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A biobjective integrated mathematical model for blood supply chain: Case of Turkish red crescent
1.  Department of Industrial Engineering, Çankaya University, Ankara, Turkey 
2.  TRT General Directorate, Ankara, Turkey 
Various criteria feature in blood supply chain (BSC) designs, where costbased and timebased are the most commonly found in the literature. In the current study, total annual cost is used together with a new timebased objective. The total time spent in the transportation of blood products is considered as time lost, and weight is given to that time according to the product amount and then normalized with respect to shelf life. In using cost and time objectives, we developed a biobjective mixedinteger mathematical programming model for the BSC of Turkish Red Crescent (TRC, the singular authority controlling BSC throughout Turkey), including collection, production, and distribution echelons, and also considering bagtype decisions for wholeblood collection. The objective of the study was to propose a BSC design model and solution approach. With all reallife TRC instances resolved optimally, a linear programming relaxationbased heuristic was developed for largescale problem sizes. Reallife data were obtained from the TRC and the remainder from opentopublic sources. The study's main finding is that cost and time objectives alone produce significantly different designs, whilst using them together to form efficientfrontier solutions for decisionmakers adds practical value.
References:
[1] 
M. Arani, Y. Chan, X. Liu and M. Momenitabar, A lateral resupply blood supply chain network design under uncertainties, Applied Mathematical Modelling, 93 (2021), 165187. doi: 10.1016/j.apm.2020.12.010. 
[2] 
A. M. Araújo, D. Santos, I. Marques and A. BarbosaPovoa, Blood supply chain: A twostage approach for tactical and operational planning, OR Spectrum, 42 (2020), 10231053. doi: 10.1007/s00291020006001. 
[3] 
M. Arvan, R. TavakkoliMoghaddam and M. Abdollahi, Designing a biobjective and multiproduct supply chain network for the supply of blood, Uncertain Supply Chain Management, 3 (2015), 5768. 
[4] 
M. Y. N. Attari, S. H. R. Pasandideh and S. T. Akhavan Niaki, A hybrid robust stochastic programming for a biobjective blood collection facilities problem (Case study: Iranian blood transfusion network), Journal of Industrial and Production Engineering, 36 (2019), 154167. 
[5] 
G. Bruno, A. Diglio, C. Piccolo and L. Cannavacciuolo, Territorial reorganization of regional blood management systems: Evidences from an Italian case study, Omega, 89 (2019), 5470. 
[6] 
H. M. Dilaver, A Mathematical Modeling Approach for Managing Regional Blood Bank Operations, M. Sc. thesis, Bilkent University in Ankara, 2018. 
[7] 
M. EskandariKhanghahi, R. TavakkoliMoghaddam, A. A. Taleizadeh and S. H. Amin, Designing and optimizing a sustainable supply chain network for a blood platelet bank under uncertainty, Engineering Applications of Artificial Intelligence, 71 (2018), 236250. 
[8] 
B. Fahimnia, A. Jabbarzadeh, A. Ghavamifar and M. Bell, Supply chain design for efficient and effective blood supply in disasters, International Journal of Production Economics, 183 (2017), 700709. 
[9] 
M. FazliKhalaf, S. Khalilpourazari and M. Mohammadi, Mixed robust possibilistic flexible chance constraint optimization model for emergency blood supply chain network design, Annals of Operations Research, 283 (2019), 10791109. doi: 10.1007/s1047901727293. 
[10] 
S. B. Ghorashi, M. Hamedi and R. Sadeghian, Modeling and optimization of a reliable blood supply chain network in crisis considering blood compatibility using MOGWO, Neural Computing and Applications, (2019), 1–28. 
[11] 
Habertürk, Corona and Ramadan Reduced Daily Donations from 9 Thousand Units to 2 Thousand, News of Habertürk, 2020. Available from: https://www.haberturk.com/koronaveramazanbirlesincegunlukkanbagisi9binuniteden2binedustuhaberler2664729. 
[12] 
N. Haghjoo, R. TavakkoliMoghaddam, H. ShahmoradiMoghadam and Y. Rahimi, Reliable blood supply chain network design with facility disruption: A realworld application, Engineering Applications of Artificial Intelligence, 90 (2020), 103493. 
[13] 
S. M. HosseiniMotlagh, M. R. G. Samani and S. Cheraghi, Robust and stable flexible blood supply chain network design under motivational initiatives, SocioEconomic Planning Sciences, (2020), 70. 
[14] 
S. M. HosseiniMotlagh, M. R. G. Samani and S. Cheraghi, Robust and stable flexible blood supply chain network design under motivational initiatives, SocioEconomic Planning Sciences, 70 (2020), 100725. 
[15] 
S. M. HosseiniMotlagh, M. R. G. Samani and S. Homaei, Blood supply chain management: Robust optimization, disruption risk, and blood group compatibility (a reallife case), Journal of Ambient Intelligence and Humanized Computing, 11 (2020), 10851104. 
[16] 
İ Karadaǧ, M. E. Keskin and V. Yiǧ it, Redesign of a blood supply chain organization with mobile units, Soft Computing, 25 (2021), 63116327. 
[17] 
S. Khalilpourazari and A. Arshadi Khamseh, Biobjective emergency blood supply chain network design in earthquake considering earthquake magnitude: A comprehensive study with real world application, Annals of Operations Research, 283 (2019), 355393. doi: 10.1007/s104790172588y. 
[18] 
S. Khalilpourazari, S. Soltanzadeh, G. W. Weber and S. K. Roy, Designing an efficient blood supply chain network in crisis: Neural learning, optimization and case study, Annals of Operations Research, 289 (2020), 123152. doi: 10.1007/s10479019034372. 
