Abstract
Our treatment of the shop scheduling problem in the preceding chapter has been combinatorial in character. Because of the tremendous number of schedules involved and the fact that the number of distinct schedule times is much smaller than the number of schedules, sampling from the set of semi-active schedules has elicited a great deal of theoretical study [3, 7, 9, 12, 14]. Each of these studies has essentially been the application of particular rules or procedures to generate a subset of schedules with certain properties. The characteristics of schedules in each subset determine the form of the conditional distribution of schedule values. Certainly, some conditional distribution is likely to be preferable to the others. For example, if one were to seek a good schedule from a randomly generated set of schedules, it would be more efficient to sample from a conditional distribution in which a heavier mass of schedules is very close to the optimal. Sampling from such a distribution would increase the probability of selecting good schedules while decreasing the probability of selecting others.
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Ashour, S. (1972). Statistical Aspects. In: Sequencing Theory. Lecture Notes in Economics and Mathematical Systems, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80693-3_5
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DOI: https://doi.org/10.1007/978-3-642-80693-3_5
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