Improved Fashion Buying with Bayesian Updates

We focus on the problem of buying fashion goods for the "big book" of a catalogue merchandiser. This company also owns outlet stores and thus has the opportunity, as the season evolves, to divert inventory originally purchased for the big book to the outlet store. The obvious questions are: (1) how much to order originally, and (2) how much to divert to the outlet store as actual demand is observed. We develop a model of demand for an individual item. The model is motivated by data from the women's designer fashion department and uses both historical data and buyer judgement. We build a stochastic dynamic programming (DP) model of the fashion buying problem that incorporates the model of demand. The DP model is used to derive the structure of the optimal inventory control policy. We then develop an updated Newsboy heuristic that is intuitively appealing and easily implemented. When this heuristic is compared to the optimal solution for a wide variety of scenarios, we observe that it performs very well. Similar numerical experiments show that the current company practice does not yield consistently good results when compared to the optimal solution.