Minimum Buffer Capacity for Preserving Performance in Fulfillment Scheduling

A buffer requirement inferred from one optimized schedule can depend on the solver’s choice among equally good schedules. This study develops a mixed-integer model of batching and picking-packing scheduling with effective order deadlines and instantaneous whole-batch admission and a target-constrained model that minimizes waiting space over all schedules attaining the certified relaxed lexicographic optimum; equivalent event states reduce repeated matrix coefficients. Generated experiments used eight exact demand families, 24 search families, and a scalability extension with 8 to 192 orders. Minimum-buffer boundaries were verified for 30 of 32 exact configurations, requiring 0–3 positions, and the selected relaxed schedule exceeded this minimum in 16 cases. One position below the minimum, the component lost was the late-order count in 3, tardiness in 7, and picking effort in 10 of 20 configurations; raising a positive buffer from one to two positions never reduced late orders. Certification extended to 10 orders within 180 s per call. The sparse formulation reduced nonzeros by 70.19–82.31%. Guided search won 56 and lost 148 comparisons against ILS/VND, the compact-repair package won 66 and lost 132 against guided search, and at 96 and 192 orders with 30 s budgets, guided search won 17 and lost 16. Under one-tick duration deviations, the certified minimum was exceeded in 38.8% of re-timed samples, and one additional position reduced this to 4.9%. The conclusions are limited to the tested generated configurations.