Optimal production run length for products sold with warranty in a deteriorating production system with a time varying defective rate under allowable shortages

This paper develops a mathematical model for determining an optimal production run length for a deteriorating production system with allowable shortages for products sold with a free minimal repair warranty period. The length of the warranty period is dependent upon the quality of the product. To reduce warranty cost, a shorter production run length may be desirable. It may result in a higher setup cost and a higher restoration cost, but possibly produce fewer non-conforming items. A longer production run may result in a lower setup cost, but possibly produce a large number of nonconforming items. The objective of the study is to minimise the total cost per item for determining the optimal production run length, the optimal warranty period and the length of time when the backorder is replenished. It is shown that there exists a unique optimal production run length to minimise the expected total cost. Numerical examples are provided to illustrate the features of the model. A sensitivity analysis is performed with respect to the parameters' changes on the decision variables and the objective function.