Order and rack sequencing with a rack buffer area and order due dates in robotic mobile fulfillment systems.

With the increasing requirements for fulfillment timeliness in e-commerce and the wide application of robotic mobile fulfillment systems, the order picking process needs to balance rack reuse efficiency and on-time order completion. This paper studies an order and rack sequencing problem with a rack buffer area under order due dates. Given limited rack buffer capacity, known order requirements, and order due dates, we jointly optimize the order entry sequence, rack service sequence, and buffer retention decisions. To minimize rack movements and total weighted order tardiness, we formulate a mixed-integer programming model and develop a deadline-aware interactive heuristic with neighborhood search (DA-IHNS). The performance of the proposed model and algorithm is evaluated through randomly generated instances and comparative experiments. In the exact-solution validation, DA-IHNS matches the CPLEX objective on all instances with N = 4 and 6, while the mean relative difference is 3.33% for N = 8. For the main test instances with N = 30, 50, and 80, DA-IHNS achieves mean paired objective reductions of 83.65%-93.98% relative to IH and 79.86%-90.26% relative to EDD-IH, the two rule-based benchmarks. Across the tested synthetic settings, the mean advantage of DA-IHNS over the two rule-based benchmarks remains positive under all examined due-date tightness levels, while buffer capacity and the tardiness penalty coefficient affect the balance between rack reuse and order timeliness. This paper provides a reference for rack buffer configuration, order and rack sequencing, and tardiness control in e-commerce warehousing.