A Decomposition-Based Pricing Method for Solving a Large-Scale MILP Model for an Integrated Fishery

Abstract

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.