ROTHSCHILD and BALSIGER: LINEAR-PROGRAMMING SOLUTION 



is a common opinion that salmon caught in traps 

 are of better condition and higher vahie than 

 the salmon which are taken by gill netting, for 

 example), the reduction in cannery days used 

 to process the fish, the cost of building traps, 

 and the political problems which are described 

 in some detail in Crutchfield and Pontecorvo 

 (1969). It would not, however, be dithcult to 

 determine the discounted present value of the 

 various alternate ijrocedures and thus evaluate 

 the wisdom of engaging in any. In this eval- 

 uation, we need not be bound by what are per- 

 haps extreme solutions such as traps, but we 

 could examine the value of other selectivity pro- 

 cedures such as modifying gill net selectivity, 

 etc. In general, then, we can evaluate the value 

 of information by approximating that informa- 

 tion, employing it in the model, and contrasting 

 the change in the objective function with the 

 objective function when the information is not 

 in the model. 



Additional information is needed on the pat- 

 tern of the run. For the earlier years, this is 

 available in Royce (1965), a publication which 

 needs to be updated and implemented to obtain 

 even rough estimates of the temporal movement 

 of the fish of various entities through the fishery. 

 This might be quite difficult to accomplish with 

 present concepts, and the feasibility of a system 

 which would acoustically monitor the passage 

 of salmon through the entire river system and 

 developing a central computer-oriented unit 

 which would process the signals from all acoustic 

 units and provide, in real time, through appro- 

 priate algorithms, rules for catching fish and 

 making observations on escapement is presently 

 being explored. 



In our model, because of a lack of information, 

 we used the total run and allocated this propor- 

 tionately among the days of the fishery to de- 

 termine the daily run. This emphasizes the need 

 to have, for the purpose of management, a fairly 

 accurate preseason guess of the total magnitude 

 of the run and the Xij's. These guesses are 

 already being made and the predictions need 

 to be judged on the basis of whether the pre- 

 dictions do better than simply averaging the 

 run for cycle years and simply averaging the 

 run for noncycle years and applying these aver- 



ages as predictions. The trick then may not be 

 to estimate the average catch but rather to de- 

 termine which years are cycle years. 



We have included cannery capacity in a rather 

 simple way in our model and this is a subject 

 that also needs additional data since the can- 

 nery capacity constraint can be formulated in 

 a variety of ways. It would be interesting to 

 explore in a simulation setting the behavior of 

 the slack variables in the cannery constraint. 

 This is because it seems quite likely that there 

 is a positive correlation between the cost of op- 

 erating a cannery and the magnitude of the 

 slack variable in the cannery constraint. If the 

 run was constant from year to year, then it 

 would be relatively easy to determine an optimal 

 value for the magTiitude of the slack variable in 

 the canneiy constraint. But the run varies con- 

 siderably from year to year, and so in those 

 years when the cannery constraint might be too 

 low, we have an opportunity cost which appears 

 as a slack variable in the dual formulation of 

 the cannery constraint. It would seem then that 

 the best value of the cannery constraint would 

 be somewhere in between the capacity for a 

 maximum run and a minimum run and that this 

 might be investigated by employing the LP 

 model in a simulation setting. 



We have also emjjloyed egg and sex ratio con- 

 straints in our model. The egg constraints re- 

 quire information on fecundity and escapement. 

 There is not much information on fecundity but 

 this should be either easily obtainable or easily 

 approximated. Again, the static nature of the 

 LP problem makes it difiicult to attribute a val- 

 ue to an egg for years in the future. This is, 

 of course, important, emphasizing the need of 

 thinking not, as is conventionally done, in terms 

 of the forthcoming year, but rather in terms of, 

 for example, a series of years maximizing (c/. 

 Riff'enburgh, 1969) economic benefits. In other 

 words, the utilizers of resources may not be 

 interested (even though they may think they 

 are) in management on a year-to-year basis; 

 rather, they are interested in some long-run sat- 

 isfactory behavior of the time stream of economic 

 benefits. Alternatively, though, we must be 

 cautious of on-the-average management schemes 

 which are typically presented in fishery appli- 



137 



