Optimal production run length for products sold with warranty in an imperfect production system with allowable shortages

This paper investigates an imperfect production system with allowable shortages for products sold with free minimal repair warranty. We seek to minimize the total cost per item through optimal determination of the production run length and the time length when backorder is replenished. From the optimality conditions of the proposed model, an efficient algorithm is developed to find the optimal solutions. Also, numerical examples are provided to illustrate the features of the model and sensitivity analyses are performed with respect to the parameters' changes on the decision variable and objective function.