[19] 
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G. W. Weber, A robust optimization model for sustainable and resilient closedloop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization, 11 (2021), 221. doi: 10.3934/naco.2020023. 
[20] 
R. Lotfi, S. Safavi, A. Gharehbaghi, S. Ghaboulian Zare, R. Hazrati and G. W. Weber, Viable supply chain network design by considering blockchain technology and cryptocurrency, Mathematical Problems in Engineering, (2021). 
[21] 
R. Lotfi, B. Kargar, A. Gharehbaghi and G. W. Weber, Viable medical waste chain network design by considering risk and robustness, Environmental Science and Pollution Research, (2021), 1–16. 
[22] 
R. Lotfi, N. Mardani and G. W. Weber, Robust bilevel programming for renewable energy location, International Journal of Energy Research, 45 (2021), 75217534. 
[23] 
R. Lotfi, B. Kargar, S. H. Hoseini, S. Nazari, S. Safavi and G. W. Weber, Resilience and sustainable supply chain network design by considering renewable energy, International Journal of Energy Research, 45 (2021), 118. 
[24] 
R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh, E. B. Tirkolaee and G. W. Weber, A robust timecostqualityenergyenvironment tradeoff with resourceconstrained in project management: A case study for a bridge construction project, Journal of Industrial & Management Optimization, (2020). doi: 10.3934/jimo. 2020158. 
[25] 
G. Mavrotas, Effective implementation of the $\epsilon$constraint method in multiobjective mathematical programming problems, Applied mathematics and computation, 213 (2009), 455465. doi: 10.1016/j.amc.2009.03.037. 
[26] 
A. Nagurney, A. H. Masoumi and M. Yu, Supply chain network operations management of a blood banking system with cost and risk minimization, Computational Management Science, 9 (2012), 205231. doi: 10.1007/s102870110133z. 
[27] 
J. Nahofti Kohneh, H. Derikvand, M. Amirdadi and E. Teimoury, A blood supply chain network design with interconnected and motivational strategies: A case study, Journal of Ambient Intelligence and Humanized Computing, (2021), 1–21. 
[28] 
NTV, Reduced Blood Stocks Caused TRC to Offer VIP Service to Donors, News of NTV, 2020. Available from: https://www.ntv.com.tr/galeri/saglik/kanstoklariazaldikizilaybagiscilaraviphizmetbaslatti,dXQI2jsHk6VBnoVXd1xRQ/EMpFQyAyoUuOP_sDU5AjXQ. 
[29] 
A. F. Osorio, S. C. Brailsford and H. K. Smith, A structured review of quantitative models in the blood supply chain: a taxonomic framework for decision making, International Journal of Production Research, 53 (2015), 71917212. 
[30] 
A. F. Osorio, S. C. Brailsford, H. K. Smith and J. Blake, Designing the blood supply chain: How much, how and where?, Vox sanguinis, 113 (2018), 760769. 
[31] 
D. Rahmani, Designing a robust and dynamic network for the emergency blood supply chain with the risk of disruptions, Annals of Operations Research, 283 (2019), 613641. doi: 10.1007/s1047901829606. 
[32] 
G. Șahin, H. Süral and S. Meral, Locational analysis for regionalization of Turkish Red Crescent blood services, Computers & Operations Research, 34 (2007), 692704. 
[33] 
M. R. G. Samani, S. M. HosseiniMotlagh and S. F. Ghannadpour, A multilateral perspective towards blood network design in an uncertain environment: Methodology and implementation, Computers & Industrial Engineering, 130 (2019), 450471. 
[34] 
S. A. SeyfiShishavan, Y. Donyatalab, E. Farrokhizadeh and S. I. Satoglu, A fuzzy optimization model for designing an efficient blood supply chain network under uncertainty and disruption, Annals of Operations Research, (2021), 1–55. 
[35] 
P. N. Thanh, O. Péton and N. Bostel, A linear relaxationbased heuristic approach for logistics network design, Computers & Industrial Engineering, 59 (2010), 964975. 
[36] 
A. S. Torrado and A. BarbosaPóvoa, Towards an optimized and sustainable blood supply chain network under uncertainty: A literature review, Cleaner Logistics and Supply Chain, (2022). doi: 10.1007/s00291020006001. 
[37] 
Turkish Rec Crescent, Emergency Blood Call, News of Turkish Rec Crescent, 2020. Available from: https://www.kizilay.org.tr/Haber/KurumsalHaberDetay/5116. 
[38] 
M. Yegül, Simulation Analysis of the Blood Supply Chain and a Case Study, M. Sc. thesis, Middle East Technical University in Ankara, 2007. 
[39] 
M. Yegül, Blood Supply Network Design, Ph. D thesis, Middle East Technical University in Ankara, 2016. 
[40] 
V. Yolcu, Logistics Management for Blood Collection and Blood Products Distribution in Turkish Red Crescent, M. Sc. thesis, Çankaya University in Ankara, 2019. 
[41] 
B. Zahiri, S. A. Torabi, M. Mohammadi and M. Aghabegloo, A multistage stochastic programming approach for blood supply chain planning, Computers & Industrial Engineering, 122 (2018), 114. 
[42] 
Y. Zhou, T. Zou, C. Liu, H. Yu, L. Chen and J. Su, Blood supply chain operation considering lifetime and transshipment under uncertain environment, Applied Soft Computing, (2021), 106. 
show all references
References:
[1] 
M. Arani, Y. Chan, X. Liu and M. Momenitabar, A lateral resupply blood supply chain network design under uncertainties, Applied Mathematical Modelling, 93 (2021), 165187. doi: 10.1016/j.apm.2020.12.010. 
[2] 
A. M. Araújo, D. Santos, I. Marques and A. BarbosaPovoa, Blood supply chain: A twostage approach for tactical and operational planning, OR Spectrum, 42 (2020), 10231053. doi: 10.1007/s00291020006001. 
[3] 
M. Arvan, R. TavakkoliMoghaddam and M. Abdollahi, Designing a biobjective and multiproduct supply chain network for the supply of blood, Uncertain Supply Chain Management, 3 (2015), 5768. 
