Modelling, analysis, and optimization in resource planning for outpatient clinics
Nguyen Thi Thu Ba
Date of Issue2014
School of Mechanical and Aerospace Engineering
Singapore-MIT Alliance Programme
Outpatient services in Singapore have been facing an increasing and lengthy appointment lead-time, which is regarded as being unacceptable for healthcare services. Specifically, Tan Tock Seng Hospital (TTSH) has been under the great pressure in reducing the outpatients’ long appointment leadtime to meet the guidelines of Singapore Ministry of Health (MOH) in terms of the median, 95th percentile, 100th percentile. This brings various challenges to TTSH in operating its re-entry outpatient appointment system in which patients may need to re-visit for follow-up treatments. The thesis focuses on both the strategic and tactical levels for the optimal capacity planning, and on the operational level for every individual appointment scheduling. Mathematical models of capacity planning and appointment scheduling rules with quantitative admission constraints are developed to achieve the MOH’s appointment lead-time targets. The capacity planning approach aims to match the capacity of healthcare provider to patients’ demands restricted by the patients’ appointment lead-time targets. The capacity planning approach contains two parts: capacity design and admission management problems. Mixed integer programming models are proposed with the minimization of maximum required resource and the maximum number of appointed patients as objectives of the capacity design and the admission management problems, respectively. In the models, a finite planning horizon, multiple types of patients, identical physicians, dependent demands between types of patients, and constant discharge rates are assumed. Initially, deterministic new arrival demand is assumed; however, the assumption is later expanded to be stochastic. Under uncertainty of arrival demands, safe and tractable deterministic equivalents are derived. Branch and Cut algorithm are used to solve deterministic models and deterministic equivalents. The capacity designs and admission management models are tested with numerical experiments using real data of the Urology specialty. The results show the feasibility and efficiency of the proposed models. Finally, sensitivity analyses are carried out, which provides some deeper insights into the findings. The appointment scheduling rule approach is to determine either the optimal required capacity or the optimal admission schemes, at the operational level. The approach entails decision making for every individual patient whose arrival information is unknown. Two different rules, the exact and relaxed rules, are derived for scheduling patients’ appointments with the maximization of resource utilized as their objective. In addition, the rules account for the need to maintain the MOH’s appointment lead-time targets. The appointment scheduling rules are then simulated using the real data from the Urology specialty and optimal capacity planning scheme. Simulation results show the efficacy of the proposed policies. The capacity planning models and the appointment scheduling rules can decrease the probability of failure to satisfy the guidelines of MOH’s appointment lead-time. Using the proposed models and rules helps TTSH to cope with challenges that it encounters.