Order-Optimal Correlated Rounding for Fulfilling Multi-Item E-Commerce Orders

Problem definition: We study the dynamic fulfillment problem in e-commerce, which incoming (multi-item) customer orders must be immediately dispatched to (a combination of) centers that have required inventory. Methodology/results: A prevailing approach this problem, pioneered by Jasin and Sinha 2015 , has been write a “deterministic” linear program dictates, for each item an multi-item order from particular region, how frequently it should center (FC). However, dispatching items way satisfies these frequency constraints, without splitting across too many FCs, is challenging. identified as correlated rounding proposed intricate scheme they proved was suboptimal factor of at most [Formula: see text] on q-item order. This paper provides, our knowledge, first substantially improved text]. provide another sparse networks, d if stored FCs. show both guarantees tight terms dependence q or d. Our schemes are simple fast, based intuitive idea; wait FCs “open” random times but observe them “dilated” time scales. also implies new randomized method classical Set Cover could general interest. Managerial implications: numerically test under same realistic setups find improve runtimes, shorten code, robustly performance. code made publicly available online. History: selected Fast Track M&SOM Journal 2022 MSOM Supply Chain Management SIG Conference. Funding: research partially funded grant Amazon.com Inc., awarded through collaboration with Columbia Center AI Technology (CAIT).