[4] 
M. Y. N. Attari, S. H. R. Pasandideh and S. T. Akhavan Niaki, A hybrid robust stochastic programming for a biobjective blood collection facilities problem (Case study: Iranian blood transfusion network), Journal of Industrial and Production Engineering, 36 (2019), 154167. 
[5] 
G. Bruno, A. Diglio, C. Piccolo and L. Cannavacciuolo, Territorial reorganization of regional blood management systems: Evidences from an Italian case study, Omega, 89 (2019), 5470. 
[6] 
H. M. Dilaver, A Mathematical Modeling Approach for Managing Regional Blood Bank Operations, M. Sc. thesis, Bilkent University in Ankara, 2018. 
[7] 
M. EskandariKhanghahi, R. TavakkoliMoghaddam, A. A. Taleizadeh and S. H. Amin, Designing and optimizing a sustainable supply chain network for a blood platelet bank under uncertainty, Engineering Applications of Artificial Intelligence, 71 (2018), 236250. 
[8] 
B. Fahimnia, A. Jabbarzadeh, A. Ghavamifar and M. Bell, Supply chain design for efficient and effective blood supply in disasters, International Journal of Production Economics, 183 (2017), 700709. 
[9] 
M. FazliKhalaf, S. Khalilpourazari and M. Mohammadi, Mixed robust possibilistic flexible chance constraint optimization model for emergency blood supply chain network design, Annals of Operations Research, 283 (2019), 10791109. doi: 10.1007/s1047901727293. 
[10] 
S. B. Ghorashi, M. Hamedi and R. Sadeghian, Modeling and optimization of a reliable blood supply chain network in crisis considering blood compatibility using MOGWO, Neural Computing and Applications, (2019), 1–28. 
[11] 
Habertürk, Corona and Ramadan Reduced Daily Donations from 9 Thousand Units to 2 Thousand, News of Habertürk, 2020. Available from: https://www.haberturk.com/koronaveramazanbirlesincegunlukkanbagisi9binuniteden2binedustuhaberler2664729. 
[12] 
N. Haghjoo, R. TavakkoliMoghaddam, H. ShahmoradiMoghadam and Y. Rahimi, Reliable blood supply chain network design with facility disruption: A realworld application, Engineering Applications of Artificial Intelligence, 90 (2020), 103493. 
[13] 
S. M. HosseiniMotlagh, M. R. G. Samani and S. Cheraghi, Robust and stable flexible blood supply chain network design under motivational initiatives, SocioEconomic Planning Sciences, (2020), 70. 
[14] 
S. M. HosseiniMotlagh, M. R. G. Samani and S. Cheraghi, Robust and stable flexible blood supply chain network design under motivational initiatives, SocioEconomic Planning Sciences, 70 (2020), 100725. 
[15] 
S. M. HosseiniMotlagh, M. R. G. Samani and S. Homaei, Blood supply chain management: Robust optimization, disruption risk, and blood group compatibility (a reallife case), Journal of Ambient Intelligence and Humanized Computing, 11 (2020), 10851104. 
[16] 
İ Karadaǧ, M. E. Keskin and V. Yiǧ it, Redesign of a blood supply chain organization with mobile units, Soft Computing, 25 (2021), 63116327. 
[17] 
S. Khalilpourazari and A. Arshadi Khamseh, Biobjective emergency blood supply chain network design in earthquake considering earthquake magnitude: A comprehensive study with real world application, Annals of Operations Research, 283 (2019), 355393. doi: 10.1007/s104790172588y. 
[18] 
S. Khalilpourazari, S. Soltanzadeh, G. W. Weber and S. K. Roy, Designing an efficient blood supply chain network in crisis: Neural learning, optimization and case study, Annals of Operations Research, 289 (2020), 123152. doi: 10.1007/s10479019034372. 
[19] 
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G. W. Weber, A robust optimization model for sustainable and resilient closedloop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization, 11 (2021), 221. doi: 10.3934/naco.2020023. 
[20] 
R. Lotfi, S. Safavi, A. Gharehbaghi, S. Ghaboulian Zare, R. Hazrati and G. W. Weber, Viable supply chain network design by considering blockchain technology and cryptocurrency, Mathematical Problems in Engineering, (2021). 
[21] 
R. Lotfi, B. Kargar, A. Gharehbaghi and G. W. Weber, Viable medical waste chain network design by considering risk and robustness, Environmental Science and Pollution Research, (2021), 1–16. 
[22] 
R. Lotfi, N. Mardani and G. W. Weber, Robust bilevel programming for renewable energy location, International Journal of Energy Research, 45 (2021), 75217534. 
[23] 
R. Lotfi, B. Kargar, S. H. Hoseini, S. Nazari, S. Safavi and G. W. Weber, Resilience and sustainable supply chain network design by considering renewable energy, International Journal of Energy Research, 45 (2021), 118. 
[24] 
R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh, E. B. Tirkolaee and G. W. Weber, A robust timecostqualityenergyenvironment tradeoff with resourceconstrained in project management: A case study for a bridge construction project, Journal of Industrial & Management Optimization, (2020). doi: 10.3934/jimo. 2020158. 
[25] 
G. Mavrotas, Effective implementation of the $\epsilon$constraint method in multiobjective mathematical programming problems, Applied mathematics and computation, 213 (2009), 455465. doi: 10.1016/j.amc.2009.03.037. 
[26] 
A. Nagurney, A. H. Masoumi and M. Yu, Supply chain network operations management of a blood banking system with cost and risk minimization, Computational Management Science, 9 (2012), 205231. doi: 10.1007/s102870110133z. 
[27] 
J. Nahofti Kohneh, H. Derikvand, M. Amirdadi and E. Teimoury, A blood supply chain network design with interconnected and motivational strategies: A case study, Journal of Ambient Intelligence and Humanized Computing, (2021), 1–21. 
[28] 
