Patients undergoing surgery frequently require blood transfusions both during and after the operation. Patients often have their own blood collected for this purpose over a standard 3- to 4-week presurgical period. However, a large percentage of patients are not able to pre-donate their own blood for transfusion. Agents that can facilitate self-donation in less time than the conventional 3 weeks before surgery and reduce the need for transfusions from others, may improve the overall safety of surgery. This is a randomized, double-blind, placebo-controlled, parallel group, multicenter study to determine whether epoetin alfa will enable the self-donation of at least 4 units of blood in the shortened presurgical time period of 11 days before surgery (which is a shorter period of time than the conventional 3 week blood donation period before surgery) in patients who are not anemic and who are undergoing orthopedic, heart and blood vessel, or breast reduction surgery. The study consists of a 7-day screening period during which patients will be tested for eligibility for the study; an 11-day treatment, blood collection, and evaluation period that ends on Day 11 (the day of surgery); and a post-surgery follow-up period beginning on the evening of Day 11 and ending with a final study visit at the time a patient is discharged from the hospital after surgery. Patients will be randomly assigned to one of four treatment groups: epoetin alfa 300 units/kilogram (U/kg), epoetin alfa 600 U/kg, placebo to match the volume of epoetin alfa 300 U/kg, or placebo to match the volume of epoetin alfa 600 U/kg, given by injection into a vein. Twice as many patients will receive treatment with epoetin alfa as will receive treatment with placebo. A total of 3 doses of study drug will be administered before surgery; one dose will be given on each of Days 1, 4, and 7 of the study. Additionally, from Day 1 to the day of hospital discharge, all patients will receive 200 milligrams of iron and 5 milligrams of a folate supplement daily by mouth to help the body to increase the production of red blood cells. On Day 1, before the first dose of study medication, one unit of blood will be collected from each patient and stored for self-donated blood transfusion. An additional unit of blood will be obtained from each patient (before the administration of study drug) and stored for self-donated blood transfusion on each of Days 4, 7, and 11 (the day of surgery, before the operation); this will only be performed if the patient's hemoglobin is >11.0 g/dL. If a patient's hemoglobin is lower than 11.0 g/dL, no blood will be collected from that patient on these days, although study drug will continue to be given. Normovolemic hemodilution (NVHD) will be performed on Day 11, the day of surgery, before and during the operation. Safety evaluations include laboratory tests, vital signs, and the recording of adverse events. Effectiveness will be assessed by comparing the number of self-donated units of blood obtained within 11 days among the 4 treatment groups, and secondarily by comparing the change in hemoglobin, immature red blood cells, and erythropoietin (the red blood cell stimulating hormone) levels in the blood among the 4 treatment groups from before the start of study to the end of the study. The study hypothesis is that in an abbreviated time period before surgery (11 days), epoetin alfa will stimulate the generation of 4 units of self-donated blood in patients who are not anemic who are undergoing orthopedic, heart and blood vessel, or breast reduction surgery. Epoetin alfa 300 units/kilogram (U/kg), epoetin alfa 600 U/kg, or placebo, by injection into a vein; given on each of Days 1, 4, and 7 of the study.