Recourse in Kidney Exchange Programs

We introduce the problem of selecting patient-donor pairs in a kidney exchange program to undergo a crossmatch test, and we model this selection problem as a two-stage stochastic integer programming problem. The optimal solutions of this new formulation yield a larger expected number of realized transplants than previous approaches based on internal recourse or subset recourse. We settle the computational complexity of the selection problem by showing that it remains NP-hard even for maximum cycle length equal to two. Furthermore, we investigate to what extent different algorithmic approaches, including one based on Benders decomposition, are able to solve instances of the model. We empirically investigate the computational efficiency of this approach by solving randomly generated instances and study the corresponding running times as a function of maximum cycle length, and of the presence of nondirected donors. Summary of Contribution: This paper deals with an important and very complex issue linked to the optimization of transplant matchings in kidney exchange programs, namely, the inherent uncertainty in the assessment of compatibility between donors and recipients of transplants. Although this issue has previously received some attention in the optimization literature, most attempts to date have focused on applying recourse to solutions selected within restricted spaces. The present paper explicitly formulates the maximization of the expected number of transplants as a two-stage stochastic integer programming problem. The formulation turns out to be computationally difficulty, both from a theoretical and from a numerical perspective. Different algorithmic approaches are proposed and tested experimentally for its solution. The quality of the kidney exchanges produced by these algorithms compares favorably with that of earlier models.

Mathematical Model for Cargo Allocation Problem in Synchromodal Transportation

Synchromodality is a freight transport process in which information is exchanged expeditiously in order to maximize the benefits of different modes of transport and transport nodes in terms of efficiency and environmental impact. The aim of the study is to analyze the problems of synchronized intermodal traffic management between the main port and inland transport nodes in European transport corridors and to find reliable solutions to these problems. Therefore, the main purpose of this article is to investigate the problem of the distribution of containers transported by rail between two transport terminals in a synchronous transport network. A specific optimization model is presented in this article. This optimization task is formulated as a stochastic integer programming model between the terminals located in Vilnius and Klaipeda Seaport, the essence of which is as follows: (a) to minimize the waiting time for container cargo at the location—terminal No. 1; (b) to minimize the total journey time of the train; (c) to minimize the waiting time for containerized cargo at the point of arrival—terminal No. 2.

Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem

We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recent results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.