Location of Repository

This thesis is a reflection of my research in max-algebra. The idea of max-algebra is replacing the conventional pairs of operations (+,x) by (max, +). It has been known for some time that max-algebraic linear systems and eigenvalue-eigenvector problem can be used to describe industrial processes in which a number of processors work interactively and possibly in stages. Solutions to such max-algebraic 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 max-algebraic 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

Topics:
QA Mathematics

Year: 2010

OAI identifier:
oai:etheses.bham.ac.uk:858

Downloaded from
http://etheses.bham.ac.uk/858/1/Tam10PhD.pdf

- (2007). A generalized eigenvalue problem in the max algebra,
- (2005). Discrete max-plus spectral theory,
- (1988). Duality between probability and optimization in: Gunawardena(Ed.), Idempotency,
- (2007). Max-plus algebra, in:
- (2003). Mode`les mathe´matiques pour Poptimisation des rotations, Comptes Rendus de Acade´mie d’Agriculture de France,
- (1995). Pattern properties and spectral inequalities in max-algebra,
- (1979). R.J.Plemmons, Nonnegative matrices in the mathematical sciences,
- Set coverings and invertibility of functional Galois connections, Idemoptent mathematics and mathematical physics,
- (1992). Synchronization and Linearity, An Algebra for Discrete Event Systems,
- (1993). The eigenproblem in max algebra, DMS-631-IR,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.