NTV, Reduced Blood Stocks Caused TRC to Offer VIP Service to Donors, News of NTV, 2020. Available from: https://www.ntv.com.tr/galeri/saglik/kanstoklariazaldikizilaybagiscilaraviphizmetbaslatti,dXQI2jsHk6VBnoVXd1xRQ/EMpFQyAyoUuOP_sDU5AjXQ. 
[29] 
A. F. Osorio, S. C. Brailsford and H. K. Smith, A structured review of quantitative models in the blood supply chain: a taxonomic framework for decision making, International Journal of Production Research, 53 (2015), 71917212. 
[30] 
A. F. Osorio, S. C. Brailsford, H. K. Smith and J. Blake, Designing the blood supply chain: How much, how and where?, Vox sanguinis, 113 (2018), 760769. 
[31] 
D. Rahmani, Designing a robust and dynamic network for the emergency blood supply chain with the risk of disruptions, Annals of Operations Research, 283 (2019), 613641. doi: 10.1007/s1047901829606. 
[32] 
G. Șahin, H. Süral and S. Meral, Locational analysis for regionalization of Turkish Red Crescent blood services, Computers & Operations Research, 34 (2007), 692704. 
[33] 
M. R. G. Samani, S. M. HosseiniMotlagh and S. F. Ghannadpour, A multilateral perspective towards blood network design in an uncertain environment: Methodology and implementation, Computers & Industrial Engineering, 130 (2019), 450471. 
[34] 
S. A. SeyfiShishavan, Y. Donyatalab, E. Farrokhizadeh and S. I. Satoglu, A fuzzy optimization model for designing an efficient blood supply chain network under uncertainty and disruption, Annals of Operations Research, (2021), 1–55. 
[35] 
P. N. Thanh, O. Péton and N. Bostel, A linear relaxationbased heuristic approach for logistics network design, Computers & Industrial Engineering, 59 (2010), 964975. 
[36] 
A. S. Torrado and A. BarbosaPóvoa, Towards an optimized and sustainable blood supply chain network under uncertainty: A literature review, Cleaner Logistics and Supply Chain, (2022). doi: 10.1007/s00291020006001. 
[37] 
Turkish Rec Crescent, Emergency Blood Call, News of Turkish Rec Crescent, 2020. Available from: https://www.kizilay.org.tr/Haber/KurumsalHaberDetay/5116. 
[38] 
M. Yegül, Simulation Analysis of the Blood Supply Chain and a Case Study, M. Sc. thesis, Middle East Technical University in Ankara, 2007. 
[39] 
M. Yegül, Blood Supply Network Design, Ph. D thesis, Middle East Technical University in Ankara, 2016. 
[40] 
V. Yolcu, Logistics Management for Blood Collection and Blood Products Distribution in Turkish Red Crescent, M. Sc. thesis, Çankaya University in Ankara, 2019. 
[41] 
B. Zahiri, S. A. Torabi, M. Mohammadi and M. Aghabegloo, A multistage stochastic programming approach for blood supply chain planning, Computers & Industrial Engineering, 122 (2018), 114. 
[42] 
Y. Zhou, T. Zou, C. Liu, H. Yu, L. Chen and J. Su, Blood supply chain operation considering lifetime and transshipment under uncertain environment, Applied Soft Computing, (2021), 106. 
Reference  BSC Echelons  Objective(s)  Decisions  Solution  
Collection  Production  Inventory  Distribution  Single/Multi  Aggregated  Bag type  WB test  Lateral transport.  Reallife case  Heuristic developed  
[14]  Y  Y  Y  Y  S  ——  Y  N  N  Y  Y 
[32]  N  N  N  Y  M  Y  N  N  N  Y  N 
[5]  Y  N  N  N  S  ——  N  N  N  Y  N 
[39]  Y  Y  Y  Y  S  ——  N  N  N  Y  Y 
[33]  Y  Y  Y  Y  M  Y  N  Y  N  Y  N 
[10]  Y  Y  Y  Y  M  Y  N  Y  N  N  Y 
[4]  Y  Y  N  Y  M  Y  N  Y  N  Y  N 
[16]  Y  N  N  Y  M  Y  N  N  N  Y  N 
[41]  Y  Y  Y  Y  M  N  N  N  Y  N  Y 
[1]  Y  Y  Y  Y  M  Y  N  N  Y  N  N 
[2]  Y  Y  Y  Y  S  ——  N  N  N  Y  Y 
[3]  Y  Y  N  Y  M  N  N  Y  Y  N  N 
Our study  Y  Y  N  Y  M  N  Y  Y  Y  Y  Y 
Y: Yes, N: No, M: Multi, S: Single, ——: Not applicable. 
Reference  BSC Echelons  Objective(s)  Decisions  Solution  
Collection  Production  Inventory  Distribution  Single/Multi  Aggregated  Bag type  WB test  Lateral transport.  Reallife case  Heuristic developed  
[14]  Y  Y  Y  Y  S  ——  Y  N  N  Y  Y 
[32]  N  N  N  Y  M  Y  N  N  N  Y  N 
[5]  Y  N  N  N  S  ——  N  N  N  Y  N 
[39]  Y  Y  Y  Y  S  ——  N  N  N  Y  Y 
[33]  Y  Y  Y  Y  M  Y  N  Y  N  Y  N 
[10]  Y  Y  Y  Y  M  Y  N  Y  N  N  Y 
[4]  Y  Y  N  Y  M  Y  N  Y  N  Y  N 
[16]  Y  N  N  Y  M  Y  N  N  N  Y  N 
[41]  Y  Y  Y  Y  M  N  N  N  Y  N  Y 
[1]  Y  Y  Y  Y  M  Y  N  N  Y  N  N 
[2]  Y  Y  Y  Y  S  ——  N  N  N  Y  Y 
[3]  Y  Y  N  Y  M  N  N  Y  Y  N  N 
Our study  Y  Y  N  Y  M  N  Y  Y  Y  Y  Y 
Y: Yes, N: No, M: Multi, S: Single, ——: Not applicable. 
Product  Treatment Case  Shelf Life  
ES  Erythrocyte suspension  Surgery with major blood loss, treatment of anemic patients, premature infants  42 days 
TS  Thrombocyte suspension  Major blood loss, cancer treatment  5 days 
FFP  Fresh frozen plasma  Blood loss and curbs in surgery, treatment of liver disease, treatment of burn injuries  2 years 
Product  Treatment Case  Shelf Life  
ES  Erythrocyte suspension  Surgery with major blood loss, treatment of anemic patients, premature infants  42 days 
TS  Thrombocyte suspension  Major blood loss, cancer treatment  5 days 
FFP  Fresh frozen plasma  Blood loss and curbs in surgery, treatment of liver disease, treatment of burn injuries  2 years 
Notations for the COST Model:  
Superscripts:  
AS  Apheresis Set 
BC  Buffy Coat 
ES  Erythrocyte Suspension 
FFP  Fresh Frozen Plasma 
JH  Relation between an RBC and a TFC 
JJ  Relation between one RBC and another RBC 
JK  Relation between an RBC and a BDC 
JL  Relation between an RBC and a CL 
LP  Liquid Plasma 
TB  Top & Bottom (bag type) 
TS  Thrombocyte Suspension 
TSA  Thrombocyte Suspension obtained by apheresis donation 
TT  Top & Top (bag type) 
Indices:  
Cities in Turkey 

