(471e) Using Machine Learning to Decompose Large-Scale MILP Supply Chain Models | AIChE

(471e) Using Machine Learning to Decompose Large-Scale MILP Supply Chain Models


Triantafyllou, N. - Presenter, Imperial College London
Bernardi, A., Imperial College London
Shah, N., Imperial College London
Papathanasiou, M., Imperial College London
Chimeric Antigen Receptor (CAR) T-cell therapies are an advanced medicinal therapy product that owing to their promising clinical results have led the way for the approval of numerous personalized cell therapy products by regulatory agencies [1]. Unlike typical cancer treatments, personalized medicine therapies are often characterized by patient-specific supply chains that consider bespoke parallel manufacturing lines and dedicated distribution nodes. CAR T-cell therapy manufacturing begins at specialized clinical centers, where the patient’s T-cells are isolated from the bloodstream in a procedure called leukapheresis (Fig. 1). The leukapheresis material is then shipped to the manufacturing facility, where it undergoes a series of processing steps including expansion, genetic modification, and quality control. Once the therapy is manufactured, it is shipped to the hospital for administration to the patient (Fig. 1). The supply chain involves the coordination and availability of different raw materials, as well as expert handling (e.g. cryopreservation) during the transportation of the samples and/or therapies. Ideally, all the processes involved should take place over a short time period (e.g. within 3 weeks). Simultaneously, the patient-specific nature of the supply chain, which suggests patient-specific manufacturing batches, places the patient schedule at the center [2]. This means that the available parallel lines in the manufacturing facilities and the delivery should be coordinated based on the clinical condition and location of each patient. At the moment, the CAR T-cell supply chain is mostly dependent on white-glove logistics and lacks a systematic way towards orchestrated decision-making. In that respect, process systems engineering tools can steer decision-making by aiding manufacturers, suppliers, and clinicians to optimally coordinate these tasks for thousands of patients simultaneously.

In this work, we present a hybrid model that describes the CAR T-cell supply chain based on Mixed Integer Linear Programming (MILP) and Artificial Neural Networks (ANNs). We utilize our previously developed MILP formulation that describes the CAR T-cell therapy supply chain and tracks each patient/sample/therapy throughout the CAR T-cell lifecycle [3]. The model is used for the identification of optimal supply chain network structures (planning), and the optimal coordination of therapies in the manufacturing facilities (scheduling), given randomized demand profiles of patients being treated at clinical centers in the UK throughout the year. From a modeling perspective, the patient-specific nature of these therapeutics leads to complex large-scale models that grow exponentially as the demand increases. Indicatively, for demands of 2000 therapies per year, the model consists of 26,975,374 linear constraints and 6,190,134 binary variables (Fig. 2). We, therefore, harness the potential of machine learning to decrease the computational complexity of the MILP model. The data-driven part of the model is responsible for strategic planning by forecasting the optimal supply chain structure [4–5] based on uncertain annual patient demand profiles. The MILP model becomes then a subproblem of the original MILP, as it is solved for a fixed supply chain network determined by the ANN and it is now solely responsible for the detailed scheduling of the patient samples to the predefined manufacturing facilities.

We assess and evaluate the performance of different artificial neural network (ANN) configurations including feed-forward neural networks and convolutional neural networks and train them to perform multi-label classification, where the labels are the candidate manufacturing facilities and the possibility of MILP infeasible solutions due to limited facility capacity. To ensure that the hybrid model is transferable, we train the ANNs using different probability distributions for the demand profiles to account for the demand uncertainty in the emerging cell and gene therapy sector. The results showcase a reduction of up to 81% and 83% in the number of linear constraints and binary variables, respectively, for examined (Fig. 2).

Keywords: supply chain optimization, MILP decomposition, machine learning


Funding from the UK Engineering & Physical Sciences Research Council (EPSRC) for the Future Targeted Healthcare Manufacturing Hub hosted at University College London with UK university partners is gratefully acknowledged (Grant Reference: EP/P006485/1). Financial and in-kind support from the consortium of industrial users and sector organizations is also acknowledged.


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[2] M. M. Papathanasiou, C. Stamatis, M. Lakelin, S. Farid, N. Titchener-Hooker, N. Shah, 2020, Autologous CAR T-cell therapies supply chain: challenges and opportunities?, Cancer Gene Ther., 27, 799-809.

[3] N. Triantafyllou, A. Bernardi, M. Lakelin, N. Shah, M. M. Papathanasiou, 2022, A digital platform for the design of patient-centric supply chains, Scientific Reports, 12, 17365.

[4] D. Goettsch, K. K. Castillo-Villar, M. Aranguren, 2020, Machine-Learning Methods to Select Potential Depot Locations for the Supply Chain of Biomass Co-Firing, Energies, 13, 6554.

[5] B. Abbasi, T. Babaei, Z. Hosseinifard, K. Smith-Miles, M. Dehghani, 2020, Predicting solutions of large-scale optimization problems via machine learning: A case study in blood supply chain management, Computers & Operations Research, 119, 104941.