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In this paper, a production inventory model is developed by considering two different rates of production with exponential demand rate. It is assumed that rate of deterioration is linear function of time and shortages are not allowed. Production rates are different in two different phases of production. Likewise demand rate also changed. Optimal production inventory model is developed to determine the optimal production quantity and minimized the total cost, i.e. minimized the sum of production cost, setup cost, holding cost and deterioration cost. A numerical example for the verification of the problem is also given. Sensitivity analysis is also carried out for the different parameters.

Two level production inventory model with exponential demand and time dependent deterioration rate