Assortment Optimization with Multinomial Logit Choice Model in Multi-Channel Retailing

We analyze the assortment optimization problem faced by a monopolistic firm selling n substitutable products in both store and online channels. In our problem, a subset of products (the assortment) are offered in store while all products are sold online. Compared to purchasing in store, purchasing online would lead to an additional cost to customers in the form of a delivery fee or waiting cost. Interestingly, we find that the introduction of online channel hurts the firm and renders the firm to offer more products in store. However, with capacity constraint in store, the online channel, which enables customers to purchase high profit-margin products that are removed out of the assortment due to capacity limit, might benefit the firm