Heuristics for the Assortment Planning Problem under Ranking-based Consumer Choice Models

We model a retailer’s assortment planning problem under a ranking-based choice model of consumer preferences. Under this consumer choice model each customer belongs to a type, where a type is a ranking of the potential products by the order of preference, and the customer purchases his highest ranked product (if any) offered in the assortment. In our model we consider products with different price/cost parameters, we assume that the retailer incurs a fixed carrying cost per product offered, a substitution penalty for each customer who does not purchase his first choice and a lost sale penalty cost for each customer who leaves the store empty-handed. In the absence of any restrictions on the consumer types, searching for the optimal assortment using enumeration or integer programming is not practically feasible. The optimal assortment has very little structure so that simple greedy-type heuristics often fail to find the optimal assortment and have very poor worst case bounds. We develop an effective algorithm, called the In-Out Algorithm, which always provides an optimal solution and show numerically that it is very fast, e.g., more than 10,000 times faster than enumeration on a problem with 20 products.