FISHERY BULLETIN: VOL. 69. NO. 1 



knowing in advance of the run the information 

 that we actually used in the allocation and having 

 the ability to select the entities in the run as 

 they are selected in the allocation. 



Next, an examination of the 1960 optimal 

 allocation reflects that this optimal allocation 

 not only increases the value of the fish on the 

 dock, it also shortens the length of time which 

 a cannery needs to operate. Thus, the same 

 amount of fish could be processed in a shorter 

 period of time, by the same labor force, etc. 

 In the optimal allocation for the 1960 run, all 

 of the fish could have been processed in the first 

 13 days of the season, 5 days less than the actual 

 operation. Naturally, we need to assume that 

 a policy of catching salmon only from the early 

 part of the run would not aff"ect the genetic 

 constituency of the stock. Furthermore, we 

 must be careful here because, as we have em- 

 phasized in several places, by our LP assump- 

 tions, we cannot, a priori, let the cannery oper- 

 ations on day ;/-l, for example, affect the can- 

 nery operations on day / and we cannot at least 

 in our formulation allow operating at peak ca- 

 pacity to affect quality of the fish or overtime 

 payments since the variables are external to 

 our model. 



Another indication is that the values of fish 

 change during the course of the season and that 

 these values change in rather subtle ways de- 

 pending upon the "rules" that we set forth (e.g., 

 contrast Figures 8 and 9) and that in the fishery 

 the marginal value of less valuable entities in 

 Table 2 can be greater than the more valuable 

 entities in Table 2. These changes in values 

 need to be acknowledged in any management 

 scheme. 



Thus, it appears that we have the opportunity 

 to increase the economic efliciency of some salm- 

 on runs. This is, of course, not a new concept, 

 having been treated in some detail by, for ex- 

 ample, Crutchfield and Pontecorvo (1969). Our 

 approach is slightly different, however, in that 

 we have concentrated on oiitimality only from 

 the point of view of increasing the value, as we 

 have defined it, of the fish on the dock. Any full 

 treatment of the management problem must, of 

 course, consider the distribution of fishing eff'ort 

 and its ancillary fishing and economic implica- 



tions. 



Now if we accept the premise that conserva- 

 tion is "optimum" allocation of resources in the 

 times-space stream (c.f. Crutchfield and Ponte- 

 corvo, 1969), and if we observe that mathema- 

 tical programming provides guidance for optimal 

 allocation, and note that LP is a special case of 

 mathematical programming, and suggest that 

 the kinds of information required to allocate 

 salmon among the days of the run in an LP 

 model are not going to be much different from 

 the kinds of information required for more so- 

 phisticated programming procedure, then we are 

 led to the conclusion that perhaps we have not 

 addressed ourselves to asking, in our research, 

 the "right questions" concerning salmon man- 

 agement. Following our argument, it would 

 then be implicit that the right questions are con- 

 tained in our formulation of the LP model. 

 These answers must be feasible to obtain and 

 they would contain either needed data or doc- 

 umented policies which would be reflected in 

 the right-hand side of the constraint ecjuations 

 and, more importantly, provide an opportunity 

 for enlightened dialogue. There is unfortu- 

 nately a cost associated with asking right ques- 

 tions. This cost involves the cost of doing new 

 work, or that which inevitably results when ex- 

 isting research activities are reallocated. Are 

 these costs worth the expenditure? These, how- 

 ever, are the kind of questions, the answers to 

 which can be guided by the LP problem. For 

 the salmon management model, we impute values 

 to units of cannery capacity, etc., but, and per- 

 haps of equivalent importance, we impute a val- 

 ue, in meaningful terms, to information. Thus, 

 for our salmon jn'oblem, we have cleverly avoid- 

 ed indicating how we could catch Xij fish for 

 some /,,/. But it is well known that catching can 

 be approximated because it is i)ossible to catch 

 salmon in traps (although this has never been 

 done to any large extent in Bristol Bay) and, 

 upon visual inspection, to distinguish between 

 large and small, male and female fish, and doing 

 this by virtue of ceteris paribus, the allocative 

 process, we could add about 0.5 million dollars 

 to the value of the salmon on the dock. This is, 

 of course, not the full picture, because we would 

 have to trade off the added value of salmon (it 



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