Managing Flounder Openings for Maximum Revenue

Every year, the federal government regulates how many pounds of summer flounder (while these fish are called summer flounder, they are caught throughout the year) can be caught along the eastern seaboard. Annually, the federal government sets the total allowable landings (TAL) based on biological considerations and the each state gets a percentage of the TAL as a quota. The percentage of TAL each state receives is based on historical landings. Each state can then allocate its quota among the months. The purpose of this paper is to establish an optimization model to maximize the annual revenue from catching summer flounder by allocating their annual quota among twelve months. The first stage of this research is to specify and estimate a model to predict monthly summer flounder prices with an inverse demand function. Since the federal government sets the TAL, the total supply of fluke and summer flounder is fixed each year. The market price at equilibrium clears this pre-determined quantity. Two major approaches to estimation are compared in terms forecasting accuracy. The first approach is the structural model approach using log transformed data. The second approach is time series modeling, which includes ARIMA and VAR models. In the time series approach, both original and log transformed data are evaluated. The forecasting accuracy evaluation and out of sample testing of all models with both approaches, resulted in the structural model producing the best results. Regression analysis on the out-of-sample residuals for the structural model indicates that its forecasting is optimal and efficient. Diagnostic tests show that the model is statistically adequate. The structural model selected is a log transformed data model, which is applied in the second stage to maximize the revenue of summer flounder landings. The estimated log transformed model of the monthly real prices for summer flounder is as follows: the log of monthly real prices of summer flounder is a function of the log of monthly landing quantities of summer flounder, the log of monthly landing quantities of Atlantic flounder, the log of monthly landing quantities of winter flounder, the log of monthly landing quantities of yellowtail flounder, the log of monthly imports of frozen flounder, interaction and quadratic terms, yearly dummy variables, and a quantity index. Atlantic flounder, winter flounder, yellowtail flounder and total imported frozen flounder are substitutes for summer flounder in the structural model. In the second stage of the project, a revenue maximizing nonlinear programming problem is solved with different scenarios based on different monthly landing constraints for summer flounder. In each scenario, sensitivity analyses of the optimized revenue to the monthly substitute quantities from 1991 through 2005 are conducted. In all scenarios, the total revenue of summer flounder landings is least sensitive to the winter flounder landings. To study revenue change with the application of the optimization model, historical total annual landings are put into the optimization model as quota constraints. Total annual revenues for various scenarios from 1991 through to 2005 are higher than the historical revenues. In the various scenarios, the largest 15 year total increase is $46.60 million and the lowest total increase is $36.54 over actual landings.