Dynamic Programming and Stochastic Control
Dynamic Programming and Stochastic Control
Introduction to Dynamic Programming
Introduction to Dynamic Programming
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Dynamic programming (DP) has shown itself to be an appropriate methodology for devising strategies of fisheries management. The present paper has several goals in the same area: to elucidate the process of formulation and its requirements; to illustrate how practical constraints may be incorporated into the problems; to examine the realities of computation; to show that models of other than an equilibrium nature may be of use and that finite horizon models are more realistic; to emphasize the relevance of some models, not previously employed; and to correct some abuses and misconceptions. We also make some effort to reveal practical benefits to real-world decision-making in this problem area occasioned by the nature of DP. Certain significant advantages have been overlooked by previous researches. Among the model improvements suggested are: backward formulations for more realistic decisions in both the cases of invertible and non-invertible transformations; the introduction of varying catch capacity and associated costs for changes and for underutilized capacity; the relevance of maximin objectives; and the computational implications of multispecies models. For elementary deterministic models possible sources of error are identified and recommendations made for dealing with certain of these. A careful presentation is made of the effort involved in handling one-dimensional problems with random variables of known probability distributions. In the absence of distributions adaptive models are mentioned, along with their attending complications and some empirical evidence promoting optimism in that case.