Production inventory model for two-level production with deteriorative items and shortages

Abstract

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 decision on optimum production and total cost. The total cost of production is dependent on production rate, demand rate, and rate of deteriorative items. In this paper, a production inventory model with deteriorative items in which two different rates of productions 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. The variation in production rate provides a way resulting consumer satisfaction and earning potential profit. Two models are considered; the production inventory model without shortages is studied first and with shortages is investigated next. A suitable mathematical model is developed, and the optimal production lot size which minimizes the total cost is derived. The global 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.