Abstract
When each patient of a kidney exchange program has a preference ranking over its set of compatible donors, questions naturally arise surrounding the stability of the proposed exchanges. We extend recent work on stable exchanges by introducing and underlining the relevance of a new concept of locally stable, or L-stable, exchanges. We show that locally stable exchanges in a compatibility digraph are exactly the so-called local kernels (L-kernels) of an associated blocking digraph (whereas the stable exchanges are the kernels of the blocking digraph), and we prove that finding a nonempty L-kernel in an arbitrary digraph is NP-complete. Based on these insights, we propose several integer programming formulations for computing an L-stable exchange of maximum size. We conduct numerical experiments to assess the quality of our formulations and to compare the size of maximum L-stable exchanges with the size of maximum stable exchanges. It turns out that nonempty L-stable exchanges frequently exist in digraphs which do not have any stable exchange. All the above results and observations carry over when the concept of (locally) stable exchanges is extended to the concept of (locally) strongly stable exchanges.

Abstract
In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. We show that, for strict preferences, the unique strong core allocation respects improvement-if an agent's object becomes more desirable for some other agents, then the agent's allotment in the unique strong core allocation weakly improves. We extend this result to weak preferences for both the strong core (conditional on nonemptiness) and the set of competitive allocations (using probabilistic allocations and stochastic dominance). There are no counterparts of the latter two results in the two-sided matching literature. We provide examples to show how our results break down when there is a bound on the length of exchange cycles. Respecting improvements is an important property for applications of the housing markets model, such as kidney exchange: it incentivizes each patient to bring the best possible set of donors to the market. We conduct computer simulations using markets that resemble the pools of kidney exchange programs. We compare the game-theoretical solutions with current techniques (maximum size and maximum weight allocations) in terms of violations of the respecting improvement property. We find that game-theoretical solutions fare much better at respecting improvements even when exchange cycles are bounded, and they do so at a low efficiency cost. As a stepping stone for our simulations, we provide novel integer programming formulations for computing core, competitive, and strong core allocations.

Abstract
In this work, we study last-mile delivery with the option of crowd shipping. A company uses occasional drivers to complement its fleet in the activity of delivering products to its customers. We model it as a variant of the stochastic capacitated vehicle routing problem. Our approach is data-driven, where not only customer orders but also the availability of occasional drivers are uncertain. It is assumed that marginal distributions of the uncertainty vector are known, but the joint distribution is difficult to estimate. We optimize considering a worst-case joint distribution and model with a strategic planning perspective, where we calculate an optimal a priori solution before the uncertainty is revealed. A limit on the infea-sibility of the routes due to the capacity is imposed using probabilistic constraints. We propose an extended formulation for the problem using column-dependent rows and implement a branch-price-and-cut algorithm to solve it. We also develop a heuristic approximation to cope with larger instances of the problem. Through computational experiments, we analyze the solution and performance of the implemented algorithms.

Abstract
Kidney exchange programs (KEPs) represent an additional possibility of transplant for patients suffering from end-stage kidney disease. If a patient has a willing living donor with whom the patient is not compatible, the pair recipient-donor can join a pool of incompatible pairs and, if compatibility between recipient and donor in two or more pairs exists, organs can be exchanged between them. The problem can be modelled as an integer program that in general aims at finding the pairs that should be selected for transplant such that maximum number of transplants is performed. In this paper, we consider that for each recipient there may exist a preference order over the organs that he/she can receive, since a recipient may be compatible with several donors but the level of compatibility with the recipient might vary for different donors. Under this setting, the aim is to find the maximum cardinality stable exchange, a solution where no blocking cycle exists, i.e., there is no cycle such that all recipients prefer the donor in that cycle rather than that in the exchange. For this purpose we propose four novel integer programming models based on the well-known edge and cycle formulations, and also on the position-indexed formulation. These formulations are adjusted for both finding stable and strongly stable exchanges under strict preferences and for the case when ties in preferences may exist. Further-more, we study a situation when the stability requirement can be relaxed by addressing the trade-off between maximum cardinality versus number of blocking cycles allowed in a solution. The effectiveness of the proposed models is assessed through extensive computational experiments on a wide set of in-stances. Results show that the cycle-edge and position-indexed formulations outperform the other two formulations. Another important practical outcome is that targeting strongly stable solutions has a much higher negative impact on the number of transplants (with an average reduction of up to 20% for the bigger instances), when compared to stable solutions.

Abstract
We study a setting in which a company not only has a fleet of capacitated vehicles and drivers available to make deliveries but may also use the services of occasional drivers (ODs) willing to make deliveries using their own vehicles in return for a small fee. Under such a business model, a.k.a crowdshipping, the company seeks to make all the deliveries at the minimum total cost, i.e., the cost associated with their vehicles plus the compensation paid to the ODs.We consider a stochastic and dynamic last-mile delivery environment in which customer delivery orders, as well as ODs available for deliveries, arrive randomly throughout the day, within fixed time windows.We present a novel deep reinforcement learning (DRL) approach to the problem that can deal with large problem instances. We formulate the action selection problem as a mixed-integer optimization program.The DRL approach is compared against other optimization under uncertainty approaches, namely, sample -average approximation (SAA) and distributionally robust optimization (DRO). The results show the effective-ness of the DRL approach by examining out-of-sample performance.