Long-term scheduling models for multi-stage biopharmaceutical processes with effective inventory planning and early delivery
Vaibhav Kumar & Munawar A. Shaik
What the paper says
In this work, we propose two mixed-integer linear programming (MILP) scheduling models using unit-specific event-based time representation for the continuous production of biopharmaceuticals. These models explore different delivery strategies for final products, depending on whether early delivery is permitted and the choice of delivery rates. The first model (M1) incorporates four key features: (i) sequencing of final product storage, (ii) inventory planning based on instantaneous delivery on the due date or a finite and known delivery rate, (iii) improved bounds, and (iv) enhanced shelf-life constraints. It ensures that products produced before the due date are fully stored until the deadline, guaranteeing on-time or late delivery with precise inventory control. While some literature models unintentionally allow early delivery, thus reducing storage costs and boosting profits, our second model (M2) intentionally supports reliable early delivery. Built on a finite but unknown delivery rate, M2 includes (i) improved material balances, (ii) refined sales constraints, (iii) clearer penalty structures, and (iv) an improved objective function. Both the models are designed with real-world applications in mind. We implemented them using eight benchmark examples from the literature (four per model), demonstrating superior performance and practical benefits.
Evidence weight
Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40
| F · citation impact | 0.50 × 0.4 = 0.20 |
| M · momentum | 0.50 × 0.15 = 0.07 |
| V · venue signal | 0.50 × 0.05 = 0.03 |
| R · text relevance † | 0.50 × 0.4 = 0.20 |
† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.