Application of mixed-Integer linear programming to cost optimization in enteral nutrition: a multi-patient comparative study

Introduction Manual prescription of enteral nutrition (EN) requires consideration of nutritional/economic factors, making it susceptible to inconsistent nutritional compliance and inefficient resource utilization.Objectives We evaluated whether a Mixed-Integer Linear Programming (MILP) model could improve nutritional adequacy/cost-effectiveness of EN prescriptions compared with manual prescriptions .Methodology Thirteen practitioners independently prescribed enteral nutrition regimens for clinical scenarios, generating 39 practitioner–scenario instances. Their prescriptions were compared with solutions obtained using MILP model that optimized formula selection while satisfying practitioner-defined nutritional requirements. Compliance, prescription cost, and cost efficiency were evaluated using paired statistical tests, stratified bootstrap counterfactual analysis, sensitivity analysis, and quantitative exploration of relationships between nutritional requirements and cost.Results The MILP model achieved 100% compliance across instances, whereas manual prescriptions achieved full compliance in only 20.5% of cases (p < 0.001). Optimized prescriptions reduced costs by 14.7%, increasing to an 21.1% after adjusting manual prescriptions to full compliance through counterfactual analysis. Quantitative analyses showed that protein requirements were the principal determinant of prescription cost and that MILP produced more systematic/economically efficient formula selection than manual prescribing.Practical implications Proposed model provides practical decision-support tool capable of improving nutritional accuracy while reducing costs, supporting consistent and economically efficient ENprescribing.