FISHERY BULLETIN: VOL. 71, NO. 4 



type) spawner-return curve, there will be an 

 additional loss due to decreased returns. Final- 

 ly, the linear programming formulation is es- 

 sentially static although Hillier and Lieberman 

 (1967) discuss certain techniques that are ap- 

 plicable to a limited class of stochastic and dy- 

 namic allocation problems. However, the only 

 such technique that would be readily applicable 

 to the fishery management case is chance con- 

 strained programming in which the admissibil- 

 ity of "soft" constraints, i.e., constraints which 

 may be violated with certain allowable proba- 

 bilities, is permitted. 



In the subsequent analysis an attempt is made 

 to simulate directly the inherently stochastic 

 and dynamic nature of the management of a 

 typical salmon fishery. A brief discussion of the 

 assumptions made as well as a comparison with 

 the linear programming formulation of Roths- 

 child and Balsiger will also be given. This com- 

 parison of methods should be considered to be 

 somewhat subjective and reflects, to a certain 

 extent, the author's own opinions and predilec- 

 tions. The interested reader may be able to arrive 

 at more meaningful comparisons and conclu- 

 sions after studying the respective analyses in 

 more detail. 



We will assume here gear of fixed selectivity 

 with regard to sexes and year classes. This 

 corresponds to the status quo with respect to 

 Bristol Bay although Rothschild and Balsiger 

 showed that an optimum allocation among the 

 various entities comprising the run was eco- 

 nomically advantageous, particularly in the 

 case of altered sex ratios. The fixed selectivity 

 assumption, which results in an allocation 

 based only on total numbers offish, is made prin- 

 cipally in the interests of tractability although 

 it is possible to generalize the loss functions and 

 probability densities to include the various indi- 

 vidual entities. 



Hillier and Lieberman list and discuss the 

 basic features which serve to characterize dy- 

 namic programming problems. The principal 

 characteristics will be repeated here, paraphrased 

 slightly, and it will be shown here and in the 

 subsequent analysis that the salmon fishery man- 

 agement problem conforms quite naturally to 

 the class of problems for which dynamic pro- 

 gramming is applicable. 



1) The problem can be divided into stages 

 with a policy decision required at each 

 stage. This is obviously the case in 

 Bristol Bay where the stages consist of 

 discrete fishing periods, for each of which 

 a management decision must be made. 

 Discreteness is not an essential feature, 

 however, since continuous time alloca- 

 tion problems may also be treated by 

 dynamic programming techniques. 



2) Each stage has associated with it a (pos- 

 sibly infinite) number of states. The state 

 of the system is somewhat difficult to 

 characterize precisely. It will be sufficient 

 to treat the state of the system, in this 

 case the salmon fishery, at the start of 

 any stage as reflecting the true state of 

 nature, e.g., run size, time profile, mi- 

 gration patterns, etc., as well as the ef- 

 fects of all previous policy decisions 

 through the preceding time period. Close- 

 ly related is: 



3) The effect of the policy decision at each 

 stage is to transform the current state 

 into a state associated with the next 

 stage. We will generalize this slightly 

 to include sequentially acquired data as 

 an additional quantity serving to char- 

 acterize the state of the system and the 

 transformation from one state to the 

 next. The remainder of the characteriz- 

 ing features enumerated by Hillier and 

 Lieberman are related to the very funda- 

 mental "Principle of Optimality," the 

 statement and discussion of which will 

 will be deferred until the section on 

 Discussion. 



The close correspondence of the concepts of 

 dynamic programming, and also the closely 

 related sequential statistical decision theory, 

 to the problem of salmon fishery management 

 suggests that together they provide potentially 

 powerful tools for the description and simula- 

 tion of such processes. A caveat is appropriate 

 here, however. In general there will be the loss 

 of a considerable portion of the economic "fine 

 structure" of the problem, particularly in com- 

 parison with the solution as a linear program. 

 The solution of the linear programming primal 



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