GPU-accelerated Multi-Wave Fix-and-Optimize Matheuristic for the Wave Order Picking Problem: Vectorized Instance Reduction and Fractional Treatment with Rigid and Flexible Regimes

Wave Order Picking selects, at each operational cycle, subsets of orders that maximize the ratio between processed volume and visited aisles. This paper evaluates the tractability of a Multi-Wave Fix-and-Optimize matheuristic combining vectorized GPU reduction in the Fix phase with fractional-objective handling in the Optimize phase. At each iteration, the method selects one wave, updates the backlog, and repeats the cycle until the time budget is exhausted or no processable orders remain. The Inverse Formulation and Dinkelbach’s method are compared under rigid and f lexible constraint regimes. Results indicate that the flexible regime is required for the operability of the Inverse Formulation under aggressive reduction, whereas Dinkelbach delivers higher-quality solutions at greater computational cost. GPU reduction enables large-scale instances that would be inaccessible without preprocessing.