SummaryFundamentalsThe study aims to carry out a comparative analysis of the technical efficiency of hospital management based on public‐private collaboration, as compared with traditional management. Specifically, we compare traditionally managed public hospitals, public hospitals managed by a private finance initiative (PFI), public hospitals managed through a public‐private partnership (PPP), and hospitals managed through other forms of management, during the period 2009 to 2014, in the hospitals dependent on the Madrid Health Service (SERMAS).MethodsThe study covers all publicly owned general hospitals under SERMAS, consisting of seven PFI hospitals, three PPP hospitals, 11 traditionally managed public hospitals (with the category of general hospital), and four hospitals managed through other forms of hospital management. The technical efficiency indices of the hospitals were calculated using the data envelopment analysis technique. Subsequently, a sensitivity analysis was performed by bootstrapping and variation of model variables to verify their impact on efficiency. Finally, an analysis of the evolution of efficiency in the analyzed period was carried out using the Malmquist Index.ResultsIn all the analysis models carried out in the analyzed period, the hospitals managed based on public‐private collaboration were more efficient than the hospitals under traditional management.ConclusionsThe greater efficiency of hospitals managed based on public‐private collaboration, as compared with traditional management, could be attributed to greater organizational and management flexibility.

Traditional uneven-aged forest management seeks a balance between equilibrium stand structure and economic profitability, which often leads to harvesting strategies concentrated in the larger diameter classes. The sustainability (i.e., population persistence over time) and influence of such economically optimal strategies on the equilibrium position of a stand (given by the stable diameter distribution) have not been sufficiently investigated in prior forest literature. This article therefore proposes a discrete optimal control model to analyze the sustainability and stability of the economically optimal harvesting strategies of uneven-aged Pinus nigra stands. For this model, we rely on an objective function that integrates financial data of harvesting operations with a projection matrix model that can describe the population dynamics. The model solution reveals the optimal management schedules for a wide variety of scenarios. To measure the distance between the stable diameter distribution and the economically optimal harvesting strategy distribution, the model uses Keyfitz's delta, which returns high values for all the scenarios and, thus, suggests that those economically optimal harvesting strategies have an unstabilizing influence on the equilibrium positions. Moreover, the economically optimal harvesting strategies were unsustainable for all the scenarios. OPEN ACCESSForests 2013, 4 831

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This study proposes a discrete optimal control model to obtain harvest strategies that maximize the net present value (NPV) of the timber harvested from uneven-aged Pinus nigra stands located in the Spanish Iberian System, between two stable positions. The model was constructed using an objective function that integrates financial data on the harvesting operations with a matrix model describing the population dynamics. The initial and final states are given by the stable diameter distribution of the stand, and the planning horizon is 70 years. The scenario analysis corresponding to the optimal solutions revealed that the stand diameter distribution does not deviate substantially from the equilibrium position over time and that the NPV for the optimal harvesting schedule was always greater than the NPV for the "sustainable/stable" harvesting strategy. The NPV increase for the different scenarios is between 5.36% and 14.43%, showing a greater increase in higher site index scenarios and higher recruitments.

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This study analyzes the stability of De Liocourt's distribution, investigating the influence of factors such as site index, recruitment, and basal area. It is proved that De Liocourt's distribution is not stable, and some simple models providing better fit to the stable diameter distribution of the stand than De Liocourt's are introduced. The stable diameter distributions obtained were characterized by a decrease in stem density in relation to the corresponding De Liocourt's distributions for low-and high-diameter classes and an increase for intermediate-diameter classes. Despite their instability, De Liocourt's distributions have shown a high degree of fit to the corresponding stable diameter distributions. The goodness of fit between both distributions was better for high recruitment, high site quality, and low basal area. FOR. SCI. 58 (1) 2009). These models are defined by the finite difference linear system of equations N(t ϩ 1) ϭ AN(t), where N(t) and N(t ϩ 1) are column vectors that contain the number of stems/ha within each diameter class at time t and t ϩ 1, respectively, and A is a square primitive matrix that contains, for each time step, the transition probabilities between adjacent classes and individual recruitments. The population growth rate is the dominant eigenvalue 0 of matrix A. By asymptotic analysis (long-term behavior), we know that, independent of the initial conditions, when 0 Ͼ 1, the total number of stems/ha of the tree population increases exponentially over time (unless harvests are conducted), when 0 Ͻ 1, the population is decaying until extinction, and when 0 ϭ 1, a stable distribution proportional to the right eigenvector W 0 of A corresponding to 0 is obtained. Gotelli (2001) refers to this special case of stable distribution when 0 ϭ 1 as the "stationary distribution," and this is also the case that we are referring to here.In general, the concept of stability is closely associated with the concept of perturbation: a system is considered stable if it always returns to a reference position (equilibrium) after small perturbations (otherwise, the system is said to be unstable). In the case of these projection matrix models, this stability property is stronger, because the stable distribution (stationary distribution) is reached independently of the initial conditions. Applied to tree populations, the stable diameter distribution of a stand is reached when it neither increases in size nor changes in structure; that is, the number of stems/ha within each diameter class remains constant after each time step. These stable diameter distributions are closely dependent on recruitment, removal, and stem migration throughout the diameter classes over time (Schütz 2006). A method to obtain these distributions, closely related to the right eigenvector W 0 of the transition matrix A corresponding to the dominant eigenvalue 0 , the stand basal area G, and the global amount of recruitment R, was introduced in López et al.

Background The aim of this paper is to analyze the differences in the coordination of chronic illness care between the different public hospital management models coexisting in the Spanish region of Madrid (25 hospitals) during the period 2013–2017. Methods The performance of hospitals might be affected by the characteristics of the population they serve and, therefore, this information should be taken into account when estimating efficiency measures. For this purpose, we apply the nonparametric Data Envelopment Analysis (DEA) conditioned to some contextual variables and adapted to a dynamic framework, so that we can assess hospitals during a five-year period. The outputs considered are preventable hospitalizations, readmissions for heart failure and readmissions for chronic obstructive pulmonary disease, whereas the inputs considered are the number of beds, personnel (physicians and other healthcare professionals) and total expenditure on goods and services. Results The results suggest that the level of efficiency demonstrated by the public-private collaboration models of hospital management is higher than traditionally managed hospitals throughout the analyzed period. Nevertheless, we notice that efficiency differences among hospitals are significantly reduced when contextual factors were taken into account. Conclusions Hospitals managed under public-private collaboration models are more efficient than those under traditional management in terms of chronic illness care coordination, being this difference attributable to more agile and flexible management under the collaborative models.

This study proposes a simple and direct method based on dimensionless numbers to provide reliable approximations of the population growth rate, the “sustainable/stable” harvest rate, the proportion of trees that has to remain unharvested to retain the stable diameter distribution, and the stable diameter distribution of a forest stand. Those numbers, obtained under conditions of stable equilibrium from a matrix model, could also serve to estimate boundaries between sustainable and unsustainable harvesting. To exemplify and test the results, the model uses data from uneven-aged managed Pinus nigra Arnold stands, considering three levels of tree diameter growth, six levels of basal area, and 33 levels of recruitment, creating a total of 594 planning scenarios. The best approximation of all the variables observed occurred in any case for the scenarios with the lowest level of diameter growth, the lowest level of basal area, and the highest recruitment level. Furthermore, the study reveals the existence of a strong positive linear correlation between those variables and their respective approximations, as well as a small distance between the stable diameter distribution of the stand and its approximation. Finally, we incorporate natural disturbances into the dimensionless numbers and criteria.