Sustainable robotic mobile fulfillment system with pod repositioning in warehousing 5.0

This paper explores energy-efficient operations in Robotic Mobile Fulfillment Systems (RMFS) by jointly optimising order assignment, pod selection, and pod repositioning under a wave picking strategy. In line with Warehousing 5.0 objectives, the aim is to reduce energy consumption through the intelligent coordination of robotic movements while ensuring workload balance and operational feasibility. We first propose a multi-period, integrated optimisation model with perfect foresight of future demand, serving as a theoretical benchmark. Recognizing the limitations of this assumption in practice, we develop three alternative methods: (i) a two-phase myopic approach that decouples assignment and repositioning; (ii) an integrated myopic model that solves them jointly; and (iii) a two-stage stochastic programming model that captures demand uncertainty through scenario sampling. To enhance scalability, we introduce a local search matheuristic that improves myopic solutions by exploring repositioning options under expected demand. Computational experiments based on realistic RMFS configurations demonstrate the value of incorporating pod repositioning into the decision process. Results show that the integrated and stochastic models yield notable energy savings compared to sequential approaches, offering actionable insights for sustainable automation in warehouse operations.