Conference Agenda

We study the dynamic retail assortment problem with two sources of stochasticity. In particular, we consider stochasticity in terms of the products purchased by the customers, and in terms of replenishment, i.e., stochasticity regarding the newly incoming products. In addition, we account for the fact that the products suffer a loss in value over time, whereby we compare multiple different types of value loss functions. The considered setting is motivated by a joint project with the German car manufacturer BMW. We formulate the stochastic dynamic assortment problem as dynamic program and prove it to be NP-hard. Since the stochastic dynamic programming algorithm is intractable for instances of medium to large size in our setting, we additionally propose a heuristic solution approach that is based on the idea of solving the static problem per period using some base policy as well as an approximate dynamic programming based solution approach called Truncated Stochastic Rollout. We conduct extensive numerical studies to compare the proposed solution approaches for various base policies and obtain managerial insights regarding the choice of the most suitable value loss function.

We propose a new problem to the assortment optimization literature: the (constrained) assortment problem under the nested logit model with heterogeneous customers. So far, only nested logit models with homogenous customers are considered (i.e., each customer evaluates the assortment similarly). In contrast, empirical nested logit product choice models almost always consider customer characteristics like income, age, and location, for example. We account for this heterogeneity in our new problem and show that the resulting problem is (i) NP-hard, (ii) non-linear, and (iii) non-convex. However, we present a MIP reformulation based on a piece-wise linearization that yields a (1+e)/(1-e) approximation. We develop a lower bound for the number of breakpoints for the piece-wise linearization given an arbitrary e. First numerical studies show promising results.

Consumers often search for product information to resolve valuation uncertainties before purchasing. Since they cannot examine all alternatives because of their limited information-acquisition ability, they conduct a two-stage search, called consider-then-choose. In the first stage, they decide a consideration set which is a subset of all available alternatives, In the second stage, they resolve the uncertainty about all products in this consideration set and choose the one with the highest utility. We extend assortment optimization under consumer choice behavior by incorporating consumer anticipated regret into the consideration set formation. Specifically, after purchase, when consumers passively notice whether an unconsidered product is more suitable than the purchased one or not, they might regret having decided a small consideration set and not devoted enough effort to searching or regret having decided a large consideration set and devoted too much effort to searching. We show that if consumers anticipate the post-purchase regret when deciding a consideration set, in some conditions the firms should offer some products that consumers will not consider. Based on this finding, we develop fully-polynomial approximation schemes or exact conic formulation for a variety of assortment problems under the consider-then-choose models with anticipated regret. For the joint assortment planning and pricing problem with homogeneous consumers, we show that the intrinsic-utility ordered assortment and the price policy that charges the same price for the products except at most those outside the consideration set and one within it are optimal.