Tam, Kin Po (2010)
Ph.D. thesis, University of Birmingham.
 AbstractThis thesis is a reflection of my research in maxalgebra. The idea of maxalgebra is replacing the conventional pairs of operations (+,x) by (max, +). It has been known for some time that maxalgebraic linear systems and eigenvalueeigenvector problem can be used to describe industrial processes in which a number of processors work interactively and possibly in stages. Solutions to such maxalgebraic linear system typically correspond to start time vectors which guarantee that the processes meet given deadlines or will work in a steady regime. The aim of this thesis is to study such problems subjected to additional requirements or constraints. These include minimization and maximization of the time span of completion times or starting times. We will also consider the case of minimization and maximization of the time span when some completion times or starting times are prescribed. The problem of integrality is also studied in this thesis. This is finding completion times or starting times which consists of integer values only. Finally we consider maxalgebraic permuted linear systems where we permute a given vector and decide if the permuted vector is a satisfactory completion time or starting time. For some of these problems, we developed exact and efficient methods. Some of them turn out to be hard. For these we have proposed and tested a number of heuristics.

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