Total Allowable Catch Constraint 



Presumably there will be a year's total allow- 

 able catch (TAG) set for each species for each area. 

 However, because of the bycatch problem, if the 

 number of pounds of each species taken in a di- 

 rected fishery equaled the TAG for each species, 

 then all of the TAC's would be exceeded. To deal 

 with this problem the following constraint is for- 

 mulated: 



^ A I 



■^ "^ mijl '-'ijl 



(2) 



where A, 



number of pounds of species m 

 caught per pound of species ; in a 

 directed fishery for species ; in 

 area / during period t. It is as- 

 sumed that these A„„y, are the 

 same for all vessel categories. 

 TAG for species m in areaj for all 

 periods. . 



Processing Capacity 



Generally there exists an upper bound on the 

 total amount of species processing capacity avail- 

 able during a particular ti me period. To reflect this 

 situation the following constraint was formulated: 



S b„ L„ 



B, 



(3) 



where b,, 



B, 



- the number of pounds of processing 

 capacity required when a pound of 

 species ( is caught in a directed 

 fishery for species i in areaj during 

 period t 



= the number of pounds of processing 

 capacity available during period /. 



Harvesting Capacity 



The final restriction used in this model is a phys- 

 ical upper limit on the amount offish that can be 

 caught by the fleet in a particular time period or 

 season. To address this problem, the following 

 constraint was formulated: 



fishing area. If these changes were incorporated into the LP 

 model, they would certainly make the problem more realistic 

 However, the purpose of this was to initially formulate a simple 

 problem and then to develop more complex models m future 

 research. A drawback to this assumption of a given price in each 

 time period js that the quantity landed would be expected to 

 influence pnce. At the time of this analysis, appropriate demand 

 functions had not been estimated. 



FISHERY BULLETIN: VOL 77. NO. 2 

 (4) 



S d,„ L,_„ ^ FC„ 



where rf,„ = the number of units of physical 

 harvesting capacity required when 

 a pound of species ; is caught in a 

 directed fishery for species / in area 

 j during period t. 

 FCi, = the total number of pounds of fish 

 that a fleet consisting of a specified 

 number of vessels (given technol- 

 ogy and gear) is physically capable 

 of catching in area / during a par- 

 ticular time period t . 



AN APPLICATION TO THE NEW 

 ENGLAND OTTER TRAWL FLEET 



New England Otter Trawl Fisher>' 



The fishery to be studied is the otter trawl 

 fishery in New England. The output consists of 

 landings by vessels using otter trawls in Maine, 

 Massachusetts, and Rhode Island during the 

 1955-74 period (Table 1). In the late 1950's land- 

 ings in this fishery averaged more than 304,000 

 metric tons (t). However, by 1972 landings had 

 declined sharply to about 126.8 thousand t. 



The catch per gross registered ton (CGRT) 

 reached a maximum value of 9.03 t in 1957 (Table 

 2 1. The total associated catch in 1957 also peaked 

 at 3 18.5 thousand t. By 1973 both GGRT and land- 

 ings sharply declined to 3.45 t and 127.4 thousand 

 t, respectively. This decrease can be generally at- 

 tributed to a lower stock abundance of target 



T.^BLE 1 . — Landings (metric tonsi of fish by otter trawl vessels in 

 Maine, Massachusetts, and Rhode Island. (Sources: U.S. De- 

 partment of Commerce 1971-77, US. Fish and Wildlife Service 

 1957-69.) 



428 



