Abstract
In this paper, we propose a branch-and-price approach for solving the problem of maximizing the expected number of transplants in Kidney Exchange Programs (KEPs). In these programs, the decision on which transplants will be conducted is usually made with the support of optimization models with the assumption that all operations will take place. However, after a plan of transplants is defined, a pair may leave the KEP or a more accurate compatibility evaluation exam may invalidate a transplant. To model these possible events we consider probabilities of failure of vertices and of arcs and the objective of maximizing the expected number of transplants. The proposed approach is based on the so-called cycle formulation, where decision variables are associated with cycles. Built on the concept of type of cycle a branch-and-price algorithm is conceived. One subproblem is defined for each type of cycle. We present computational results of the proposed branch-and-price algorithm and compare them with solving directly the cycle formulation (with a general purpose mixed integer programming solverCPLEX) showing that the proposed approach is the only one suitable for larger instances.

Abstract
Kidney exchange programs aim at matching end-stage renal disease patients who have a willing but incompatible kidney donor with another donor. The programs comprise a pool of such incompatible patient-donor pairs and, whenever a donor from one pair is compatible with the patient of another pair, and vice versa, the pairs may be matched and exchange kidneys. This is typically a two-step process in which, first, a set of pairs is matched based on preliminary compatibility tests and, second, the matched pairs are notified and more accurate compatibility tests are performed to verify that actual transplantation can take place. These additional tests may reveal incompatibilities not previously detected. When that happens, the planned exchange will not proceed. Furthermore, pairs may drop out before the transplant, and thus the planned exchange is canceled. In this paper, we study the case in which a new set of pairs may be matched if incompatibilities are discovered or a pair withdraws from the program. The new set should be as close as possible to the initial set in order to minimize the material and emotional costs of the changes. Various recourse policies that determine the admissible second-stage actions are investigated. For each recourse policy, we propose a novel adjustable robust integer programming model. Wealso propose solution approaches to solve this model exactly. The approaches are validated through thorough computational experiments. Summary of Contribution: In the paper, we present an original work related to the modeling and optimization approaches for Kidney Exchange Programs (KEPs). Currently, KEPs represent an alternative way for patients suffering from renal failure to find a compatible (living) donor. The problem of determining an assignment of patients to (compatible) donors that maximizes the number of transplants in a KEP can be seen as a vertex-disjoint cycle packing problem. Thus, KEPs have been extensively studied in the literature of integer programming. In practice, the assignment determined to a KEP might not be implemented due to withdraws from the program (e.g., a more accurate compatible test shows a new incompatibility or a patient health condition unable him/her to participate on the KEP). In our paper, we model the problem of determining a robust solution to the KEP, i.e., a solution that minimizes the material and emotional costs of changing an assignment. In this way, we propose and design solution approaches for three recourse policies that anticipate withdraws. Through computational experiments we compare the three recourse policies and validate the practical interest of robust solutions.

Abstract
Nowadays there are several countries running independent kidney exchange programmes (KEPs). These programmes allow a patient with kidney failure, having a willing healthy but incompatible donor, to receive a transplant from a similar pair where the donor is compatible with him. Since in general larger patient-donor pools allow for more patients to be matched, this prompts independent programmes (agents) to merge their pools and collaborate in order to increase the overall number of transplants. Such collaboration does however raise a problem: how to assign transplants to agents so that there is a balance between the contribution each agent brings to the merged pool and the benefit it gets from the collaboration. In this paper we propose a new Integer Programming model for multi-agent kidney exchange programmes (mKEPs). It considers the possible existence of multiple optimal solutions in each matching period of a KEP and, in consecutive matching periods, selects the optimal solution among the set of alternative ones in such a way that in the long-term the benefit each agent gets from participating in the mKEP is balanced accordingly to a given criterion. This is done by use of a memory mechanism. Extensive computational tests show the benefit of mKEPs, when compared to independent KEPs, in terms of potential increase in the number of transplants. Furthermore, they show that, under different policies, the number of additional transplants each agent receives can vary significantly. More importantly, results show that the proposed methodology consistently obtains more stable results than methodologies that do not use memory.

Abstract
The complex multi-criteria optimisation problems arising in Kidney Exchange Programmes have received considerable attention both in practice and in the scientific literature. Whereas theoretical advancements are well reviewed and synthesised, this is not the case for practice. We present a synthesis of models and methods applied in present European Kidney Exchange Programmes, which is based on detailed descriptions we created for this purpose. Most descriptions address national programmes, yet we also present findings on emerging cross-national programmes. The synthesis provides a systematic and detailed description of the models and methods the programmes use, revealing important commonalities as well as considerable variation among them. Rather than distilling a single best practice from these results, we find that the variation in models and methods arises because of variation in country characteristics, policies, and ethics. The synthesised state of the art may benefit future national and cross-national initiatives and direct future theoretical contributions within and across the boundaries of the Operations Research discipline. (c) 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract
Kidney Exchange Programs (KEP) are valuable tools to increase the options of living donor kidney transplantation for patients with end-stage kidney disease with an immunologically incompatible live donor. Maximising the benefits of a KEP requires an information system to manage data and to optimise transplants. The data input specifications of the systems that relate to key information on blood group and Human Leukocyte Antigen (HLA) types and HLA antibodies are crucial in order to maximise the number of identified matched pairs while minimising the risk of match failures due to unanticipated positive crossmatches. Based on a survey of eight national and one transnational kidney exchange program, we discuss data requirements for running a KEP. We note large variations in the data recorded by different KEPs, reflecting varying medical practices. Furthermore, we describe how the information system supports decision making throughout these kidney exchange programs.

Abstract
We study a variant of the Probabilistic Travelling Salesman Problem arising when retailers crowdsource last-mile deliveries to their own customers, who can refuse or accept in exchange for a reward. A planner must identify which deliveries to offer, knowing that all deliveries need fulfilment, either via crowdsourcing or using the retailer's own vehicle. We formalise the problem and position it in both the literature about crowdsourcing and among routing problems in which not all customers need a visit. We show that to evaluate the objective function of this stochastic problem for even one solution, one needs to solve an exponential number of Travelling Salesman Problems. To address this complexity, we propose Machine Learning and Monte Carlo simulation methods to approximate the objective function, and both a branch-and-bound algorithm and heuristics to reduce the number of evaluations. We show that these approaches work well on small size instances and derive managerial insights on the economic and environmental benefits of crowdsourcing to customers.