The forecast horizon is defined as a property of a class of functions. Some general existence conditions are derived. The results are applied to the process x(·) described by the differential equationẋ(t) = e(t,u(t)) - f(t,x(t)), ,where e, f are nonnegative and increasing in the second variable, and u(·) denotes a control variable.A cost functional is associated with the process and the control. The cost is characterized by three functions: g(t,u), h(t,x), k(x), and a time interval. A class of...
A production inventory problem with limited backlogging and with stockouts is described in a discrete time, stochastic optimal control framework with finite horizon. It is proved by dynamic programming methods that an optimal policy is of (s,S)-type. This means that in every period the policy is completely determined by two fixed levels of the stochastic inventory process considered.
This paper deals with an unreliable manufacturing system in which limited backlog is allowed. An admissible production policy is described by two decision parameters: upper and lower hedging points. The objective is to find the optimum hedging points so as to minimize the long run average expected cost under an additional condition. The condition expresses a constraint for the limiting probability of the event that the system stays at the lower hedging point, which corresponds to a limit of backlog....
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