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1 Introduction

Assembly 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 since Henry Ford‘s 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 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 the 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 (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 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 industries 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 Today‘s 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 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 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 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 problem maybe unusable in some industries. 2 OR Definitions of LB

The 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 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 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 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 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 escaped 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 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 reported by Becker and Scholl (2004) 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 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 problem 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. 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 available 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 implicitly 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-world 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, or the production targets. This has some far-reaching implications, outlined below.

3.2 Workstations Have Identities

As 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 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 constraints (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 place 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 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 the algorithm are in fact necessary because of zoning constraints.

4 Conclusions

The 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 balancing 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 (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 the ergonomic constraints and precedence constraints defined on operations, as well as zoning constraints and possible drifting operations

? Solve the within-workstation schedulng problem on all workstations, 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 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.

We‘ve 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 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 optimization 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 . References

1 Becker C. and Scholl, A. (2004) `A survey on problems and methods in generalized assemblyline 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 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 Resource Dependent Task Times', Proceedings of the Fourth International Conference on Neural Information Processing (ICONIP‘97), 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) Computers and Intractability - A Guide to the Theory of NP-completeness, W.H.Freeman Co., San Francisco, USA. Book.

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