Despite the patient’s care and treatment was a priority, OR models had the important duty of relieving the economic effects of war on healthcare services management, hence, focusing mainly on the optimization and correct allocation of the available resources [8].

The need to find methods to balance OR’s main objectives arose in this decade: resource use versus quality patient’s attention. Flagle [8] identified --based on his experience-- the main scenarios for the action of OR within the medical scope in the United States at that time. So, dividing the review in four sections, some approaches focused on the solution of facility use, patient flow, resource optimization and allocation problems were listed. At the same time, he suggested orienting the development of OR in the health sector toward stochastic systems and probabilistic decision models.

After a year and using a similar classification, Feldstein [1] put forward the relevance of quantitative-based decision methods and their use as support tool for decisions of the medical staff based on common sense and value judgment, which were, in a beginning, the main decision tools. Among the principal applications were: medical treatment selection, medicine inventory management and monitoring, required hospitalization time determination, bed number planning and medical and nurse staff scheduling.

Brant E. Fries stands out for his attention and follow up with the development of OR in the health care. In his documents [9,10], Fries contributed with a list of over more than 350 references organized in 15 different medical areas of interest. Another summary for OR applications in medical and hospital issues during the 60’s and part of the 70’s was delivered by Papageorgiou [11] and it concurs with Fries [10] in some items of his classification. This author points out some cases in which linear programming and variable maximization and minimization functions are used.

Figure 1. Overview Source: The authors, based on Scopus statistics

Despite OR was consolidating as one of the most important tools for decision making and optimization in health care, Rosenhead [12], who was knowledgeable of healthcare services’ situation and development level in the United States and the United Kingdom, focused his paper on using strategic planning horizons and disclosed the flaws in the applicability of certain decision-making tools and models.

Barber [13] also poses flaws in the applicability of some decision-making tools. First, the need to define a sole objective for OR optimization (this flaw would be later mended through the application of multi-objective optimization approaches). Second, problems related to accuracy and distortion that social issues quantification and its use as input data for OR models bring about.

In in a selective literature review, Boldy & O’Kane [14] also agree with Fries [9, 10] in part of his classification and delivered an interesting conclusion about his contribution: they observed a larger amount of OR application papers between 1970 and 1973 than in the overall scientific production of the two previous decades. Although many applications and case studies related to this topic were not included in Fries’ list, the upsurge and development of OR in the health care during these years is evident [15].

Resource planning and its optimal management has always been a key element within economic and social development. As Kemball-Cook & Wright [16] mentioned, when considering certain cost-benefit relationships, limited resources, and lack of qualified personnel, OR seemed like a feasible tool for problem solving and decision making processes in certain “problem areas” like health care. In this review, they presented numerous application cases of this kind.

However, some years after, Reynolds [17] studied OR application in decision-making and data gathering processes for policy planning and definition of national programs in different countries on primary healthcare attention. As these are social matters from a community, the author concluded that traditional OR tools would not be very useful in some cases since countless variables -sometimes not identifiable or measurable-were involved [18]. This also relates to Rosenhead’s ideas [12] and the issues presented by Barber [13].

In 1987, Boldy [19] put forward the relationship between OR models and decision support systems (DSS) in the health sector. Through the compilation of case studies and OR applications in strategic decision making, the author emphasized in DSS features posed by Sprague [20], which he found relevant for decision making in the health sector. These were grounded on today’s CDSS (Clinical Decision Support Systems) functioning.

A little before and during the 90’s, the optimization and productive approach of OR applications in health revolved around social aspects. The use of quantitative-based decision models for problem solving and decision making in health care was addressed by Parker [21]. This author also made great emphasis in the relevance of applying them in developing countries.

Parker suggested the use of heuristics and programming models grounded on quantitative decision models (QDMs). Moreover, he noticed that the upsurge of OR for problem solving processes of social issues or “Social OR” would not be feasible in developing countries since the value of decision making models applied was restricted and these were not applied due to the non-quantitative nature of certain problems and the limited competences of analysts, information access, and technological obstacles. This problem of the non-quantitative nature of social problems relates again to Rosenhead [12] and Reynolds’ [17] conclusions.

Later, through the collection of 286 scientific papers and case studies (which were divided in seven categories), Datta [22] concluded that the applicability of basic OR models was feasible, mainly, in problems related to hospital management, certain diseases’ control and public health. On the other hand, problems revolving around strategic planning [23], such as facility location, nutrition plans, and health management, would need different and more elaborated methodologies and approaches.

Pierskalla & Brailer's [24] review is mostly centered in operative and tactical applications. These authors divided their work in three main categories: design and planning of the system, operation management, and medical management.

Toward the end of the decade, Royston [25] poses the need to achieve a balance between certain aspects (planning horizon, scope, approach, complexity, etc.) in the application of OR models in the health care. In addition, this author mentions some of the most used ORMS (Operations Research and Management Science) tools, for example, scenario forecasting and analysis methods, neural networks and expert systems, simulations, and multi-criteria analysis methods.

Lagergren [26] summarizes the influence and impact of modeling approaches in the health care. This author highlights that technology improvements in hardware and software allowed, to a great extent, the creation and use of more complex models.

