Optimal production run length for products sold with warranty

The paper studies the optimal production run length for a deteriorating production system. The optimal warranty cost is determined by a balance between the warranty cost of the manufacturer and the buyer during its warranty period. It is assumed that the elapsed time until the production process shift is age dependent and arbitrarily distributed. The objective is to minimize the total cost per item for determining the optimal production run length and the length of time when backorder is replenished. It shows that there exists a unique optimal production run length to minimize the expected total cost.