This paper studies a joint inventory and fulfillment problem for an omnichannel retailer under stochastic demand. The retailer first allocates inventory across fulfillment locations and then decides how to fulfill customer orders after demand is realized. We formulate the problem as a two-stage stochastic optimization model that minimizes expected holding, fulfillment, and penalty costs. To reduce the computational effort, we use a scenario reduction method based on a modified Wasserstein distance that accounts for the cost structure of the problem. Numerical results show that this method achieves lower costs than the benchmark algorithm.