Abstract
The optimal control model of the production-inventory system has investigated in several past studies, but without taking into account the integer condition. This study suggested a new approach to find the integer solution of production-inventory control model under periodic review policy. A new approach is based on the modified some equations of Pontryagin maximum principle that used to find the solution of the non-integer model. Our numerical results showed the efficiency of the new approach by saving the paths of inventory level and production rate up to reach its goals over time. The total penalty costs of the model were the same, despite a difference in the values of initial inventory level. Also, we testified a new approach by formulating the quadratic programming problem of the production-inventory system. The solution was the same for the two problems; quadratic programming and new approach.
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