This paper is concerned with the development of an inventory-production model for a special class of generalized extreme value, that is, gumbel distributed deterioration items. The production system with inventory-level-dependent demand is considered and Pontryagin maximum principle is used to determine the optimal control, which is the production rate that minimizes the optimal control model, while satisfying the system dynamics. The necessary optimality conditions are also derived in this case. It is then illustrated with the help of examples.
Key words: Inventory-production systems, gumbel distributed deterioration, optimal control, pontryagin maximum principle.
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