Kristiaan Glorie

A two-stage approach to the orienteering problem with stochastic weights

The Orienteering Problem (OP) is a routing problem which has many interesting applications in logistics, tourism and defense. The aim of the OP is to find a maximum profit path or tour, which is feasible with respect to a capacity constraint on the total weight of the selected arcs. In this paper we consider the Orienteering Problem with Stochastic Weights (OPSWs) to reflect uncertainty in real-life applications. We approach this problem by formulating a two-stage stochastic model with recourse for the OPSW where the capacity constraint is hard. The model takes into account the effect that stochastic weights have on the expected total profit value to be obtained, already in the modeling stage. Since the expected profit is in general non-linear, we introduce a linearization that models the total profit that can be obtained for a given tour and a given scenario of weight realizations. This linearization allows for the application of Sample Average Approximation (SAA). The SAA solution asymptotically converges to the optimal solution of the two-stage model, but is computationally expensive. Therefore, to solve large instances, we developed a heuristic that exploits the problem structure of the OPSW and explicitly takes the associated uncertainty into account. In our computational experiments, we evaluate the benefits of our approach to the OPSW, compared to both a standard deterministic approach, and a deterministic approach that is extended with utilization of real-time information.

Allocation and matching in kidney exchange programs

Living donor kidney transplantation is the preferred treatment for patients suffering from end‐stage renal disease. To alleviate the shortage of kidney donors, many advances have been made to improve the utilization of living donors deemed incompatible with their intended recipient. The most prominent of these advances is kidney paired donation (KPD), which matches incompatible patient–donor pairs to facilitate a kidney exchange. This review discusses the various approaches to matching and allocation in KPD. In particular, it focuses on the underlying principles of matching and allocation approaches, the combination of KPD with other strategies such as ABO incompatible transplantation, the organization of KPD, and important future challenges. As the transplant community strives to balance quantity and equity of transplants to achieve the best possible outcomes, determining the right long‐term allocation strategy becomes increasingly important. In this light, challenges include making full use of the various modalities that are now available through integrated and optimized matching software, encouragement of transplant centers to fully participate, improving transplant rates by focusing on the expected long‐run number of transplants, and selecting uniform allocation criteria to facilitate international pools.

Kidney exchange with long chains: An efficient pricing algorithm for clearing barter exchanges with branch-and-price

Barter exchange markets are markets in which agents seek to directly trade their goods with each other. Exchanges occur in cycles or in chains in which each agent gives a good to the next agent. Kidney exchange is an important type of barter exchange market that allows incompatible patient–donor pairs to exchange kidneys so the involved patients can receive a transplant. The clearing problem is to find an allocation of donors to patients that is optimal with respect to multiple criteria. To achieve the best possible score on all criteria, long cycles and chains are often needed, particularly when there are many hard-to-match patients. In this paper we show why this may pose difficulties for existing approaches to the optimization of kidney exchanges. We then present a generic iterative branch-and-price algorithm that can deal effectively with multiple criteria, and we show how the pricing problem may be solved in polynomial time for a general class of criteria. Our algorithm is effective even for large, realistic patient–donor pools. Our approach and its effects are demonstrated by using simulations with kidney exchange data from the Netherlands and the United States.

Coordinating unspecified living kidney donation and transplantation across the blood-type barrier in kidney exchange.

Background This article studies multicenter coordination of unspecified living kidney donation and transplantation across the blood-type barrier in kidney exchange. Important questions are whether such coordination should use domino paired donation or nonsimultaneous extended altruistic donor chains, what the length of the segments in such chains should be, when they should be terminated, and how much time should be allowed between matching rounds. Furthermore, it is controversial whether the different modalities should be coordinated centrally or locally and independently. Methods Kidney exchange policies are simulated using actual data from the Dutch national kidney exchange program. Sensitivity analysis is performed on the composition of the population, the time unspecified and bridge donors wait before donating to the waitlist, the time between matching rounds, and donor renege rates. Results Central coordination of unspecified donation and transplantation across the blood-type barrier can increase transplants by 10% (P<0.001). Especially highly sensitized and blood type O patients benefit. Sufficient time between matching rounds is essential: three-monthly exchanges result in 31% more transplants than weekly exchanges. Benefits of nonsimultaneous extended altruistic donor chains are limited in case of low numbers of highly sensitized patients and sufficient unspecified donors. Chains are best terminated when no further segment is part of an optimal exchange within 3 months. Conclusions There is clear synergy in the central coordination of both unspecified donation and transplantation across the blood-type barrier in kidney exchange. The best configuration of a national program depends on the composition of the patient–donor population.