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Scheduling by Non-Commutative Algebra

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DOI: 10.1016/s0304-0208(08)72954-2

Abstract

The connection is discussed between the use of the matrix iteration v = u ⊕ DT⊗v over the semiring (z,∪{∞}, min, +) = (z,⊕, ⊗), and the use of the z-transform, in relation to network scheduling involving a single vehicle. By introducing non-commuting variables the ideas can be extended to producing efficient itineraries involving scheduled interchanges of travellers among the vehicles of a multi-vehicle transport system.

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