Regional blood centers (RBCs) 

Blood donation centers (BDCs) 

Transfusion centers (TFCs) 

Central laboratories (CLs) 

Transportation modes 

Set of TFCs located within a city i 

Parameters:  
Donation amounts:  
Annual donation amount in BDC k  
Annual apheresis donation amount in BDC k  
WB and BP bag amounts:  
Average amount of blood in a whole blood bag (liters/bag)  
Average amount of BC in one readyforsale bag (liters/bag)  
Average amount of TS in one readyforsale bag (liters/bag)  
Average amount of TS (obtained by apheresis donation) in one readyforsale bag (liters/bag)  
Average amount of LP in one readyforsale bag (liters/bag)  
Average amount of FFP in one readyforsale bag (liters/bag)  
Average amount of ES in one readyforsale bag (liters/bag)  
BP production amounts:  
Average amount of ES produced with one T & T bag (liters)  
Average amount of LP produced with one T & T bag (liters)  
Average amount of ES produced with one T & B bag (liters)  
Average amount of LP produced with one T & B bag (liters)  
Average amount of BC produced with one T & B bag (liters)  
Average amount of TS produced with one apheresis set (liters)  
BP demand amounts:  
Annual TS demand at TM h (liters/year)  
Annual ES demand at TM h (liters/year)  
Annual FFP demand at TM h (liters/year)  
Transportation costs: (Note: TL refers to Turkish Lira; ISO code: TRY)  
Unit cost of transportation from RBC j to BDC k with mode t (TL/liter/kilometer)  
Unit cost of transportation from RBC j' to RBC j with mode t (TL/liter/kilometer)  
Unit cost of transportation from RBC j to TFC h with mode t (TL/liter/kilometer  
Unit cost of transportation from RBC j to CL l with mode t (TL/liter/kilometer)  
Blood bag costs:  
T & T bag cost (TL/bag)  
T & B bag cost (TL/bag)  
Apheresis set cost (TL/set)  
Operation and production costs:  
Estimated operational cost of whole blood donation with T & T bag (TL/bag)  
Estimated operational cost of whole blood donation with T & B bag (TL/bag)  
Estimated production cost of ES (TL/bag)  
Estimated production cost of LP (TL/bag)  
Estimated production cost of BC (TL/bag)  
Estimated production cost of FFP (TL/bag)  
Estimated production cost of TS (TL/bag)  
Destruction costs:  
Estimated destruction cost of whole blood in T & T bag (TL/bag)  
Estimated destruction cost of whole blood in T & B bag (TL/bag)  
Estimated destruction cost of apheresis (TL/set)  
Estimated destruction cost of ES (TL/bag)  
Estimated destruction cost of LP (TL/bag)  
Estimated destruction cost of BC (TL/bag)  
Estimated destruction cost of FFP (TL/bag)  
Estimated destruction cost of TS (TL/bag)  
Lot size:  
Average lot size of blood products in a vehicle per TFC shipment j dispatched from an RBC via ground transportation mode  
Distances:  
1, if BDC k is close to RBC j; 0, otherwise  
Distance from BDC k to RBC j with mode t (kilometers)  
Distance from RBC j to RBC j' with mode t (kilometers)  
Distance from TFC h to RBC j with mode t (kilometers)  
Distance from CL l to RBC j with mode t (kilometers)  
Decision variables:  
Rate of whole blood donations collected with T & B bag in BDC k  
1, if BDC k is assigned to RBC j with mode t; 0, otherwise  
1, if TFCs in city i are assigned to RBC j with mode t; 0, otherwise  
1, if RBC j is assigned to CL l with mode t; 0, otherwise  
Annual production of BC in BDC k (liters/year)  
Annual BC produced and destroyed in BDC k (liters/year)  
Annual production of TS (from BC) in BDC k (liters/year)  
Annual production of TS in BDC k (liters/year)  
Annual TS produced and destroyed in BDC k (liters/year)  
Annual production of TS (with apheresis) in BDC k (liters/year)  
Annual TS produced (with apheresis) and destroyed in BDC k (liters/year)  
Annual production of LP in BDC k (liters/year)  
Annual LP produced and destroyed in BDC k (liters/year)  
Annual production of FFP in BDC k (liters/year)  
Annual FFP produced and destroyed in BDC k (liters/year)  
Annual production of ES in BDC k (liters/year)  
Annual ES produced and destroyed in BDC k (liters/year)  
Annual lateral transshipment amount of TS from RBC j to RBC j' with mode t (liters/year)  
Annual lateral transshipment amount of ES from RBC j to RBC j' with mode t (liters/year)  
Annual lateral transshipment amount of FFP from RBC j to RBC j' with mode t (liters/year)  
Annual ES produced from donated whole blood at BDC k and sent to RBC j with mode t (and then used to satisfy demand) (liters/year)  
Annual ES produced from donated whole blood at BDC k and sent to RBC j with mode t (but then destroyed at RBC j) (liters/year)  
Annual TS produced from donated whole blood at BDC k and sent to RBC j with mode t (and then used to satisfy demand) (liters/year)  
Annual TS produced from donated whole blood at BDC k and sent to RBC j with mode t (but then destroyed at RBC j) (liters/year)  
Annual FFP produced from donated whole blood at BDC k and sent to RBC j with mode t (and then used to satisfy demand) (liters/year)  
Annual FFP produced from donated whole blood at BDC k and sent to RBC j with mode t (but then destroyed at RBC j) (liters/year)  
Total annual BSC cost (TL) 
Notations for the COST Model:  
Superscripts:  
AS  Apheresis Set 
BC  Buffy Coat 
ES  Erythrocyte Suspension 
FFP  Fresh Frozen Plasma 
JH  Relation between an RBC and a TFC 
JJ  Relation between one RBC and another RBC 
JK  Relation between an RBC and a BDC 
JL  Relation between an RBC and a CL 
LP  Liquid Plasma 
TB  Top & Bottom (bag type) 
TS  Thrombocyte Suspension 
TSA  Thrombocyte Suspension obtained by apheresis donation 
TT  Top & Top (bag type) 
Indices:  
Cities in Turkey 

Regional blood centers (RBCs) 

Blood donation centers (BDCs) 

Transfusion centers (TFCs) 

Central laboratories (CLs) 

