In this paper, we explore dynamic ad allocation with limited slots upon each customer arrival for e-commerce platforms when customers follow a choice model to click the ads. Motivated by the recent advocacy for the algorithmic fairness, we adjust the value from advertising by a general fairness metric evaluated with the click-throughs of different ads and customer types. We propose a two-stage stochastic program and design a debt-weighted offer-set algorithm to solve the online problem.

Motivated by the middle-mile delivery operations of an e-retailer, we consider the problem of designing a sparse graph that supports a large matching after random node deletion. We study three families of sparse graph designs (namely, Clusters, Rings, and Erdos Renyi graphs) and show that their performances are close to the complete graph. We test our theory using real data and conclude that adding a little flexibility to the routing network can significantly reduce transportation costs.

We provide the first improvements to the celebrated correlated rounding procedure of Jasin and Sinha (2015), which has become a fundamental problem in multi-item e-commerce order fulfillment.

We derive rounding schemes with guarantees of $1+\ln(n)$ and $d$, where $d$ is the maximum number of fulfillment centers containing an item.

The first of these improves their guarantee of ~n/4 by an entire order of magnitude in terms of the dependence on $n$.

We also show our guarantees to be tight.