Production inventory model for two levels production with defective items and incorporating multi-delivery policy

Production inventory model plays a dominant role in production scheduling and planning. The EPQ model is commonly used by practitioners in the fields of production and inventory management to assist them in making a decision on optimum production and total cost. The total cost of production is dependent on production rate, demand rate and rate of defective items. This paper incorporates a multi‐delivery policy into a production inventory model with defective items in which two different rates of production are considered and it is possible that production started at one rate and after some time it may be switched over to another rate where 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, with the purpose of reducing the holding cost. A suitable mathematical model is developed and the optimal production lot size, which minimises the total cost is derived. The global optimal solution is derived and an illustrative example is provided and numerically verified. The validation of the result in this model was coded in Microsoft Visual Basic 6.0.