A method and apparatus for maximizing the total amount of blood processed during an apheresis procedure by optimizing the concentration of anticoagulant in a donor/patient and the associated extracorporeal tubing set is provided. A simplified model of an anticoagulant accumulation in a donor/patient's body is used to calculate an optimal anticoagulant infusion rate profile to the donor/patient during a blood processing procedure. A maximum acceptable anticoagulant concentration in the donor/patient acts as an upper limit on the rate at which anticoagulant may be infused to the donor/patient using the optimized infusion rate profile. A minimum acceptable anticoagulant level acts as a lower limit in optimally controlling the anticoagulant concentration in the extracorporeal tubing set. Both the maximum acceptable anticoagulant level in the donor/patient and the minimum acceptable anticoagulant level in the extracorporeal tubing set may be customized for a specific donor/patient thereby allowing the optimized infusion rate profile and the extracorporeal tubing set anticoagulant concentration to be customized for the specific patient.