Transportation modes 

Set of TFCs located within a city i 

Parameters:  
Donation amounts:  
Annual donation amount in BDC k  
Annual apheresis donation amount in BDC k  
WB and BP bag amounts:  
Average amount of blood in a whole blood bag (liters/bag)  
Average amount of BC in one readyforsale bag (liters/bag)  
Average amount of TS in one readyforsale bag (liters/bag)  
Average amount of TS (obtained by apheresis donation) in one readyforsale bag (liters/bag)  
Average amount of LP in one readyforsale bag (liters/bag)  
Average amount of FFP in one readyforsale bag (liters/bag)  
Average amount of ES in one readyforsale bag (liters/bag)  
BP production amounts:  
Average amount of ES produced with one T & T bag (liters)  
Average amount of LP produced with one T & T bag (liters)  
Average amount of ES produced with one T & B bag (liters)  
Average amount of LP produced with one T & B bag (liters)  
Average amount of BC produced with one T & B bag (liters)  
Average amount of TS produced with one apheresis set (liters)  
BP demand amounts:  
Annual TS demand at TM h (liters/year)  
Annual ES demand at TM h (liters/year)  
Annual FFP demand at TM h (liters/year)  
Transportation costs: (Note: TL refers to Turkish Lira; ISO code: TRY)  
Unit cost of transportation from RBC j to BDC k with mode t (TL/liter/kilometer)  
Unit cost of transportation from RBC j' to RBC j with mode t (TL/liter/kilometer)  
Unit cost of transportation from RBC j to TFC h with mode t (TL/liter/kilometer  
Unit cost of transportation from RBC j to CL l with mode t (TL/liter/kilometer)  
Blood bag costs:  
T & T bag cost (TL/bag)  
T & B bag cost (TL/bag)  
Apheresis set cost (TL/set)  
Operation and production costs:  
Estimated operational cost of whole blood donation with T & T bag (TL/bag)  
Estimated operational cost of whole blood donation with T & B bag (TL/bag)  
Estimated production cost of ES (TL/bag)  
Estimated production cost of LP (TL/bag)  
Estimated production cost of BC (TL/bag)  
Estimated production cost of FFP (TL/bag)  
Estimated production cost of TS (TL/bag)  
Destruction costs:  
Estimated destruction cost of whole blood in T & T bag (TL/bag)  
Estimated destruction cost of whole blood in T & B bag (TL/bag)  
Estimated destruction cost of apheresis (TL/set)  
Estimated destruction cost of ES (TL/bag)  
Estimated destruction cost of LP (TL/bag)  
Estimated destruction cost of BC (TL/bag)  
Estimated destruction cost of FFP (TL/bag)  
Estimated destruction cost of TS (TL/bag)  
Lot size:  
Average lot size of blood products in a vehicle per TFC shipment j dispatched from an RBC via ground transportation mode  
Distances:  
1, if BDC k is close to RBC j; 0, otherwise  
Distance from BDC k to RBC j with mode t (kilometers)  
Distance from RBC j to RBC j' with mode t (kilometers)  
Distance from TFC h to RBC j with mode t (kilometers)  
Distance from CL l to RBC j with mode t (kilometers)  
Decision variables:  
Rate of whole blood donations collected with T & B bag in BDC k  
1, if BDC k is assigned to RBC j with mode t; 0, otherwise  
1, if TFCs in city i are assigned to RBC j with mode t; 0, otherwise  
1, if RBC j is assigned to CL l with mode t; 0, otherwise  
Annual production of BC in BDC k (liters/year)  
Annual BC produced and destroyed in BDC k (liters/year)  
Annual production of TS (from BC) in BDC k (liters/year)  
Annual production of TS in BDC k (liters/year)  
Annual TS produced and destroyed in BDC k (liters/year)  
Annual production of TS (with apheresis) in BDC k (liters/year)  
Annual TS produced (with apheresis) and destroyed in BDC k (liters/year)  
Annual production of LP in BDC k (liters/year)  
Annual LP produced and destroyed in BDC k (liters/year)  
Annual production of FFP in BDC k (liters/year)  
Annual FFP produced and destroyed in BDC k (liters/year)  
Annual production of ES in BDC k (liters/year)  
Annual ES produced and destroyed in BDC k (liters/year)  
Annual lateral transshipment amount of TS from RBC j to RBC j' with mode t (liters/year)  
Annual lateral transshipment amount of ES from RBC j to RBC j' with mode t (liters/year)  
Annual lateral transshipment amount of FFP from RBC j to RBC j' with mode t (liters/year)  
