Supply Chain Network Design of a Sustainable Blood Banking System
5.4 Summary and Conclusions
Table 5.5 Total cost, total discarding cost, and total investment cost functions, initial capacities, and solution for numerical example 5
Linka αa cˆa(fa) ˆza(fa) πˆa(ua) u¯a fa∗ u∗a γa∗ 1 0.97 6f12+15f1 0.8f12 0.8u21+u1 48.00 43.02 −0.62 0.00 2 0.99 9f22+11f2 0.7f22 0.6u22+u2 40.00 34.54 −0.83 0.00 3 1.00 0.7f32+f3 0.6f32 u23+2u3 26.00 23.77 −1.00 0.00 4 0.99 1.2f42+f4 0.8f42 2u24+u4 20.00 17.54 −0.25 0.00 5 1.00 f52+3f5 0.6f52 u25+u5 19.00 15.45 −0.50 0.00 6 1.00 0.8f62+2f6 0.8f62 1.5u62+3u6 21.00 18.40 −1.00 0.00 7 0.92 2.5f72+2f7 0.5f72 7u27+12u7 44.00 38.99 −0.86 0.00 8 0.96 3f82+5f8 0.8f82 6u28+20u8 37.00 32.91 −1.67 0.00 9 0.98 0.8f92+6f9 0.4f92 3u29+2u9 39.00 34.43 −0.33 0.00 10 1.00 0.5f102 +3f10 0.7f102 5.4u210+2u10 35.00 30.96 −0.19 0.00 11 1.00 0.3f112 +f11 0.3f112 u211+u11 26.00 23.49 −0.50 0.00 12 1.00 0.5f122 +2f12 0.4f122 1.5u122 +u12 13.00 10.25 −0.33 0.00 13 1.00 0.4f132 +2f13 0.3f132 1.8u132 +1.5u13 18.00 18.85 0.85 4.57 14 1.00 0.6f142 +f14 0.4f142 u214+2u14 17.00 12.11 −1.00 0.00 15 1.00 0.4f152 +f15 0.7f152 0.5u215+1.1u15 6.00 5.52 −0.48 0.63 16 1.00 0.8f162 +2f16 0.4f162 0.7u216+3u16 25.00 20.68 −2.14 0.00 17 0.98 0.5f172 +3f17 0.5f172 2u217+u17 14.00 16.15 2.15 9.59 18 1.00 0.7f182 +f18 0.7f182 u218+u18 0.00 0.00 0.00 1.00 19 1.00 0.6f192 +4f19 0.4f192 u219+2u19 16.00 14.58 −1.00 0.00 20 0.98 1.1f202 +5f20 0.5f202 0.8u220+u20 13.00 7.34 −0.62 0.00
Table5.5displays the optimal solution to this example.
As expected, most of the computed capacity changes were negative as a result of the diminished demand for blood at our demand points. Accordingly, the projected demand values were as follows:
v1∗=5.52, v∗2 =35.25, and v∗3=23.02.
The value of the total cost criterion for this Example was 51,221.32.
processing of, and the distribution of this product. The model has several novel features:
1. it captures the perishability of this life-saving product through the use of arc multipliers;
2. it contains discarding costs associated with waste/disposal;
3. it determines the optimal enhancement/reduction of link capacities as well as the determination of the capacities from scratch;
4. it can capture the cost-related effects of shutting down specific modules of the supply chain due to an economic crisis;
5. it handles uncertainty associated with demand points;
6. it assesses costs associated with shortages/surpluses at the demand points, and 7. it quantifies the supply-side risk associated with procurement.
We illustrated the model through several numerical examples, which vividly demon- strate the flexibility and generality of our sustainable supply chain network design model for blood banking systems. For the sake of generality, and the establishment of the foundations that will enable further extensions and applications, we used a variational inequality approach for both model formulation and solution.
The framework developed here can be applied, with appropriate adaptation, to other perishable products, also in the health care arena, such as medicines and vaccines, as well as to agricultural products, including food.
Acknowledgements This research was supported, in part, by the John F. Smith Memorial Foundation. This support is gratefully acknowledged.
The authors acknowledge Mr. Len Walker, the Director of Business Development for the Amer- ican Red Cross Blood Services in the greater Boston area, who shared valuable information on the subject. They also thank Dr. Jorge Rios, the Medical Director for the American Red Cross North- east Division Blood Services, who graciously agreed to be interviewed twice, and who provided enlightening thoughts on the model.
