Abstract
We studied the optimal control of an inventory-production system with deterioration and defective items. Our objective is to develop an optimal inventory control model with Gamma distributed deterioration and beta distributed defective item. The explicit solution of the inventory-production model is derived under continuous review policy using the Pontryagin maximum principle. The optimality conditions are derived from the dynamic of the inventory-production level. Moreover, the simulation and sensitivity analysis results are illustrated numerically in this optimal control model with different demand patterns. The results of the inventory system are analyzed against different parametric values of Beta and Gamma distributions. As a result, the optimal total production strategy is increasing with increase the value of the Beta distribution parameter and decreasing with an increase in the value of the Gamma distribution parameter.
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