Coordinated Inventory Stocking and Assortment Personalization

We study a joint inventory stocking and assortment personalization problem. We have access to a set of products that can be used to stock a storage facility with limited capacity. At the beginning of the selling horizon, we decide how many units of each product to stock. Customers of different types with different product preferences arrive into the system over the selling horizon. Depending on the remaining product inventories and the type of the customer, we offer a personalized product assortment to the arriving customer. The customer makes a choice within the assortment according to a choice model. Our goal is to choose the stocking quantities at the beginning of the selling horizon and to find a policy to offer a personalized assortment to each customer so that we maximize the total expected revenue over the selling horizon. Our work is motivated by online platforms making same-day delivery promises or selling fresh groceries, which require operating out of an urban warehouse to be close to customers, but allow the flexibility to personalize the assortment for each customer. Finding a good assortment personalization policy requires approximating a high-dimensional dynamic program with a state variable that keeps track of the remaining inventories. Making the stocking decisions requires solving an optimization problem that involves the value functions of the dynamic program in the objective function. We give an approximation framework for the joint inventory stocking and assortment personalization problem. Using our framework, we obtain a $\frac{1}{4}(1-\frac 1e)$-approximate solution when the customers choose under the multinomial logit model. Under a general choice model, letting $n$ be the number of products and $K$ be the total number of units we can stock, we give a \mbox{$(1- (\sqrt{2}+1) \sqrt[3]{\frac nK})$}-approximate solution, which is asymptotically optimal for large storage capacity. To our knowledge, these are the first guarantees for our problem class. Our computational experiments on synthetically generated datasets, as well as on a real-world supermarket dataset, show that our approximation framework performs well against both upper bounds on the optimal performance and other possible heuristics