Recycled incomplete identification procedures for blood screening

The operation of blood banks aims at the cost-efficient supply of uncontaminated human blood. Each unit of donated blood goes through multiple testing for the presence of various pathogens which are able to cause transfusion-transmitted diseases. The blood screening process is comprised of two phases. At the first phase, blood units are screened together in pooled groups of a certain size by the ELISA (Enzyme Linked Immuno-Sorbent Assay) test to detect various virus-specific antibodies. The second phase of the screening process is conducted by PCR (Polymerase Chain Reaction) testing of the individual blood units of the groups found clean by the initial ELISA phase. Thousands of units of donated blood arrive daily at the central blood bank for screening. Each screening scheme has associated testing costs and testing times. In addition, each blood unit arrives with an expiration date. As a result, the shorter the testing time, the longer the residual lifetime that is left for the blood unit for future use. The controller faces a natural and well-motivated operations management problem. He will attempt to shorten the testing period and reduce the testing costs without compromising too much on the reliability. To achieve these goals, we propose a new testing procedure that we term Recycled Incomplete Identification Procedure (RIIP). In RIIP, groups of pooled blood units which are found contaminated in the ELISA test are divided into smaller subgroups and again group-tested by ELISA, and so forth, until eventually the PCR test is conducted for those subgroups which are found clean. We analyze and optimize the performance of RIIP by deriving explicit formulas for the cost components of interest and maximize the profit associated with the procedure. Our numerical results suggest that it can indeed be profitable to do several cycles at ELISA.