In this period, and in a general way, resource management is still a high priority in the health systems management [27]. The first decade of the 21st century witnessed the upsurge of decision support systems (DSS) and the establishment of the concept of Clinical Decision Support Systems -CDSS [28,29], OR models became the force in the functioning of these computer tools [30-33] and its fast development led to an assessment requirement so as to compare them to traditional medical decision-making procedures [34,35].

Rais & Viana’s [36] work gathers a great amount of sources concerning OR applications in health care. Taking into account their conclusions and the high amount of sources, the study of OR development in health faces the arduous task of differentiating successful models’ implementations, their advantages, disadvantages, and improvement opportunities in order to attain a general overview of the discipline’s evolution, current status, and future.

The scientific journals that published literature reviews related to the development of OR in the healthcare are shown in Fig. 2. In this list, the European Journal of Operational Research stands out for having the highest number of reviews. It is also important to underline that the rising levels of scientific contributions brings an upward trend in the number of specialized journals focused in the study of OR applied to health care.

Figure 2 Source: The authors

The application of decision trees in the health care goes back to the decade of the 1970’s [37]. The analysis of medical decisions [38 - 41], illness diagnosis [42,43], and assessment of treatment alternatives [44-52] are some of the most frequent uses for this type of decision model.

In accordance with the report (Fig. 4), when using the search terms Decision trees AND health* between the years 1973 and 2016, approximately 4600 scientific and literature review papers related to the use of this type of model in the health sector were presented.

Figure 4 Source: The authors, based on Scopus statistics

These contributions were mainly published in journals related to Medicine, Nursing, Biochemistry, Genetics, Molecular Biology, Pharmacology, and Toxicology. This fact provides a general overview of the nature of the problems frequently addressed through the use of decision trees.

Surgery, medical staff (nurse scheduling), and patient scheduling are the most frequent subjects within the literature consulted [53-64]. Using the search terms “Scheduling” AND Health*, the Scopus database reports 11839 documents between the years 1961 and 2016 (Fig. 4). Of all the documents indexed, approximately 9564 correspond to scientific research papers, 1146 to literature reviews, and 1129 to conference papers. Nearly a 77% of the papers were published in Medicine and Nursing scientific journals.

Exact models of mathematical programming (mixed, linear, and nonlinear) are common in the health field. These allow finding optimal and faster solutions for problems with a relatively low complexity. For this reason, it is useful within operational planning.

With the search terms “Programming” AND Health*, the database reports a total of 11263 documents: a 66% are research papers, a 12% review papers, and a 22% conference papers. Around 90% of the documents were published in scientific journals of Medicine (nearly a 50%), Computer Sciences, and Engineering. According to Fig. 4, the behavior of scientific production for this type of model reaches the highest values. This may be consequence of the great amount of variations this model can provide along with the generalization of the search term used.

Waiting line optimization is a common topic within OR and its development goes hand in hand with health systems’ growth and functioning [65].

Queueing studies sometimes are key elements in the definition of necessary abilities for health system designs, and for the improvement of service and attention periods in medical units and emergency services [66-70].

Using the search terms Queu* AND Health*, the database reported a total of 1052 published documents between 1961 and 2016. Of all these documents regarding the queueing model in health issues, a 71% correspond to research papers, a 22% to conference papers, and a 5% to review articles.

As seen in Fig. 4, this type of model, together with routing models, represent substantially less documents indexed in scientific literature. As of the decade of 2000, an increase is observed.

Determination of quantity and location of medical facilities to increase healthcare service coverage is one of the main applications of location models in this field. These models are commonly used in supply chain design and, together with routing models, they help in travel reduction and resource optimization [71,72].

When using the search terms Location - Allocation AND health*, a total of 125 documents are reported between 1976 and 2016. Of these, a 76% refers to scientific research papers. Regarding routing models, the search terms used were Routing AND Health*. The database reported a total of 1258 documents produced during the years 1971 and 2016. A 52% belongs to conference papers, a 44% to research papers, and the remaining 3% to review papers. The documents comprising this list were mostly published in Computer Science and Medicine journals, and the number is similar to that previously presented for the queueing theory.

The use of this type of models in the health sector is quite new. As they are based on statistical methods, Markov chains are usually combined with other models like queueing and scheduling. Some of their applications comprise prognosis and inventory management of hospital resources [73], waiting time reduction [74], and prognosis of a patient’s condition or the development of illnesses [75].

Using the search term Markov AND health*, the database reports a total of 6390 documents of which an 82% are scientific papers, an 11.4% are conference papers, and a 6.3% accounts for literature reviews.

Simulation models in healthcare and hospital milieus have contributed to the study and behavior understanding of variables within health systems by considering objectives, resources, and restrictions established [76-79].

Simulation environments have played an integrating role in the application of strategic decision-making models [80], in programming and scheduling [81], resource and hospital facility allocation, waiting line time reduction, and attention and service levels enhancement [82]. Using the search terms Discrete Event Simulation AND health*, the database reports a total of 790 documents.

In the Figs. 2, 3, 4, previously shown, high similarity is observed in the behavior of the literature related to the general term of “operations research” (Fig. 3) and that related to the specific operational models (Fig. 4). Hence, a similar behavior development is evident, however, the values for every type of model is different