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 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

Abstract
A recent relevant innovation in last-mile delivery is to consider the possibility of goods being delivered by couriers appointed through crowdsourcing. In this paper we focus on the setting of in-store customers delivering goods, ordered by online customers, on their way home. We assume that not all the proposed delivery tasks will necessarily be accepted, and use logistic regression to model the crowd agents' willingness to undertake a delivery. This model is then used to build a novel compensation scheme that determines reward values, based on the current plan for the professional fleet's routes and on the couriers' probabilities of acceptance, by employing a direct search algorithm that seeks to minimise the expected cost.

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.