Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 56404, 11 pages
A Decomposition-Based Pricing Method for Solving a Large-Scale MILP Model for an Integrated Fishery
Department of Management, University of Canterbury, Private Bag 4800, Christchurch 8020, New Zealand
Received 6 September 2006; Revised 11 January 2007; Accepted 5 June 2007
Academic Editor: Stefanka Chukova
Copyright © 2007 M. Babul Hasan and John F. Raffensperger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the integrated fishery planning problem (IFP). In this problem, a fishery
manager must schedule fishing trawlers to determine when and where the trawlers should
go fishing and when the trawlers should return the caught fish to the factory. The manager
must then decide how to process the fish into products at the factory. The objective is to maximize
profit. We have found that IFP is difficult to solve. The initial formulations for several planning
horizons are solved using the AMPL modelling language and CPLEX with branch and bound.
The IFP can be decomposed into a trawler-scheduling subproblem and a fish-processing subproblem
in two different ways by relaxing different sets of constraints. We tried conventional decomposition
techniques including subgradient optimization and Dantzig-Wolfe decomposition, both of which were
unacceptably slow. We then developed a decomposition-based pricing method for solving the large
fishery model, which gives excellent computation times. Numerical results for several planning
horizon models are presented.