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1、Line Balance ResearchAbstract: 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 solving it, one is each
2、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 the past, and despit
3、e 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 actual problem faced by th
4、e industry.Keyword: Line Balancing, Assembly lines, OptimizationLine Balancing Research1 IntroductionAssembly Line Balancing, or simply Line Balancing (LB), is the problem of assigning operations to workstations along an assembly line, in such a way that the assignment be optimal in some sense. Ever
5、 since Henry Fords introduction of assembly lines, LB has been an optimization problem of significant industrial importance: the efficiency difference between an optimal and a sub-optimal assignment can yield economies (or waste) reaching millions of dollars per year. LB is a classic Operations Rese
6、arch (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 the problem, and the OR efforts that have been made to tackle it, little commercially available software is available to help in
7、dustry in optimizing their lines. In fact, according to a recent survey by Becker and Scholl (2004), there appear to be currently just two commercially available packages featuring both a state of the art optimization algorithm and a user-friendly interface for data management. Furthermore, one of t
8、hose 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 industries such as automotive. This situation appears to be paradoxical, or at least unexpected: given the huge economies LB can
9、 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 Todays industry, is probably due to a misalignment between the academic LB problem addressed by most of the OR approaches
10、, 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 taken by OR has typically been to simplify it, in order to bring it to a level of complexity amenable to OR tools. While this
11、 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, many of the aspects that have been left out in the OR approach are in fact crucial to industries such as automotive, in the
12、 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 how the actual line balancing problem faced by the industry differs from them, and why a solution to the classic OR proble
13、m 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 and Scholl (2004), goes as follows. Given a set of tasks of various durations, a set of precedence constraints among the
14、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 criterion gives rise to two variants of the problem: either a cycle time is given that cannot be exceeded by the sum of
15、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 largest sum of durations of task assigned to a workstation, is to be minimized.Although the SALBP only takes into account
16、 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 been the most researched. We have contributed to that effort in Falkenauer and Delchambre (1992), where we proposed a
17、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 (1998).However well researched, the SALBP is hardly applicable in industry, as we will see shortly. The fact has not esca
18、ped the attention of the OR researches, and Becker and Scholl (2004) define many extensions to SALBP, yielding a common denomination GALBP (Generalized Assembly Line Balancing Problem). Each of the extensions reported in their authoritative survey aims to handle an additional difficulty present in r
19、eal-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 reported by Becker and Scholl (2004) is that they generalize the simple SALBP in just one or two directions. The real wor
20、ld 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 SALBP is NP-hard, it is far from capturing the true complexity of the problem in its real-world incarnations.
21、 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 problem can be solved closet optimality by hand. That is however not the case in the automotive and related indus
22、tries (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. Those industries are therefore the prime targets for line balancing software.Unfortunately, those same indust
23、ries 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 available software seems tube currently available for those industries.We identify below some of the additional diffi
24、culties (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 implicitly assume that the problem to be solved involves a new, yet-to-be-built assembly line, possibly housed in a
25、 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-world line balancing tasks involve existing lines, housed in existing factories infect, the target line typically
26、 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, or the production targets. This has some far-reaching implications, outlined below.3.2 Workstations Have Ident
27、itiesAs 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 has one far-reaching consequence, namely that each workstation in the line does have its own identity. This id
