Bi-Objective optimisation for synchronising replenishment and storage assignment: achieving energy efficiency and blocking avoidance in forward-reserve warehousing

The forward-reserve warehouse is an integrated robotic storage and picking system, which combines a reserve area equipped with an automatic storage/retrieval system and a forward area supported by a robotic mobile fulfilment system. Blocking in FRWs leads to energy dissipation and inefficiency, strongly affected by storage assignment and replenishment timeliness. However, existing research rarely focuses on systematically quantifying the benefits of replenishment and storage assignment synchronous optimisation with blocking avoidance. To address this gap, we formulate a new bi-objective model to improve both energy efficiency and timeliness, explicitly developing two tailored mathematical evaluation models for energy consumption and blocking. We design a novel ENSGA-II algorithm and integrate it with an LSTM network to solve the problem. Experimental results show that the ENSGA-II achieves superior distribution and faster convergence, as measured by HV/GD/IGD across all scales. We also conduct a comprehensive sensitivity analysis and discuss the results in detail. The findings reveal that a medium number of picking stations ensures the best balance between energy efficiency and timeliness objectives. The FRW achieves optimal performance when the station ratio between the forward and reserve areas remains in a medium range (e.g., 4/20 to 12/8). Additionally, SKU-type diversity in the forward area significantly affects system costs. Both low and high diversity reduce costs, while medium diversity (e.g., 0.5) results in the least benefits. In particular, small-scale warehouses benefit more from higher SKU-type diversity.