Production inventory model for two levels of production with defective items and shortages

In this paper, a production inventory model with defective items in which two levels of production are considered and it is possible that production started at one rate and after some time it may be switched over another rate such a situation is desirable in the sense that by starting at a low rate of production, a large quantum stock of manufacturing items at the initial stage is avoided, leading to reduction in the holding cost. A suitable mathematical model is developed and the optimal production lot size which minimizes the total cost is derived. The optimal solution is derived and an illustrative example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.