Optimal inventory management with buy-one-give-one promotion

Recently, the Buy-One-Give-One (BOGO) model, where the firm donates one unit of its product for every unit purchased, has emerged as a viable option to practice corporate social responsibility. Despite growing public attention to the BOGO model, optimal inventory management and profitability associated with BOGO has not yet been explored adequately in the academic literature. Under the BOGO promotion, inventory management naturally becomes a key decision, since the firm has to produce an extra unit for each unit sold. In this article, we examine optimal inventory management of the BOGO model under stochastic demand and compare it to the standard newsvendor model as well as a model with cash donation. Analogous to the standard newsvendor model, we clearly define the BOGO fractile and optimal stocking quantity. We show that, counterintuitively, it is not necessarily optimal to produce more units under BOGO, due to the trade-off between give-away commitment and reduced product margin. Moreover, although the BOGO model invariably yields a lower profit than the classic newsvendor model or cash donation model if demand remains the same, there often exists a certain level of positive demand shift that renders BOGO more profitable, which helps explain growing presence of BOGO in the marketplace.