Inverse Optimization for Warehouse Management

Day-to-day operations in industry are often planned in an ad-hoc manner by managers, instead of being automated with the aid of mathematical optimization. To develop operational optimization tools, it would be useful to automatically learn management policies from data about the actual decisions made in production. The goal of this study was to investigate the suitability of inverse optimization for automating warehouse management on the basis of demonstration data. The management decisions concerned the location assignment of incoming packages, considering transport mode, classification of goods, and congestion in warehouse stocking and picking activities. A mixed-integer optimization model and a column generation procedure were formulated, and an inverse optimization method was applied to estimate an objective function from demonstration data. The estimated objective function was used in a practical rolling horizon procedure. The method was implemented and tested on real-world data from an export goods warehouse of a container port. The computational experiments indicated that the inverse optimization method, combined with the rolling horizon procedure, was able to mimic the demonstrated policy at a coarse level on the training data set and on a separate test data set, but there were substantial differences in the details of the location assignment decisions.