A Three-Stage Integer-Programming Framework for Minimum-Workforce Scheduling at a Logistics Sorting Center with Optimality Guarantees

Abstract

Staff scheduling at a logistics sorting center must reconcile time-varying parcel arrivals, intraday service commitments, heterogeneous within-shift capacity, and monthly roster rules. We propose the Three-Stage Integer-Programming Scheduling Framework (TS-ISF). Stage 1 is an hourly-causal, same-day-clearing baseline in which parcel arrivals are exogenous data and backlog, processing, and the resulting staffing requirement are endogenous. Stage 2 independently refines the daily problem by assigning every worker exactly one low-throughput hour through linear worker-subgroup variables and by imposing the morning deadline. Stage 3 converts the resulting daily requirement vector into the minimum monthly workforce size. The aggregate flow formulation does not identify parcel-level order; instead, under homogeneous parcels it admits a FIFO-compatible realization. On the accepted 30-day real-data run, Stage 1 requires 10,791 worker-days, the full Stage 2 model requires 11,859 worker-days, and Stage 3 requires 581 workers. The Stage 2 increase is the joint effect of the low-throughput-hour and deadline restrictions, not a deadline-only effect. Exact HiGHS termination records and matched Stage 3 bounds provide distinct computational and analytical evidence, while a formulation-matched monolithic model confirms the decomposition objective under stated separability conditions. Controlled synthetic instances are used only as internal stress tests. TS-ISF therefore provides a reproducible and auditable basis for case-specific sorting-center workforce planning.