Modeling & Optimization Problems For Healthcare Queueing Network System

Healthcare managers continually confront many challenges between limited healthcare resources and growing patients demand. In China, the "difficult and expensive" in hospital has become a social phenomenon concerned by the whole of society. The main reason for this phenomenon is caused by the uneven allocation of medical resources, poor service and efficiency, a lower level of management of the healthcare. Related operational management research in the healthcare field has become an important issue.Domestic research on healthcare operational management has just started but in the field of healthcare abroad has become an important research spot for scholars in the developed countries. Operations research methodologies and queueing theory in particular, have generated many valuable insights into operational strategies and practices, thus leading to solutions of significant problems in healthcare systems. Due to the large number of medical resources involved and complex process in hospital operation and management, research on the hospital queuing network is an important and integral part of the foundation in operation and management. For improving the quality and efficiency of hospital has an important significance.Based on the actual data and flow chart in practice, supported by National Nature Science Foundation under Grant (71021061), around the hospital queuing network, several optimization problems of healthcare process in operational management are studied. Based on the queueing network in hospital, some analysis showed the patient flow how to change in OD (Outpatient Department), internal ward and outpatient to inpatient process. Around the various queueing network models, the routing structure of queueing nerwork, the limited resources allocation, patients routing allocation and fairness, some research was carried out. From the perspective of business processes based on hospital queuing network-OD queuing network-outpatient diagnostic-internal ward queuing network-outpatient to inpatient process as the main line. From the perspective of the problem is changing around the hospital patient flow analysis and control-queuing network structure optimization-the medical resources allocation-blocking-patients routing control and fairness issues related to the analysis, modeling, optimization.To sum up, this dissertation focuses on the five key problems:(1) Based on the empirical data and the behavior of patient flow in the hospital, a general queuing network model for hospital is established. The series of parameters which including the external arrival rate, the per-server service rate are obtained by the method of parameter estimation and forecasting.(2) The queueing network with feedback patient flow and the retrial queue with feedback patient for OD are founded. Focusing on the nurse resource, a mathematical programming model is developed to determine how many nurses are allocated to each stage/division to minimize the total costs of patient waiting time and the nurses’ idle time. A neighborhood search combined Simulated Annealing is developed. The superiority of the proposed method is showed by numerical experiments. Numerical experiments are conducted to analyze the discipline of nurse allocation and the impact of the patient arrival rate and the probability of feedback patient flow on system cost, and that of the ratio of patients’ waiting time and nurses’ idle time on the number of nurses to be allocated.(3) The modeling process of no-buffer internal ward queueing network with blocking and the bed resource allocation in hospital. The reversible Markov process shows the blocking process in two stage tandem queueing system. Some analysis is made for blocking in tandem queueing system, closed queueing network and general queueing network. The blocking probability of the system is derived by an approximation method or heuristic algorithm respectively. Focus on general queueing network, a mathematical programming model with beds cost constraints is developed Numerically experimental results are compared with the literature results, showing the superiority of the proposed method.(4) Around the normal arriving patient flow and the referral patient flow influx in diagnosis-stage, some analysis is made for patients routing problem with I1 routing structure and V routing structure. Focusing on I2 routing structure, a general multi-stage queueing network model with I2 patients routing is established. Based on the model, one method of the nurse resource allocation is also developed. Focusing on V routing structure, the referral patient has high-priority than the normal arriving patient in general by supposed. Around the goal that minimizing the referral patients mean waiting time and keeping the normal patient queue stable, a general two types of patient flow with non-preemptive and homogeneous server queueing model is established. An optimal patients routing policies named cutoff policy is proposed and the main result formulas are developed. Some analysis around the result is made with I2 routing structure and V routing structure. The referral patient probability is also impact of system performance.(5) An Inverted-V model is established with single patient queue and several heterogeneous server pools which to formulate the OD to internal ward process. Around the goal of minimizing the patients mean waiting time, a routing allocation policy named FSF (Faster Server First) is analyzed under QED (Quality and Efficiency Driven) regime. The superiority of the routing allocation policy is showed by numerical experiments. Around the goal of routing allocation fairness for severs, RMI (Randomized Most-Idle) routing policy is introduced. The Inverted-V model under RMI is analyzed by the reversible Markov process in small data and the RMI is analyzed under QED with big data. At last the routing policy fairness is discussed by theory and numerically experimental results.