Deep Stacking Kernel Machines for the Data-Driven Multi-Item, One-Warehouse, Multiretailer Problems with Backlog and Lost Sales

The data-driven, multi-item, one-warehouse, multiretailer (OWMR) problem is examined by leveraging historical data and using machine learning methods to improve the ordering decisions in a two-echelon supply chain. A deep stacking kernel machine (DSKM) and its adaptive reweighting extension (ARW-DSKM), fusing deep learning and support vector machines, are developed for the data-driven, multi-item OWMR problems with backlog and lost sales. Considering the temporal network structure and the constraints connecting the subproblems for each item and each retailer, a Lagrange relaxation-based, trilevel, optimization algorithm and a greedy heuristic with good theoretical properties are developed to train the proposed DSKM and ARW-DSKM at acceptable computational costs. Empirical studies are conducted on two retail data sets, and the performances of the proposed methods and some benchmark methods are compared. The DSKM and the ARW-DSKM obtained the best results among the proposed and benchmark methods for the applications of ordering decisions with and without censored demands and with and without new items. Moreover, the implications in selecting suitable, that is, prediction-then-optimization and joint-prediction-and-optimization, frameworks, models/ algorithms, and features are investigated.