Abstract
s This 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.

Abstract
Kidney exchange programs have been set in several countries within national, regional or hospital frameworks, to increase the possibility of kidney patients being transplanted. For the case of hospital programs, it has been claimed that hospitals would benefit if they collaborated with each other, sharing their internal pools and allowing transplants involving patients of different hospitals. This claim led to the study of multi-hospital exchange markets. We propose a novel direction in this setting by modeling the exchange market as an integer programming game. The analysis of the strategic behavior of the entities participating in the kidney exchange game allowed us to prove that the most rational game outcome maximizes the social welfare and that it can be computed in polynomial time.

Abstract
Phasor Measurement Units (PMUs) are measuring devices that, when placed in electrical networks, observe their state by providing information on the currents in their branches (transmission lines) and voltages in their buses. Compared to other devices, PMUs have the capability of observing other nodes besides the ones they are placed on. Due to a set of observability rules, depending on the placement decisions, the same number of PMUs can monitor a higher or smaller percentage of a network. This leads to the optimization problem hereby addressed, the PMU Placement Problem (PPP) which aims at determining the minimum number and location of PMUs that guarantee full observability of a network at minimum cost. In this paper we propose two general mathematical programming models for the PPP: a single-level and a bilevel integer programming model. To strengthen both formulations, we derive new valid inequalities and promote variable fixing. Furthermore, to tackle the bilevel model, we devise a cutting plane algorithm amended with particular features that improve its efficiency. The efficiency of the algorithm is validated through computational experiments. Results show that this new approach is more efficient than state-of-the-art proposals.

Abstract
In 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.

Abstract

Abstract
One of the challenges in a kidney exchange program (KEP) is to choose policies that ensure an effective and fair management of all participating patients. In order to understand the implications of different policies of patient allocation and pool management, decision makers should be supported by a simulation tool capable of tackling realistic exchange pools and modeling their dynamic behavior. In this paper, we propose a KEP simulator that takes into consideration the wide typology of actors found in practice (incompatible pairs, altruistic donors, and compatible pairs) and handles different matching policies. Additionally, it includes the possibility of evaluating the impact of positive crossmatch of a selected transplant, and of dropouts, in a dynamic environment. Results are compared to those obtained with a complete information model, with knowledge of future events, which provides an upper bound to the objective values. Final results show that shorter time intervals between matches lead to higher number of effective transplants and to shorter waiting times for patients. Furthermore, the inclusion of compatible pairs is essential to match pairs of specific patient-donor blood type. In particular, O-blood type patients benefit greatly from this inclusion.