A New Distributed Fault-tolerant Algorithm for the Simple Assembly Line Balancing Problem 1

In this paper the Simple Assembly Line Balancing Problem 1 is considered. This well known NP-hard problem has been widely studied in the last thirty years. Therefore several sequential algorithms have been designed for solving it. But although these algorithms have become more and more eecient they cannot cope with a lot of instances of realistic size. For these examples the algorithms achieve only poor results or need unreasonable time for nding solutions of acceptable quality. The consequence is to use not only one processor. Based on the observation that Local-Area-Networks (LAN) with often more than 100 computers are installed in many companies today the use of distributed algorithms appears to be a promising approach for solving production-planning-problems in practice. Therefore an extended version of the up to now most eecient Branch&Bound procedure for SALBP-1 has been parallelized. Although the searching-tree of the sequential algorithm is extremly unbalanced the new distributed algorithm reaches optimal speedups if the problem-size is large enough. Besides even overlinear speedups for some instances the algorithm implemented on a 1024-transputer-network is nearly 800 times faster than the sequential version. To achieve this a new work-balancing-technique has been designed that can be used on principle for many parallel depth-rst-search Branch&Bound algorithms. Being designed for a Local-Area-Network of personal computers, the algorithm uses no special transputer-attribute. Due to its predeened communication-structure it can easily be supported by practical hardware-solutions. In addition a fault tolerant concept is supported by the algorithm. So if some node fails the algorithm can go on working without loosing any solution, which is very useful in a network of more than one hundred personal-computers.