The University of Southampton
University of Southampton Institutional Repository

Approaches for solving some scheduling and routing problems

Drake, Andrew John (2009) Approaches for solving some scheduling and routing problems University of Southampton, School of Mathematics, Doctoral Thesis , 211pp.

Record type: Thesis (Doctoral)


We study approaches for finding good solutions, and lower bounds, for three difficult combinatorial optimisation problems.
The supply ship travelling salesman problem is a simplification of a situation faced by a naval logistics coordinator who must direct a support vessel tasked with resupplying ships in a fleet. It is a generalisation of the travelling salesman problem in which the nodes are in motion, each following some predetermined route. We apply dynamic programming state-space relaxation techniques, producing lower bounds for the problem that are 73% to 84% of the best solution, on average. We also apply heuristics to find good solutions to this NP-hard problem, showing that restricted dynamic programming approaches outperform simple 2-opt and 3-opt local search procedures for instances with 20 nodes.
We introduce the supply ship scheduling problem, another roblem inspired by a support vessel environment. We wish to minimise the number of mobile machines required to process a set of jobs; each job is in a different stationary location and features a fixed start time. Jobs may be simultaneously processed by multiple machines, obtaining a speed-up in processing time. We represent the problem as a directed graph and use the minimum flow in a transformed network to determine the minimum number of machines. We present a neighbourhood structure based on the maximum cut, applying it within descent and tabu search procedures. We construct a restricted dynamic programming based approach, but this is outperformed by the tabu search algorithm.
The task allocation problem, arising in distributed computing, is to assign a set of tasks to a set of processors so that the overall cost is minimised. Costs are incurred from processor usage, interprocessor communication and task execution. We construct, and try to improve, semidefinite programming relaxations to find lower bounds for variants of this NP-hard problem. We develop a branch-and-bound approach to find optimal solutions, but this is only effective for small instances.

PDF AJ_Drake_PhD_Thesis.pdf - Other
Download (963kB)

More information

Published date: February 2009
Organisations: University of Southampton, Operational Research


Local EPrints ID: 66268
PURE UUID: 4b3f6a06-2bca-4f8d-b327-2e842a5b4bfa

Catalogue record

Date deposited: 27 May 2009
Last modified: 19 Jul 2017 00:26

Export record


Author: Andrew John Drake
Thesis advisor: Christopher Potts

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.