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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The adequate planning of home-based long-term care (HBLTC) is essential in the current European setting where long-term care (LTC) demand is increasing rapidly, and where homebased care represents a potential cost-saving alternative from traditional inpatient care. Particularly, this planning should involve proper route planning to ensure visits of health professionals to patients' homes. Nevertheless, literature in the specific area of HBLTC planning is still scarce. Accordingly, this paper proposes a tool based on a mathematical programming modelthe LTC routes -for supporting the daily planning of routes to visit LTC patients' homes in National Health Service-based countries. The model allows exploring the impact of considering different objectives relevant in this sector, including the minimization of costs and the maximization of service level. Patients' preferences, traffic conditions and budget constraints are also considered in the proposed model. To illustrate the applicability of the model, a case study based on the National Network of LTC in Portugal (RNCCI) is analysed.

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The current awareness about climate change creates the urgency in adjusting the services provided in public transport towards more sustainable operations. Recent studies have shown that the integration of electric vehicles into existing fleets is an alternative that allows reducing CO2 emissions, thus contributing to a more sustainable provision of services in the sector. When the aim is to achieve a full electrification of a bus fleet, several decisions need to be planned, such as i) the number of buses that are required, ii) the types of batteries used in those vehicles, iii) the charging technologies and strategies, iv) the location of the charging stations, and v) the frequency of charging. Nevertheless, although several planning studies have focused on the full electrification of a bus fleet, no study was found considering all these planning decisions that are deemed as essential for an adequate planning. Our study thus contributes to this gap in the literature, by proposing an optimization-based planning model that considers all these planning dimensions in the decision-making process related to the integration of electric buses in a public bus transport systemthe MILP4ElectFleet model. All these decisions are evaluated while ensuring the minimization of investment and operating costs. The MILP4ElectFleet model is applied to the Carris case study, a Portuguese public transport operator in the metropolitan area of Lisbon.