Ordering and Ranking Products for an Online Retailer

In e-commerce, product ranking and display affect customer choices and sales as items placed in top positions receive significantly more clicks than items placed at the bottom. For retailers who sell items from the inventory they have purchased and owned, product ranking has a profound impact on future demand as well as the amount of inventory to be ordered before the selling season starts. However, in many cases, inventory ordering and product ranking decisions are made separately at different times by different functional departments with little or no coordination. One of the main challenges is that the complexity of product ranking problem grows exponentially as the number of products on display increases. In this paper, we show that it is important to consider inventory ordering and product ranking decisions as a joint problem, and study how this can be done. In a problem where products are ordered and ranked only once, we show that the joint ordering-and-ranking problem can be reformulated into an easier assignment problem built on a sequence of newsvendor solutions, and thereby there exists a polynomial-time algorithm that generates an optimal ordering-and-ranking policy. We then consider a problem where product rankings can be updated over time, the above algorithm that uses static ranking is indeed asymptotically optimal. We also provide an algorithm with ranking updates, which performs better than the static ranking algorithm in both asymptotic and non-asymptotic settings. We next extend to the problem where a retailer utilizes pre-season sales (or pre-orders) to learn about future demand. Building on our analytic results, we propose a two-phase online learning algorithm with a theoretical performance guarantee. Using computational experiments, we show that our proposed algorithms significantly outperform benchmarks including the current split decision-making practices, can be scaled up to make ranking and ordering decisions with a large number of products, and generate high-quality solutions even when the underlying customer choice model is misspecified.