Hospital readmission is a large and growing concern throughout the U.S. healthcare system. The estimated national cost of preventable readmissions exceeds $17 billion annually for Medicare patients. As many as 20% of all hospitalized patients are readmitted within 30 days of discharge. The process is costly, potentially harmful, and often avoidable. Basic management engineering and Continuous Quality Improvement (CQI) methods solve similar problems; but this is an instance where more advanced methods add tremendous value when used in concert with CQI. To complement various well-known improvement efforts, we discuss a tool kit of systems engineering and management science methods for measuring, modeling, and reducing readmissions and to optimize limited intervention resources. These include:(1) statistical control charts to detect if readmission rates actually have improved; (2) simulation, Markov chain, and stochastic dynamic programming models to determine when to discharge, intervene via phone call or home visit, and preemptively readmit; (3) optimization models to allocate hospital resources in the most effective way to prevent readmissions; and (4) feedback control and Markov decision process models to determine when to discharge.