An infinite horizon mathematical programming model of a multicohort single species fishery
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An in®nite horizon mathematical programming model of a multicohort single species ®shery JJ Glen University of Edinburgh Fishery policy evaluation should take account of the initial state of the ®shery and the population dynamics of the ®sh stock. Although multicohort bioeconomic ®shery policy evaluation models have been developed, the results from these models depend on the choice of planning period and the desired state of the stock at the end of this period. In this paper it is noted that these limitations can be overcome by evaluating ®shery policy over an in®nite time horizon, and a mixed integer programming (MIP) model is developed for carrying out this form of analysis in a multicohort single species ®shery. This new MIP model allows policies to be evaluated over an in®nite horizon by incorporating results from a steady state ®shery model into a multiperiod framework. The use of this MIP model in determining policies for reaching and maintaining a steady state is illustrated. Keywords: ®sheries management; in®nite horizon model; mathematical programming
Introduction Fisheries management has increased in importance as more marine ®sheries come under pressure from over®shing, and this has stimulated the development of model based methods for ®shery policy evaluation. The simplest of these approaches are based on the Schaefer ®sh stock model (see Clark1), but since the stock is represented in terms of total biomass, namely the weight of the stock, the age dependent development of each age class, or cohort, is not considered. This model has, however, been widely used for the analysis of sustainable yield, namely the ®sh catch that can be maintained in the long run from a ®shery in a steady state, but the failure to consider policies for reaching a steady state is a fundamental weakness of all forms of sustainable yield analysis. Fishery policy evaluation should take account of the initial state of the ®shery and the population dynamics of the stock, and should therefore be based on a multicohort ®shery model. The most widely used multicohort ®shery model is the Beverton±Holt population model (see Clark1) which is based on the assumption that the instantaneous natural and ®shing mortality rates of each cohort are constant throughout any time period. This assumption is not valid over the annual time period generally adopted, but this multicohort model has been used in a number of deterministic multiperiod bioeconomic ®shery models based on simulation2,3 and, in spite of computational dif®culties arising from the form of this population model, optimisation methods4±7. Stochastic models are not widely used because of limited
 lafsson2 argue that simuladata availability. Helgason and O tion is more appropriate than optimisation as the basis of a tool for ®sheries management because the problems are multifaceted and optimisation results are perceived as being directive. However, if all relevant factors are incorporated in an optimisati
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