Abstract
Abstract The problem of finding a minimum makespan permutation schedule in a deterministic flow-shop without intermediate queues is equivalent to the shortest distance routing traveling salesman problem. If the task system is semi-ordered, the associated distance matrix of the corresponding traveling salesman problem is found to exhibit some peculiar characteristics. Consequently, we are able to derive some important results which help us to eliminate permutations in the search of the minimum makespan permutation schedule. The most important result is that the optimal permutation schedule is pyramidal. An algorithm, having quadratic worst-case complexity in terms of the number of partial schedules explicitly enumerated, has been presented. Some particular cases of the semi-ordered flow-shop are also discussed.
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