A Stochastic Constrained Optimization Model for Determining Commercial Fishing Seasons

Fisheries management must set fishing seasons that define either length of season, amount of seasonal catch, or both. These seasons are traditionally set with one overriding concern---protect the bio-mass of the fishery. In this paper, a stochastic constrained optimization model is developed for a multi-species fishery that sets the seasonal catch by species, by geographical area, and by month of the season. The model maximizes vessel fleet contribution over a one year planning horizon within certain biological, environmental, market, and production capacity constraints. The model explicitly treats such sources of uncertainty as catch per species, catch per unit of effort, weather, and markets by a computer simulation procedure. This method allows random variation of any parameter of the mathematical programming problem. The procedure selects a single set of parameter values for the problem, executes the mathematical programming algorithm, and stores that cycle's results. These steps are repeated until the desired number of cycles have been completed. A statistical summary of the objective function values, decision variable values, and slack variable values completes the procedure. The model demonstrated an 11% improvement for the 1976--1977 Alaskan crab fleet's contribution over commercial fishing seasons set by traditional means. The model continues to be updated and evaluated annually. The model of this study should be of interest to managers of organizations whose products are renewable natural resources or other organizations who must set production schedules within resource and market constraints in environments characterized by many parameters subject to random variation.