Assortment planning with premium services

Abstract

We consider the assortment planning problem of an online retailer who offers products with multiple service types which differ in delivery time. We assume that customers make their choices according to the multinomial logit model. Our objective is to find the assortment of each service type which maximizes the expected revenue. Service types with faster delivery time are stored in fulfillment centers closer to the customers. The retailer gains less profit from the products offered with faster delivery due to the higher storage and transportation costs; however, faster delivery increases the popularity of the products. Therefore, delivering products faster has a trade off between higher demand and lower revenue. We provide a linear program to solve this problem. We also find structural properties of the optimal assortment and construct a polynomial time algorithm based on the structure of the optimal solution, along with an alternative method developed by modifying an existing algorithm. We also study another version of the problem where the retailer incurs a fixed cost for including a product in the assortment. We analyze the complexity of the problem for two structures of fixed cost. In the first one, the fixed cost is the same for all products. In this case, we show that the problem can be solved in polynomial time. In the second one, the fixed cost is different for all products and the problem is NP-complete. Finally, we conducted a numerical study in which we analyzed the effects of the problem parameters on the optimal assortment.