A problem in optimal stock management
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We consider the planning of production over a prescribed period of time. More precisely, the problem is to minimize the cost integral (the time integral of the sum of the costs of production and storage) under the assumptions that the initial and final stocks are zero and that the production and the stock are nonnegative. Under this formulation, the problem can be considered as a Pontryagin-type problem with inequality constraints on the state variable and the control variable. We deduce from Pontryagin's maximum principle and Gamkrelidze's necessary conditions the existence and the uniqueness of an extremal trajectory.
KeywordsControl Variable Maximum Principle Inequality Constraint Stock Management Extremal Trajectory
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