Profitability analysis of free upgrade policy

We consider a firm selling two similar products with different prices. When the lower-priced product is out of stock, the firm supplies the customer a higher-priced product with the lower-priced product price. The policy is called free upgrade. In this paper, we study the profitability of such policy. We formulate the problem as a two-product newsvendor problem, and prove that the firm achieves more profit with the free upgrade policy. We propose a simulation algorithm to find the solution and demonstrate our findings with some numerical examples.