Two-dimensional warranty period optimization considering the trade-off between warranty cost and boosted demand

•The trade-off between boosted demand and cost is considered in 2D warranty design.•Demand based on attractiveness index is used to describe the boosted sales volume.•A profit model is proposed to estimate the manufacturer’s expected profit.•The optimal 2D base warranty periods for three different cases are derived.•Effects of different usage rates of customers in 2D warranty are considered.