Optimal ordering policies when the supplier provides a progressive interest scheme

In fact, most credit card issuers (or home equity banks) frequently offer cardholders (or customers) a teaser interest rate (say, I₁), which is significantly lower than the regular interest rate of I₂ (with I₂ > I₁) for only 6 months or a year (say, M₂) to lure new customers from their competitors. Consequently, the customer faces a progressive interest charge from the bank. If the customer pays the outstanding balance by the grace period (say, M₁ which is generally 25 days), then the bank does not charge any interest. If the outstanding amount is paid after M₁, but by M₂ (with M₂ > M₁), then the bank charges the customer the teaser interest rate of I₁ on the unpaid balance. If the customer pays the outstanding amount after M₂, then the bank charges the regular interest rate of I₂. In this paper, we first establish an appropriate EOQ model for a retailer when the bank (or the supplier) offers a progressive interest charge, and then provide an easy-to-use closed-form solution to the problem.