References
Association of Bay Area Governments (2003) Why are hospitals rethinking regulated medical waste management? Environmental Best Practices for Health Care Facilities June 2003
Boppana RV, Chalasani S (2007) Analytical models to determine desirable blood acquisition rates.
IEEE international conference on system of systems engineering
Cetin E, Sarul LS (2009) A blood bank location model: A multiobjective approach. Eur J Pure Appl Math 2(1):112–124
Dong J, Zhang D, Nagurney A (2004) A supply chain network equilibrium model with random demands. Eur J Oper Res 156:194–212
Dupuis P, Nagurney A (1993) Dynamical systems and variational inequalities. Annals of Oper Res 44:9–42
Fox News (2011) Going green in the operating room. February 21. Available online at:
http://www.foxnews.com/health/2011/02/21/going-green-operating-room
Ghandforoush P, Sen TK (2010) A DSS to manage platelet production supply chain for regional blood centers. Decis Support Syst 50(1):32–42
Giusti L (2009) A review of waste management practices and their impact on human health. Waste Manage 29(8):2227–2239
Karaesmen IZ, Scheller-WolfA, Deniz B (2011) Managing perishable and aging inventories: Review and future research directions. Planning production and inventories in the extended enterprise, international series in operations research & management acience, vol 151. Springer, New York, pp 393–436
Mustafee N, Katsaliaki K, Brailsford SC (2009) Facilitating the analysis of a UK national blood service supply chain using distributed simulation. Simulation 85(2):113–128
Nagurney A (1999) Network Economics: A variational inequality approach, second and revised edition. Kluwer Academic Publishers, Dordrecht
Nagurney A (2010a) Supply chain network design under profit maximization and oligopolistic competition. Transp Res Part E 46:281–294
Nagurney A (2010b) Optimal supply chain network design and redesign at minimal total cost and with demand satisfaction. Int J Prod Econ 128:200–208
Nagurney A, Masoumi AH, Yu M (2012) Supply chain network operations management of a blood banking system with cost and risk minimization. Comput Manag Sci 9(2):205–231
Nagurney A, Nagurney LS (2010) Sustainable supply chain network design: A multicriteria perspective. Int J Sustain Eng 3:189–197
Nagurney A,Yu M, Qiang Q (2011) Supply chain network design for critical needs with outsourcing.
Pap Reg Sci 90(1):123–143
Nagurney A, Zhang D (1996) Projected dynamical systems and variational inequalities with applications. Kluwer Academic Publishers, Boston
Pasupathi P, Sindhu S, Ponnusha BS, Ambika A (2011) Biomedical waste management for health care industry: A review. Int J Biol Med Res 2(1):472–486
Pierskalla WP (2005) Supply chain management of blood banks. In: Brandeau ML, Sanfort F, Pierskalla WP (eds) Operations research and health care, international series in operations research & management science. Kluwer Academic Publishers, Norwell, 70(2):103–145 Rios J (2010) Interviews with the medical director for the American Red Cross Northeast Division
Blood Services, Dedham, Massachusetts on July 19, 2010, and December 6, 2010
Rytila JS, Spens KM (2006) Using simulation to increase efficiency in blood supply chains. Manage Res News 29(12):801–819
Sahin G, Sural H, Meral S (2007) Locational analysis for regionalization of Turkish Red Crescent blood services. Comput Oper Res 34:692–704
Sivakumar P, Ganesh K, Parthiban P (2008) Multi-phase composite analytical model for inte- grated allocation-routing problem—application of blood bank logistics. Int J Logist Econ Glob 1(3/4):251–281
Sullivan M, Cotten R, Read E, Wallace E (2007) Blood collection and transfusion in the United States in 2001. Transfusion 47:385–394
The News International (2011) Experts call for prioritising hospital waste management.
March 3. Available online at: http://www.thenews.com.pk/TodaysPrintDetail.aspx?ID=34021&
Cat=6&dt=3/3/2011
USA Today (2008) More testing for drugs in water sought. Mendoza, M., March 3. Available online at: http://www.usatoday.com/news/nation/2008-03-16-3533657499_x.htm
Yang X (2006) Choosing transportation alternatives for highly perishable goods: a case study on nuclear medicine. Masters Thesis, Massachusetts Institute of Technology