Medical training is an intricate and long process, which is compulsory to medical practice and often lasts up to twelve years for some specialties. Health stakeholders recognise that an adequate planning is crucial for health systems to deliver necessary care services. However, proper planning needs to account for complexity related with the setting of medical school vacancies and of residency programs, which are highly influenced by multiple stakeholders with diverse perspectives and views, as well as by the specificities of medical training. Aiming at building comprehensive models with a potential to assist health decision-makers, this article develops a multi-methodological framework to assist the planning of medical training under such a complex environment. It combines the structuring of the objectives and specificities of the medical training problem with a Soft Systems Methodology through the CATWOE (Customer, Actor, Transformation, Weltanschauung, Owner, Environment) approach, and the formulation of a Mixed Integer Linear Programming model that considers all relevant aspects. Considering the specificities of countries based on a National Health Service structure, a multiobjective planning model emerges, informing on how many vacancies should be opened/closed per year in medical schools and in each specialty. This model aims at i) minimizing imbalances between medical demand and supply; ii) minimizing costs; and iii) maximizing equity across medical specialties. A case study in Portugal is explored so as to illustrate the applicability of the proposed multi-methodology, showing the relevance of proper structuring for planning models having the potential to inform health decision-makers and planners in practice.

This paper addresses the design and planning of integrated biorefineries supply chain under uncertainty. A two-stage stochastic mixed integer linear programming (MILP) model is proposed considering the presence of uncertainty in the residual lignocellulosic biomass availability and technology conversion factors. Nevertheless, when the scenario tree approach is applied to a large real world case study, it generates a computationally complex problem to solve. To address this challenge the present paper proposes the improvement of the scenario tree approach through the use of two scenario reduction methods. The results illustrate the impact of the uncertain parameters over the network configuration of a real case when compared with the deterministic solution. Both scenario reduction methods appear promising and should be further explored when solving large scenario trees problems.

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