Annual ES produced from donated whole blood at BDC k and sent to RBC j with mode t (and then used to satisfy demand) (liters/year)  
Annual ES produced from donated whole blood at BDC k and sent to RBC j with mode t (but then destroyed at RBC j) (liters/year)  
Annual TS produced from donated whole blood at BDC k and sent to RBC j with mode t (and then used to satisfy demand) (liters/year)  
Annual TS produced from donated whole blood at BDC k and sent to RBC j with mode t (but then destroyed at RBC j) (liters/year)  
Annual FFP produced from donated whole blood at BDC k and sent to RBC j with mode t (and then used to satisfy demand) (liters/year)  
Annual FFP produced from donated whole blood at BDC k and sent to RBC j with mode t (but then destroyed at RBC j) (liters/year)  
Total annual BSC cost (TL) 
Additional Notations for the TIME Model:  
Parameters:  
Shelflife:  
Shelflife of TS(minutes)  
Shelflife of ES(minutes)  
Shelflife of FFP(minutes)  
Transportation Times:  
Average time of transportation from RBC j to BDC k with mode t (minutes)  
Average time of transportation from RBC j' to RBC j with mode t (minutes)  
Average time of transportation from RBC j to TFC h with mode t (minutes)  
Decision variables  
Total annual weightedtime in transportation of TS from BDC k to RBC j (liters*minutes)  
Total annual weightedtime in transportation of TS from RBC j' to RBC j (liters*minutes)  
Total annual weightedtime in transportation of TS from RBC j to TFC h (liters*minutes)  
Total annual weightedtime in transportation of ES from BDC k to RBC j (liters*minutes)  
Total annual weightedtime in transportation of ES from RBC j' to RBC j (liters*minutes)  
Total annual weightedtime in transportation of ES from RBC j to TFC h (liters*minutes)  
Total annual weightedtime in transportation of FFP from BDC k to RBC j (liters*minutes)  
Total annual weightedtime in transportation of FFP from RBC j' to RBC j (liters*minutes)  
Total annual weightedtime in transportation of FFP from RBC j to TFC h (liters*minutes)  
Total annual weightedshelflife in transportation of TS (liters*shelflife)  
Total annual weightedshelflife in transportation of ES (liters*shelflife)  
Total annual weightedshelflife in transportation of FFP (liters*shelflife)  
Total annual weightedshelflife in transportation (liters*shelflife) 
Additional Notations for the TIME Model:  
Parameters:  
Shelflife:  
Shelflife of TS(minutes)  
Shelflife of ES(minutes)  
Shelflife of FFP(minutes)  
Transportation Times:  
Average time of transportation from RBC j to BDC k with mode t (minutes)  
Average time of transportation from RBC j' to RBC j with mode t (minutes)  
Average time of transportation from RBC j to TFC h with mode t (minutes)  
Decision variables  
Total annual weightedtime in transportation of TS from BDC k to RBC j (liters*minutes)  
Total annual weightedtime in transportation of TS from RBC j' to RBC j (liters*minutes)  
Total annual weightedtime in transportation of TS from RBC j to TFC h (liters*minutes)  
Total annual weightedtime in transportation of ES from BDC k to RBC j (liters*minutes)  
Total annual weightedtime in transportation of ES from RBC j' to RBC j (liters*minutes)  
Total annual weightedtime in transportation of ES from RBC j to TFC h (liters*minutes)  
Total annual weightedtime in transportation of FFP from BDC k to RBC j (liters*minutes)  
Total annual weightedtime in transportation of FFP from RBC j' to RBC j (liters*minutes)  
Total annual weightedtime in transportation of FFP from RBC j to TFC h (liters*minutes)  
Total annual weightedshelflife in transportation of TS (liters*shelflife)  
Total annual weightedshelflife in transportation of ES (liters*shelflife)  
Total annual weightedshelflife in transportation of FFP (liters*shelflife)  
Total annual weightedshelflife in transportation (liters*shelflife) 
MODEL  OBJECTIVE FUNCTION  OPTIMAL VALUE 
COST  3, 229.71  
TIME  1, 278.74 
MODEL  OBJECTIVE FUNCTION  OPTIMAL VALUE 
COST  3, 229.71  
TIME  1, 278.74 
OBJECTIVE FUNCTION VALUE  
MODEL  
COST  3, 229.71  4, 064.39 
TIME  3, 751.98  1, 278.74 
OBJECTIVE FUNCTION VALUE  
MODEL  
COST  3, 229.71  4, 064.39 
TIME  3, 751.98  1, 278.74 
COST GIVEN TIME (CT) RESULTS 
TIME GIVEN COST (TC) RESULTS 

