Online optimization methods applied to the management of health services

The rising costs of health care due to new technologies and the aging population is a vitally important issue for health care policy makers. At the same time there is a paradigm shift in the service concept of health care: patients are no longer prepared to accept poor quality service, either in terms of long waiting times or inconvenient appointment systems, and expect that services are well organized from a ``customer'' perspective. In the modern health care delivery, the concept of health service needs to be focused on optimizing the use of resources finding a balance between service for patients and efficiency for providers. Dealing at the same time with the uncertainty and the dynamics of health care delivery problems, the adoption of unconventional solution methodologies is necessary. In this thesis, we would propose an approach based on the online optimization methodology to manage the uncertainty and the dynamics of several health care delivery problems. Online optimization is characterized by the development of algorithms whose decisions are based only on past events without any solid information about future data. Starting from a given offline planning solution (when it exists), the basic idea is to fix such a solution in real time as soon as an unattended event will occur exploiting the available knowledge of the underlying Clinical Pathways (CPs). We identified three health care delivery problems to illustrate and develop our approach. The three problems belong to two different CPs, which are the Surgical Pathway (SP) and the Emergency Care Pathway (ECP). The first problem arises in the context of Operating Room Planning (ORP), which is characterized by (i) a well-structured but complex pathway, and (ii) by several sources of uncertainty such as the arrival of unattended patients to be operated on, and the duration of a surgery and the length of stay. The second problem arises in the context of Emergency Medical Service (EMS) management, which is characterized by (i) a well-structured but simple pathway, and (ii) by several sources of uncertainty such as the arrival of unattended phone calls asking for an emergency requests to be served as soon as possible (depending on the level or urgency) by a not always available ambulance. Finally, the third problem arises in the context of Emergency Department (ED) management, which is characterized by (i) a non-structured but complex pathway, and (ii) by several sources of uncertainty such as the arrival of unattended patients to be served as soon as possible (depending on the level or urgency) by a possible overcrowded system, and the dynamic evolution of the patient path. In the ORP and the EMS management we deal with lasagna processes: the sequence of activities to be performed is known a priori and the possible path evolutions are limited. For this reason, online optimization approaches have been used exploiting the solid knowledge of the CPs. On the contrary, the ED management is a spaghetti process: a large variety of path evolutions is possible and the sequence of activities to be performed is part itself of the lack of information taken into account by online optimization. To deal with this challenging aspect, we use an ad hoc process mining approach to extract information from historical data of a case study for predicting the possible path evolutions on the basis of the few information available, such as the past activities and the characteristics of the patient. Since the competitive analysis, which is a typical evaluation approach of the online optimization algorithms, cannot be easily applied due to the complicated nature of the considered problems, an alternative evaluation framework to evaluate the proposed methods is required. Exploiting the discrete structure of the problems under considerations, we evaluate the quality of our online solutions within a Discrete Event Simulation (DES) framework. Basically, we adopt the DES to replicate the operative context in which the candidate algorithms operate using real world or realistic data, and allows us to evaluate their impact over time, that is how the previous decisions can impact on the current decisions. Further, we always consider a baseline configuration representing a basic organization equipped with some elementary decision making tools: it should provide a simple set of rules similar to those involved in delivering the health services in real case contexts, in such a way to have a comparison with the proposed methods. There are several common lessons learned through the analysis and the comparison of the several policies proposed for the addressed problems. The same problems in different operative contexts usually obtain the best performance improvement using different method configurations, which is a further proof of the necessity of a decision support tool in health care. Standalone online optimization approaches seem to be effective in well-structured processes while they requires the support of process mining and predictive methods when the complex process is non-structured. Furthermore, the more flexible the operating context in which online optimization is applied (e.g. sharing resources among different patient classes) the greater the contribution of optimization in improving performance. Since sometimes a large flexibility is not possible because of the lack of adequate decision support tools, those proposed in the thesis can represent a solution for the management of the high complexity that derives from a flexible context.