28、entity 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 constraints (e.g. a workstation below a low ceiling cannot elevate the car above the operators heads), its own heavy eq
29、uipment 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 place welding operations just beside the painting shop), etc.3.3 Cannot Eliminate Workstations Since workstatio
30、ns 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 front of the line or its tail, their elimination would create gaping holes in the line, by virtue of the othe
31、r 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 the algorithm are in fact necessary because of zoning constraints.4 ConclusionsThe conclusions inspection 3 stem
32、s 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 balancing tool for those industries must be able to handle at least those aspects of the problem. This is very far
33、 from the “clean” academic SALBP, as well as most GALBP extensions reported by Becker and Scholl (2004). In fact, such a tool must simultaneously solve several-hard problems: Find a feasible defined replacement for all undefined (ANY) ergonomic constraints on workstations, i.e. One compatible with t
34、he 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 workstations, for all products being assembled on the line Assign the operations to workstations to achieve
35、 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 byte size of the problem encountered in the target industries, which routinely feature assembly lines with
36、 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 industries such as automotive, yet that have been either neglected in the OR work on the problem, or handled separa
37、tely 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 optimization problem. The complexity of the problem, and the need to solve it quickly, may explain why ther
38、e 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 http:/ References 1 Becker C. and Scholl, A. (2004) A survey on problems and methods in generalized assem
39、blyline balancing, European Journal of Operations Research, in press. Available online at http:/dx.doi.org/doi:10.1016/j.ejor.2004.07.023. Journal article. 2 Falkenauer, E. and Delchambre, A. (1992) Genetic Algorithm for Bin Packing and Line Balancing, Proceedings of the 1992 IEEE International Conf
40、erence 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 Resource Dependent Task Times, Proceedings of the Fourth International C
41、onference 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 Wiley& Sons, Chi Chester, UK. Book. 5 Gary. R. and Johnson D. S. (1979)
42、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研究摘要：生产线平衡（LB）是一个经典的，精心研究的显著工业重要性的运筹学（OR）优化问题。这是其中一个所在领域的专业知识并没有太大帮助的问题之一：无论花了多少年解决它，面对每一次棘手的问题与可能的天文数字的解决方案都并不是关于如何解决这个问题的最好办法，除非你假定老办法是最好的办法。在这里，我们解释一个明显的悖论：虽然很多算法已经被提出，在
43、过去，尽管该问题的实际重要性只是一个市场销售的LB软件。目前似乎可用于工业，如汽车中的应用。我们推测，这可能是由于在学术LB问题之间的没有通过运筹学路径和生产业实际面对的问题。关键词：生产线平衡，装配生产线，优化 生产线平衡研究1 引言 装配线平衡，或者简称生产线平衡（LB），是一个操作工作站沿着装配线分配的问题，在这样一种方式，该分配是在某种意义上最优的。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的最优化问题：在效率不同的最优和次优分配之间的差异可以产生经济（或浪费）达到数百万美元每年。 LB是一个经典的运筹学（OR）的优化问题，已通过被运筹学解决达以上几十年。许多算法已经被
44、提出了去解决这个问题。尽管问题的有实际重要性，并已经取得了或努力，但很少的商业软件是可以帮助行业优化其生产线。事实上，根据最近贝克尔和绍尔（2004）的一项调查显示，似乎有目前只有两个市场销售的软件包有特色，即是最先进的优化算法的状态和数据管理的用户友好的界面。此外，这些软件包，似乎只处理“干净”的提法的问题（简单装配线平衡问题，或SALBP），这让只有一个软件包可用于工业，如汽车业。这种情况似乎是自相矛盾的，或者至少是意想不到的：给定的LB可以产生的巨大经济，人们能够所期望的几个软件包争先恐后地抓住这些经济体的一部分。 看来，现有的运筹学结果以及它们在传播之间存在差距。当今的工业，很可能是由
45、于在学术LB问题之间通过运筹学大多数的或接近解决，对于企业所面对的实际问题。LB是一个困难的优化问题（即使是最简单的形式是NP-hard的形式见GAREY和约翰逊，1979），因此采取的运筹学方式通常被用以简化它，为了把它的复杂性服从运筹学工具的水平。虽然这一般是一个非常有效的方法，在LB的特定情况下，它导致了一些这种无视现实世界的问题的许多方面问题的定义。不幸的是，许多已经离开了运筹学方面，实际在至关重要的行业，如汽车，在这个意义上，任何解决方案忽略（违反）这些方面在使得在同行业中变得不可用。在下面章节中，我们先简单回顾一下经典运筹学对LB的定义，然后查看如何面对行业不同于他们的实际生产线平
46、衡问题，为什么解决经典运筹学问题可能无法使用在一些行业。 2 生产线平衡的运筹学定义经典的运筹学定义的生产线平衡问题，被称为SALBP（简单装配线平衡问题）由贝克尔和绍尔（2004）。特定一组不同期限的任务，任务之间的一组优先约束和 一系列工作站，以这样一种方式分配给每个任务只有一个工作站，没有优先约束被违反和分配是最优的。最优标准产生该问题的两种变型：要么一个周期时间是考虑到不能超过了分配给任何工作站和数量的所有任务持续时间的总和工作站将被最小化，或工作站的数量是固定的线周期时间，等于任务分配给工作站的持续时间的总和最大的，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
47、加上循环时间，或优先约束加的数量工作站），它是迄今为止生产线平衡的变体，已经被研究最多的。我们在Falkenauer和Delchambre促成了这一努力（1992），在那里我们建议取得一些最好的一个分组遗传算法的方法性能的领域。 该分组遗传算法技术本身已提交详细见Falkenauer（1998）。 但是深入研究， SALBP几乎不适用于工业，就像我们将看到不久的时间内。事实上也没有逃脱运筹学研究，和贝克尔的关注和 绍尔（2004）定义了许多扩展到SALBP，产生了常用的单位 GALBP（广义装配线平衡问题）。每个扩展报道在他们的权威调查旨在处理存在的另一个真实世界的生产线平衡困难。我们已经通过
48、采用分组遗传算法攻克了在Falkenauer（1997）的方面。与大多数报道贝克尔和舍尔的方法的主要问题 （2004）是他们推广了在短短的一个或两个方向简单SALBP。现实世界上生产线平衡，作为汽车行业所面临的特别要求进行这些遗传算法。3 在现实世界中有什么不同？但即使是简单的SALBP是NP-hard的，它是远离捕捉真实的复杂性在现实世界中的化身的问题。另一方面，即使小的情况下的问题，他们以最优难以解决一个棘手的目标对于平衡软件来说，因为这个问题的小实例，可以被近似的仿真。但是情况并非如此，在汽车及相关行业（公共汽车，卡车，飞机，重型机械等），因为这些行业的常规功能有几十个或上百个工作站，以
49、及数以百计或数以千计的组装线操作。因此，这些行业对生产线平衡软件的首要市场目标。 不幸的是，同样是这些行业也需要考虑到很多GALBP扩展的同时这也可以解释为什么尽管有令人印象深刻的运筹平衡所做的工作中，只有似乎一个市场销售的软件是目前可用于这些行业。 我们找出下面的一些额外的困难（相对于SALBP），该必须解决在生产线平衡的工具，以适用于这些行业。 3.1不均衡，但再平衡 许多运筹学办法隐含假定要解决的问题涉及一个新的，但将要建的装配生产线，或者有可能住在一个新的，但将要建造的工厂。在我们认为，这是一个经典的运筹学方法，做最严重的简单化。实际上，这是很少的情况下。真实世界的生产线平衡任务的绝大多数涉及到现有的生产线，安置在现有的工厂-事实上，目标线通常需要重新排列而非均衡，从变化的产物所产生的需要或混合车型组装的线，组装技术，可用劳动力或生产目标。这有一些深远的影响，下文将以概述。