Optimisation problems in Healthcare have received considerable attention for more than three decades. More recently, however, with decreasing birth rates in nearly all of the developed countries and increasing average longevity globally, optimisation issues in Healthcare have become noticeably important and attract keen interest from the Operations Research community. Over the years, attention has gradually expanded from resource allocation and strategic planning to include operational issues such as resource scheduling and treatment planning. This paper surveys several applications of Operations Research in the domain of Healthcare. In particular, the paper reviews key contributions addressing contemporary optimisation issues in this area. It highlights current research activities, focusing on a variety of optimisation problems as well as solution techniques used for solving the optimisation problems.

a b s t r a c tIn recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient-donor pairs. These policies lead to what is commonly known as kidney exchange programs.The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

a b s t r a c tThis paper presents a complete, quadratic programming formulation of the standard thermal unit commitment problem in power generation planning, together with a novel iterative optimisation algorithm for its solution. The algorithm, based on a mixed-integer formulation of the problem, considers piecewise linear approximations of the quadratic fuel cost function that are dynamically updated in an iterative way, converging to the optimum; this avoids the requirement of resorting to quadratic programming, making the solution process much quicker.From extensive computational tests on a broad set of benchmark instances of this problem, the algorithm was found to be flexible and capable of easily incorporating different problem constraints. Indeed, it is able to tackle ramp constraints, which although very important in practice were rarely considered in previous publications.Most importantly, optimal solutions were obtained for several well-known benchmark instances, including instances of practical relevance, that are not yet known to have been solved to optimality. Computational experiments and their results showed that the method proposed is both simple and extremely effective.