
42、Wiley& Sons, Chi Chester, UK. Book. 5 Gary. R. and Johnson D. S. (1979) Computers and Intractability - A Guide to the Theory of NP-completeness, W.H.Freeman Co., San Francisco, USA. Book.附录2:中文文献生产线平衡在现实世界摘要:生产线平衡(LB)是一种典型旳,精心研究旳明显工业重要性旳运筹学(OR)优化问题。这是其中一种所在领域旳专业知识并没有太大协助旳问题之一:无论花了多少年解决它,面对每一次棘手旳问题与也
43、许旳天文数字旳解决方案都并不是有关如何解决这个问题旳最佳措施,除非你假定老措施是最佳旳措施。在这里,我们解释一种明显旳悖论:虽然诸多算法已经被提出,在过去,尽管该问题旳实际重要性只是一种市场销售旳LB软件。目前似乎可用于工业,如汽车中旳应用。我们推测,这也许是由于在学术LB问题之间旳没有通过运筹学途径和生产业实际面对旳问题。核心词:生产线平衡,装配生产线,优化 生产线平衡在现实世界伊曼纽尔 福肯奈尔优化设计地址:珍妮大道19A,2道,B-1050布鲁塞尔,比利时+32(0)2 646 10 741 引言 装配线平衡,或者简称生产线平衡(LB),是一种操作工作站沿着装配线分派旳问题,在这样一种方
44、式,该分派是在某种意义上最优旳。自从亨利福特引进组装生产线, LB 已经成为影响工业重要性旳最优化问题:在效率不同旳最优和次优分派之间旳差别可以产生经济(或挥霍)达到数百万美元每年。 LB是一种典型旳运筹学(OR)旳优化问题,已通过被运筹学解决达以上几十年。许多算法已经被提出了去解决这个问题。尽管问题旳有实际重要性,并已经获得了或努力,但很少旳商业软件是可以协助行业优化其生产线。事实上,根据近来贝克尔和绍尔()旳一项调查显示,似乎有目前只有两个市场销售旳软件包有特色,即是最先进旳优化算法旳状态和数据管理旳顾客和谐旳界面。此外,这些软件包,似乎只解决“干净”旳提法旳问题(简朴装配线平衡问题,或S
45、ALBP),这让只有一种软件包可用于工业,如汽车业。这种状况似乎是自相矛盾旳,或者至少是意想不到旳:给定旳LB可以产生旳巨大经济,人们可以所盼望旳几种软件包争先恐后地抓住这些经济体旳一部分。 看来,既有旳运筹学成果以及它们在传播之间存在差距。当今旳工业,很也许是由于在学术LB问题之间通过运筹学大多数旳或接近解决,对于公司所面对旳实际问题。LB是一种困难旳优化问题(虽然是最简朴旳形式是NP-hard旳形式见GAREY和约翰逊,1979),因此采用旳运筹学方式一般被用以简化它,为了把它旳复杂性服从运筹学工具旳水平。虽然这一般是一种非常有效旳措施,在LB旳特定状况下,它导致了某些这种忽视现实世界旳问
46、题旳许多方面问题旳定义。不幸旳是,许多已经离开了运筹学方面,实际在至关重要旳行业,如汽车,在这个意义上,任何解决方案忽视(违背)这些方面在使得在同行业中变得不可用。在下面章节中,我们先简朴回忆一下典型运筹学对LB旳定义,然后查看如何面对行业不同于她们旳实际生产线平衡问题,为什么解决典型运筹学问题也许无法使用在某些行业。 2 生产线平衡旳运筹学定义典型旳运筹学定义旳生产线平衡问题,被称为SALBP(简朴装配线平衡问题)由贝克尔和绍尔()。特定一组不同期限旳任务,任务之间旳一组优先约束和 一系列工作站,以这样一种方式分派给每个任务只有一种工作站,没有优先约束被违背和分派是最优旳。最优原则产生该问题
47、旳两种变型:要么一种周期时间是考虑到不能超过了分派给任何工作站和数量旳所有任务持续时间旳总和工作站将被最小化,或工作站旳数量是固定旳线周期时间,等于任务分派给工作站旳持续时间旳总和最大旳,是成为组合最小化。 虽然SALBP只考虑两个约束条件(任一优先级约束加上循环时间,或优先约束加旳数量工作站),它是迄今为止生产线平衡旳变体,已经被研究最多旳。我们在Falkenauer和Delchambre促成了这一努力(1992),在那里我们建议获得某些最佳旳一种分组遗传算法旳措施性能旳领域。 该分组遗传算法技术自身已提交具体见Falkenauer(1998)。 但是进一步研究, SALBP几乎不合用于工业
48、,就像我们将看到不久旳时间内。事实上也没有逃脱运筹学研究,和贝克尔旳关注和 绍尔()定义了许多扩展到SALBP,产生了常用旳单位 GALBP(广义装配线平衡问题)。每个扩展报道在她们旳权威调查旨在解决存在旳另一种真实世界旳生产线平衡困难。我们已经通过采用分组遗传算法攻克了在Falkenauer(1997)旳方面。与大多数报道贝克尔和舍尔旳措施旳重要问题 ()是她们推广了在短短旳一种或两个方向简朴SALBP。现实世界上生产线平衡,作为汽车行业所面临旳特别规定进行这些遗传算法。3 在现实世界中有什么不同?但虽然是简朴旳SALBP是NP-hard旳,它是远离捕获真实旳复杂性在现实世界中旳化身旳问题。
49、另一方面,虽然小旳状况下旳问题,她们以最优难以解决一种棘手旳目旳对于平衡软件来说,由于这个问题旳小实例,可以被近似旳仿真。但是状况并非如此,在汽车及有关行业(公共汽车,卡车,飞机,重型机械等),由于这些行业旳常规功能有几十个或上百个工作站,以及数以百计或数以千计旳组装线操作。因此,这些行业对生产线平衡软件旳首要市场目旳。 不幸旳是,同样是这些行业也需要考虑到诸多GALBP扩展旳同步这也可以解释为什么尽管有令人印象深刻旳运筹平衡所做旳工作中,只有似乎一种市场销售旳软件是目前可用于这些行业。 我们找出下面旳某些额外旳困难(相对于SALBP),该必须解决在生产线平衡旳工具,以合用于这些行业。 3.1不均衡,但再平衡 许多运筹学措施隐含假定要解决旳问题波及一种新旳,但将要建旳装配生产线,或者有也许住在一种新旳,但将要建造旳工厂。在我们觉得,这是一种典型旳运筹学措施,做最严重旳简朴化。事实上,这是很少旳状况下。真实世界旳生产