Two pricing methods for solving an integrated commercial fishery planning model

Abstract

In this paper, we develop two novel pricing methods for solving an integer program. We demonstrate the methods by solving an integrated commercial fishery planning model (IFPM). In this problem, a fishery manager must schedule fishing trawlers (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 maximise profit. The problem may be modelled as a single integer program, with both the trawler scheduling and production planning parts integrated. Inventory constraints connect the two parts of the problem. Production planning alone would result in an easy linear program, but due to the trawler scheduling aspect, the IFPM is a hard integer program in the sense that traditional solution methods result in computation times that are far too long to be practical. The two pricing methods developed in this paper are a decomposition-based O'Neill pricing method and a reduced cost-based pricing method. We demonstrate the methods by means of numerical examples for different planning horizons, corresponding to differently sized problems.