The concept of a lung exchange scheme is similar to that of a kidney exchange scheme, with a key difference being that each patient in a lung exchange scheme requires two donors rather than one. To the best of my knowledge, lung exchange has not yet been implemented in practice, but the following recent papers discuss theoretical foundations:

• Lung Exchange. Haluk Ergin, Tayfun Sönmez, M. Utku Ünver. Working paper. Link

• Mechanism design and implementation for lung exchange. Suiqian Luo and Pingzhong Tang. IJCAI-2015, Buenos Aires, Argentina. Link

The theory of lung exchange was also discussed in a recent Economist article.

This repository contains my work so far on implementing algorithms for lung exchange. In particular, it includes integer programming formulations for:

• Optimisation with unbounded exchange size, using an edge formulation
• Optimisation with bounded exchange size, using a variant of Constantino et al.'s extended edge formulation for kidney exchange
• Optimisation with bounded exchange size, with a variable for each feasible exchange.

Google or-tools is required for solving integer programs.

To generate a lung-exchange instance with 2 patients and 4 donors, run the following command.

python lungexchange/lung_generator.py 2

I have tried to closely imitate the generator described by Ergin et al. The generator outputs an instance like this:

2 4
CF M 40 O 236
CF F 18 A 177
0 F 62 O 185
0 M 42 O 187
1 F 27 A 139
1 F 27 A 145

The first row gives (number of patients), (number of donors). The patients follow, with each row showing condition (cystic fibrosis or pulmonary hypertension), gender, age, blood type, and weight. The remaining rows are donors in the format paired-patient-ID, gender, age, blood type, weight.

To find the number of transplants in an optimal solution, run:

python lungexchange/optimise.py instance.txt 5 True

The command-line arguments are instance file name, maximum permitted cycle size, and whether weights should be taken into account whether a donor is compatible with a patient. The results look like:

instance.txt    1   50  48.0    18.0    28.0    34.0    40.0    5

The first four columns are (1) file name, (2) an indictor for whether donor and patient weights were used to determine compatibility, (3) number of patients in the instance, and (4) number of donors used in an optimal solution with unrestricted exchange size. The final column is the number of patients in the instance who have two compatible paired donors. The remaining columns are the number of donors used in an optimal solution with an exchange size limit of 2, 3, ..., n. Note that if a patient's two donors are able to give directly to the patient, these both count towards the optimal value.

More verbose output can be viewed using:

python lungexchange/optimise_verbose.py instance.txt 4

Note that if a patient P is compatible with two of P's own paired donors, then the program does not identify compatibilities between P and any other patient's paired donors, or between P's paired donors and any other patient.