BROWN ET AL.: LINEAR PROGRAMMING SIMULATIONS 



than dogfishes), were excluded. Most of these were 

 not covered by the regulations and have <1 1 (met- 

 ric ton) per 100 t of directed species caught. In in- 

 stances where no "main species sought" category 

 was indicated or where landings were attributed 

 to a mixed fishery, the monthly landings by vessel 

 classification and gear were assigned to "species 

 sought" categories according to the species which 

 formed a simple plurality of the catch. The United 

 States of America often reported mixed fisheries 

 on groundfish species. The Union of Soviet 

 Socialist Republics (U.S.S.R.), Poland, Japan, 

 and German Democratic Republic (G.D.R.) typi- 

 cally reported their pelagic and/or squid fishery 

 catches as mixed. 



The term "fishery" as used in this paper refers to 

 the vessels and associated catch on these "main 

 species sought" categories. The term "species" re- 

 fers to both individual species and species groups. 

 All reported landings were thus identified by two 

 factors: species and fisheries. Such tabulations 

 were prepared for all nations for which data were 

 available. For Romania, which has had an Atlan- 

 tic herring fishery but did not report a directed 

 Atlantic herring fishery in 1973, bycatch ratios for 

 1972 (ICNAF 1974b) were used for that species 

 fishery. The only countries with an allocated na- 

 tional quota for which 1971 and 1973 data were 

 not available and thus could not be analyzed were 

 Italy (1971 and 1973) and France (1971). 



In this paper, all catch restrictions described 

 below will all be referred to as "quotas." To apply 

 linear programming techniques to the bycatch 

 problems restraints on the total catches for each 

 species by country need to be set. For countries and 

 for species categories reported in ICNAF Statisti- 

 cal Bulletins, we used restraints in linear pro- 

 gramming (ICNAF 1974a). For countries and/or 

 species for which ICNAF had not set specific quota 

 allocations (but for which the quota was included 

 in, say, "other countries" under ICNAF regula- 

 tions — a country not giv^ a specific catch quota 

 could fish in competition with other similar coun- 



TabLE 1. — Species categories as reported to ICNAF, 1971 and 



1973. 



tries from an "other country" allocation or "other 

 flounder" category), we estimated these re- 

 straints by the following procedures. These were 

 chosen so that the categories of quota allocations 

 matched the species categories (Table 1) by which 

 the catches were reported. We proportioned the 

 "others" allocation category for each individual 

 species to countries based on the 1973 nominal 

 catch for each particular species and the catch of 

 that species of all of the countries that did not have 

 a national quota for the species. We proportioned 

 the quota for "other groundfish" and "other 

 pelagic" from the "other fish" TAC for each coun- 

 try. The quotas for American plaice and witch 

 flounder were subtracted from the "other floun- 

 der" TAC for each individual country. Since the 

 quota for pollock was set by ICNAF for Division 

 4VWX plus Subarea 5, national quota allocations 

 were estimated as an average percent of the nomi- 

 nal pollock catches during 1971, 1972, and 1973 in 

 Subarea 4VW and 5. 



Analysis Methods 



Linear programming is a optimization method 

 for which the effectiveness of an allocation scheme 

 distributed over several variables is measured by 

 the maximum or minimum value of some linear 

 function of those variables, when those variables 

 are subject to linear constraints. The problem con- 

 sidered here was to determined = (Xj, X2, . . . , x„) 

 such that 



1 = 1 



(1) 



is maximized, where for each /, c, was the weight- 

 ing coefficients of the variable x^. In the present 

 context, 

 X, = catch of species / to be taken in directed 

 fishery for species /, 

 = catch of species / in all fisheries divided by 

 catch of species i taken in directed 

 fishery for species i (c, ^ 1.00), 

 = number of directed fisheries considered, 

 and 

 z = total catch of all species. 



Solutions (Xj, X2, . . . , Xn ) of Equation (1) were sub- 

 ject to the constraints for each / 



c, 



n 





(2) 

 853 