#  #  
CT1  3, 751.98  1, 278.74  TC1  4, 064.40  3, 229.71  
CT2  3, 263.53  1, 557.30  TC2  1, 284.55  3, 281.93  
CT3  3, 260.05  1, 835.87  TC3  1, 278.84  3, 334.16  
CT4  3, 258.72  2, 114.44  TC4  1, 278.86  3, 386.39  
CT5  3, 257.55  2, 393.00  TC5  1, 279.15  3, 438.62  
CT6  3, 252.06  2, 671.57  TC6  1, 278.74  3, 490.84  
CT7  3, 249.53  2, 950.13  TC7  1, 278.74  3, 543.07  
CT8  3, 243.35  3, 228.70  TC8  1, 278.74  3, 595.30  
CT9  3, 242.91  3, 507.27  TC9  1, 278.74  3, 647.52  
CT10  3, 235.74  3, 785.83  TC10  1, 278.74  3, 699.75  
CT11  3, 229.71  4, 064.40  TC11  1, 278.74  3, 751.98 
COST GIVEN TIME (CT) RESULTS 
TIME GIVEN COST (TC) RESULTS 

#  #  
CT1  3, 751.98  1, 278.74  TC1  4, 064.40  3, 229.71  
CT2  3, 263.53  1, 557.30  TC2  1, 284.55  3, 281.93  
CT3  3, 260.05  1, 835.87  TC3  1, 278.84  3, 334.16  
CT4  3, 258.72  2, 114.44  TC4  1, 278.86  3, 386.39  
CT5  3, 257.55  2, 393.00  TC5  1, 279.15  3, 438.62  
CT6  3, 252.06  2, 671.57  TC6  1, 278.74  3, 490.84  
CT7  3, 249.53  2, 950.13  TC7  1, 278.74  3, 543.07  
CT8  3, 243.35  3, 228.70  TC8  1, 278.74  3, 595.30  
CT9  3, 242.91  3, 507.27  TC9  1, 278.74  3, 647.52  
CT10  3, 235.74  3, 785.83  TC10  1, 278.74  3, 699.75  
CT11  3, 229.71  4, 064.40  TC11  1, 278.74  3, 751.98 
TIME GIVEN COST (TC') RESULTS 

#  
TC'1  3, 229.71  4, 064.40 
TC'2  3, 234.93  1, 518.23 
TC'3  3, 240.15  1, 419.26 
TC'4  3, 245.37  1, 340.95 
TC'5  3, 250.60  1, 335.11 
TC'6  3, 255.82  1, 329.18 
TC'7  3, 261.04  1, 328.35 
TC'8  3, 266.26  1, 309.58 
TC'9  3, 271.49  1, 300.34 
TC'10  3, 276.71  1, 299.13 
TC'11  3, 281.93  1, 284.55 
TIME GIVEN COST (TC') RESULTS 

#  
TC'1  3, 229.71  4, 064.40 
TC'2  3, 234.93  1, 518.23 
TC'3  3, 240.15  1, 419.26 
TC'4  3, 245.37  1, 340.95 
TC'5  3, 250.60  1, 335.11 
TC'6  3, 255.82  1, 329.18 
TC'7  3, 261.04  1, 328.35 
TC'8  3, 266.26  1, 309.58 
TC'9  3, 271.49  1, 300.34 
TC'10  3, 276.71  1, 299.13 
TC'11  3, 281.93  1, 284.55 
OBJECTIVE FUNCTION VALUE  
MODEL  
TIMECA  3, 415.29  1, 361.12 
COSTCA  3, 341.05  1, 409.78 
OBJECTIVE FUNCTION VALUE  
MODEL  
TIMECA  3, 415.29  1, 361.12 
COSTCA  3, 341.05  1, 409.78 
OBJ.  MODELS  % deviation  
TC'8  COSTCA  TIMECA  w.r.t. COSTCA 
w.r.t. TIMECA 

3, 266.26  3, 341.05  3, 415.29  2.29%  4.56%  
1, 295.93  1, 409.78  1, 361.12  8.79%  5.03% 
OBJ.  MODELS  % deviation  
TC'8  COSTCA  TIMECA  w.r.t. COSTCA 
w.r.t. TIMECA 

3, 266.26  3, 341.05  3, 415.29  2.29%  4.56%  
1, 295.93  1, 409.78  1, 361.12  8.79%  5.03% 
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