Hindawi Publishing Corporation Journal of Applied Mathematics and Decision Sciences Volume 2007, Article ID 56404, 10 pages doi:10.1155/2007/56404 Research Article A Decomposition-Based Pricing Method for Solving a Large-Scale MILP Model for an Integrated Fishery M. Babul Hasan and John F. Raffensperger Received 6 September 2006; Revised 11 January 2007; Accepted 5 June 2007 Recommended by Stefanka Chukova We study the integrated fishery planning problem (IFP). In this problem, a fishery man- ager 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 subprob- lem 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. Copyright © 2007 M. B. Hasan and J. F. Raffensperger. This is an open access article dis- tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop- erly cited. 1. Introduction and literature review Modern commercial fisheries are often vertically integrated, that is, a firm may own fish- ing trawlers and a processing factory. To maximise profit, a fishery manager must sched- ule the fishing trawlers to determine when and where the trawlers should go fishing and when the trawlers should return the caught fish to the factory. Given a trawler schedule, the manager must then decide how to process the fish into products at the factory. The objective is to maximise profit. The difficult part of this problem is coordinating trawler scheduling and fish-processing.