A LINEAR PROGRAMMING APPROACH TO DETERMINING 

 HARVESTING CAPACITY: A MULTIPLE SPECIES FISHERY 



Robert A. Siegel," Joseph J. Mi'Ki.i.er,^ and Brian J. Rothschild^ 



ABSTRACT 



The U.S. Fishery Conservation and Management Act of 1976 (P.L. 94-265) requires that fishery 

 management plans specify the capacity of a fishing fleet. However, the Act does not provide a definition 

 of capacity. This paper considers .some of the problems of defining and measuring capacity in the 

 harvesting sector of the fishing industry and suggests an estimation procedure A linear programming 

 model is used to estimate the economic capacity of a fishing fleet. The model provides estimates of the 

 expected output in a multiple species fishery. 



Measurement of capacity in the U.S. fishing in- 

 dustry has become of increasing importance as a 

 result of the passage of the Fishery Conservation 

 and Management Act of 1 976 (FCMA). The FCMA 

 requires (Section 303 (a) (4i (A)) fishery manage- 

 ment plans prepared by Regional Fishery Man- 

 agement Councils or the Secretary of Commerce 

 to; "assess and specify . . . the capacity and the 

 extent to which fishing vessels of the United 

 States, on an annual basis, will harvest the op- 

 timum yield . . . ." 



The FCMA, however, does not provide a func- 

 tional definition of capacity that can be used in the 

 preparation of fishery management plans. This 

 raises operational difficulties since "capacity" can 

 be based on economic or physical concepts. For 

 example, physical capacity can be measured in 

 terms of the hold space of a fishing vessel, al- 

 though this generally exceeds the catch. An 

 economic measure would simply be past catches 

 (assuming these reflect equilibrium conditions), 

 but this does not necessarily provide an accurate 

 indication of future catches. 



It is apparent that the hold space or past catches 

 are only "first" approximations to "capacity" and 

 that better indicators are needed in order to have 

 meaningful estimates of the expected catch of the 

 fleet. Since estimates of capacity are of obvious 



'National Marine Fisheries Service, Office of Resource Con- 

 servation and Management. Washington, DC 20235. 



^National Marine Fisheries Service, Federal Building, 14 Elm 

 Street, Gloucester, MA 01930. 



'National Oceanic and Atmospheric Administration, Office of 

 the Administrator, Washington, DC 20230. 



Manuscript accepted October 1978 

 FISHERY BULLETIN. VOL. 77, NO. 2, 1979, 



importance in determining U.S. -foreign alloca- 

 tions, it is essential that the measurements of 

 capacity and expected catch be accurate. Thus, a 

 major effort must be made to develop meaningful 

 estimates of capacity that are consistent and to 

 indicate what these measures are designed to rep- 

 resent. 



Analysis of the capacity problem must address 

 four issues: 



1) development of a definition and measure of 

 capacity, at least initially, relevant to the 

 harvesting sector of the fishing industry: 



2) development of appropriate methods of es- 

 timating capacity; 



3) estimation of what the fleet will catch under 

 a set of economic and environmental condi- 

 tions (it will be suggested that the expected 

 domestic catch is indeed the appropriate no- 

 tion of "capacity" in the short run); and 



4) the time frame for the analysis. 



This paper will consider some of the problems of 

 measuring capacity in the harvesting sector of the 

 fishing industry and suggest possible estimation 

 procedures. Section I focuses on economic and 

 technical concepts of capacity. Section II presents 

 a linear programming model which can be used to 

 estimate the output of a fishing fleet in a multi- 

 species fishery. Section III contains an example 

 problem which shows the applicability of this 

 model to a multispecies fishery such as the New 

 England otter trawl fleet. Section IV provides a 

 summary of the paper and briefly describes areas 

 of further research. 



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