A Comprehensive Mathematical Model for Designing an Organ Transplant Supply Chain Network under Uncertainty


School of industrial engineering, college of engineering, University of Tehran, Tehran, Iran


One of the most important issues in area of health and hygiene is location-allocation of organ harvesting centers and transplant centers according to coordination between supply and demand. In this paper, a mathematical model is presented for location-allocation of organ harvesting centers and transplant centers. The proposed model does not only minimize the present value of the total system costs, but also minimizes the geographical inequalities. The presented model is a bi-objective nonlinear mathematical programming and some of the problem parameters, such as cost, transport time and the like are associated with uncertainty and considered as fuzzy sets in the mathematical formulation. In this paper, an Organ Transplant Supply Chain (OTSC) has been designed and the ε-constraint method has been used to solve the problem and Iran is considered as a case study. The results show that the patient's family satisfaction rate is more important than the viability rate in the number of transplant operations performed and for a transplant operation to be performed, the minimum satisfaction rate (Bh) should be 0.4 and organ viability rate (UD0) should be 0.2.


1. Papageorgiou, L.G., “Supply chain optimisation for the process
industries: Advances and opportunities”, Computers &
Chemical Engineering, Vol. 33, No. 12, (2009), 1931–1938.
2. Rabbani, M., Aghabegloo, M., and Farrokhi-Asl, H., “Solving a
bi-objective mathematical programming model for
bloodmobiles location routing problem”, International Journal
of Industrial Engineering Computations, Vol. 8, No. 1, (2017),
3. Harmanci Seren, A.K., Yavuz, H., Horoz, A., and Yıldız, M.,
“Opinions and Expectations of Muslim Donors’ Relatives
Deciding Organ Donation: The Sample of Istanbul”, Journal of
Religion and Health, Vol. 57, No. 6, (2018), 2515–2522.
4. Pishvaee, M.S., and Razmi, J., “Environmental supply chain
network design using multi-objective fuzzy mathematical
programming”, Applied Mathematical Modelling, Vol. 36, No.
8, (2012), 3433–3446.
5. Shariff, S.S.R., Moin, N.H., and Omar, M., “Location allocation
modeling for healthcare facility planning in Malaysia”,
Computers & Industrial Engineering, Vol. 62, No. 4, (2012),
6. Paganelli, F., Mantecchini, L., Peritore, D., Morabito, V.,
Rizzato, L., and Costa, A.N., “Network Model for Optimal
Aircraft Location for Human Organ Transportation Activities”,
Transplantation Proceedings, Vol. 51, No. 1, (2019), 100–105.
7. Caruso, V., and Daniele, P., “A network model for minimizing
the total organ transplant costs”, European Journal of
Operational Research, Vol. 266, No. 2, (2018), 652–662.
8. Zahiri, B., Tavakkoli-Moghaddam, R., and Pishvaee, M.S., “A
robust possibilistic programming approach to multi-period
location–allocation of organ transplant centers under
uncertainty”, Computers & Industrial Engineering, Vol. 74,
(2014), 139–148.
9. Zahiri, B., Tavakkoli-Moghaddam, R., Mohammadi, M., and
Jula, P., “Multi-objective design of an organ transplant network
under uncertainty”, Transportation Research Part E: Logistics
and Transportation Review, Vol. 72, (2014), 101–124.
10. Chankong, V., and Haimes, Y., Multiobjective decision making:
theory and methodology, Courier Dover Publications, (2008).
11. Ehrgott, M., and Ryan, D.M., “Constructing robust crew
schedules with bicriteria optimization”, Journal of Multi-
Criteria Decision Analysis, Vol. 11, No. 3, (2002), 139–150.
12. Mavrotas, G., “Effective implementation of the ε-constraint
method in Multi-Objective Mathematical Programming
problems”, Applied Mathematics and Computation, Vol. 213,
No. 2, (2009), 455–465.