  In this paper, we extend the model of Gao and Su (2016) and consider an
omnichannel strategy in which inventory can be replenished when a retailer
sells only in physical stores. With "buy-online-and-pick-up-in-store" (BOPS)
having been introduced, consumers can choose to buy directly online, buy from a
retailer using BOPS, or go directly to a store to make purchases without using
BOPS. The retailer is able to select the inventory level to maximize the
probability of inventory availability at the store. Furthermore, the retailer
can incur an additional cost to reduce the BOPS ordering lead time, which
results in a lowered hassle cost for consumers who use BOPS. In conclusion, we
found that there are two types of equilibrium: that in which all consumers go
directly to the store without using BOPS and that in which all consumers use
BOPS.
