A Mixed-Integer Linear Programming Model for Capacitated Lot-Sizing and Scheduling in Pharmaceutical Manufacturing with Sequence-Dependent Cleanings and Shelf-Life Constraints: A Real-World Case Study

In secondary pharmaceutical packaging lines, operational scheduling is heavily constrained by Current Good Manufacturing Practice (cGMP) guidelines, validation standards, and perishable shelf-life profiles. Production transitions between distinct active pharmaceutical ingredients (APIs) or varying dosage forms require sequence-dependent line clearances and specialized sanitization procedures, resulting in significant machine downtime and variable changeover costs. Simultaneously, finished pharmaceutical products exhibit strict shelf-life limitations, exposing excessive lot inventory to chemical degradation, obsolescence, and costly mandatory destruction. This paper proposes a discrete-time Mixed-Integer Linear Programming (MILP) formulation for the multi-item, multi-period Capacitated Lot-Sizing and Scheduling Problem (CLSP) in pharmaceutical secondary manufacturing. The model jointly determines production lots, line clearance sequences, overtime capacity allocation, and inventory aging balance across a multi-week planning horizon. Demonstrated on an empirical industrial case study from an active pharmaceutical facility, computational results show that optimizing changeover sequences eliminates stock expiration and substantially reduces total operational and setup-related downtime compared to conventional scheduling practices.