Skip to main content
SpringerLink
Log in
Book cover

Modeling and Optimization: Theory and Applications

MOPTA 2017: Modeling and Optimization: Theory and Applications pp 139–155Cite as

Optimization of Inventory and Distribution for Hip and Knee Joint Replacements via Multistage Stochastic Programming

  • Conference paper
  • First Online:

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 279))

Abstract

We introduce a multistage stochastic programming model to optimize the distribution–production network of medical devices; in particular, artificial hip and knee joints for orthopedic surgery. These devices are distributed to hospitals in kits that contain multiple sizes of the joint; the surgeon uses one device from the kit and then returns the rest of the kit to the distributor, which replaces the part that has been removed and distributes the kit anew. Therefore, the distribution problem for artificial joints has a shareability property and thus is related to closed-loop supply chains. We assume that demands for the devices follow a discrete probability distribution and therefore we use scenarios to model the random demands over time. We compare the results of our optimization model to an approximation of the simple distribution strategy that our industry partner currently uses. The proposed approach outperforms the present approach in terms of optimal cost. We also explore the sensitivity of the model’s computation time as the numbers of scenarios, hospitals, and time periods change. Finally, we extend the model to investigate the production of shareable items in sharing systems using a numerical example.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Anvari, S., Turkay, M.: The facility location problem from the perspective of triple bottom line accounting of sustainability. Int. J. Prod. Res. 55(21), 6266–6287 (2017)

    Article  Google Scholar 

  2. Bachmeier, C.J.M., March, L.M., Cross, M.J., Lapsley, H.M., Tribe, K.L., Courtenay, B.G., Brooks, P.M., Arthritis Cost, Outcome Project Group.: A comparison of outcomes in osteoarthritis patients undergoing total hip and knee replacement surgery. Osteoarthr. Cartil. 9(2), 137–146 (2001)

    Google Scholar 

  3. Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)

    Google Scholar 

  4. Bertsimas, D., Thiele, A.: A robust optimization approach to supply chain management. In: International Conference on Integer Programming and Combinatorial Optimization, pp. 86–100. Springer, Berlin (2004)

    Google Scholar 

  5. Beswick, A.D., Wylde, V., Gooberman-Hill, R., Blom, A. and Dieppe, P.: What proportion of patients report long-term pain after total hip or knee replacement for osteoarthritis? A systematic review of prospective studies in unselected patients. BMJ Open 2(1), e000435 (2012)

    Google Scholar 

  6. Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer Science & Business Media, New York (2011)

    Google Scholar 

  7. Brinkmann, J., Ulmer, M.W., Mattfeld, D.C.: Inventory routing for bike sharing systems. Transp. Res. Procedia 19, 316–327 (2016)

    Google Scholar 

  8. Carter, C.R., Ellram, L.M.: Reverse logistics: a review of the literature and framework for future investigation. J. Bus. Logist. 19(1), 85 (1998)

    Google Scholar 

  9. Chemla, D., Meunier, F., Calvo, R.W.: Bike sharing systems: solving the static rebalancing problem. Discret. Optim. 10(2), 120–146 (2013)

    Google Scholar 

  10. Chen, Z., Yan, Z.: Scenario tree reduction methods through clustering nodes. Comput. Chem. Eng. 109, 96–111 (2018)

    Article  Google Scholar 

  11. Chiariotti, F., Pielli, C., Zanella, A., Zorzi, M.: A dynamic approach to rebalancing bike-sharing systems. Sensors 18(2), 512 (2018)

    Article  Google Scholar 

  12. Chow, J.Y.J., Sayarshad, H.R.: Symbiotic network design strategies in the presence of coexisting transportation networks. Transp. Res. Part B Methodol. 62, 13–34 (2014)

    Google Scholar 

  13. Correia, I., Nickel, S., Saldanha-da Gama, F.: A stochastic multi-period capacitated multiple allocation hub location problem: formulation and inequalities. Omega 74, 122–134 (2018)

    Article  Google Scholar 

  14. Cruz, F., Subramanian, A., Bruck, B.P., Iori, M.: A heuristic algorithm for a single vehicle static bike sharing rebalancing problem. Comput. Oper. Res. 79, 19–33 (2017)

    Google Scholar 

  15. De Brito, M.P., Dekker, R.: A framework for reverse logistics. In: Reverse Logistics, pp. 3–27. Springer, Berlin (2004)

    Google Scholar 

  16. Defourny, B., Ernst, D., Wehenkel, L.: Multistage stochastic programming: a scenario tree based approach. In: Decision Theory Models for Applications in Artificial Intelligence: Concepts and Solutions, p. 97 (2011)

    Google Scholar 

  17. Devika, K., Jafarian, A., Nourbakhsh, V.: Designing a sustainable closed-loop supply chain network based on triple bottom line approach: a comparison of metaheuristics hybridization techniques. Eur. J. Oper. Res. 235(3), 594–615 (2014)

    Google Scholar 

  18. Ding, T., Yuan, H., Bie, Z.: Multi-stage stochastic programming with nonanticipativity constraints for expansion of combined power and natural gas systems. IEEE Trans. Power Syst. 33(1), 317–328 (2018)

    Article  Google Scholar 

  19. Ethgen, O., Bruyere, O., Richy, F., Dardennes, C., Reginster, J.-Y.: Health-related quality of life in total hip and total knee arthroplasty: a qualitative and systematic review of the literature. JBJS 86(5), 963–974 (2004)

    Article  Google Scholar 

  20. Gharehyakheh, A., Tavakkoli-Moghaddam, R.: A fuzzy solution approach for a multi-objective integrated production-distribution model with multi products and multi periods under uncertainty. Manag. Sci. Lett. 2(7), 2425–2434 (2012)

    Article  Google Scholar 

  21. Gharehyakheh, A., Cantu, J., Rogers, K.J.: A systematic review of quantitative modeling approach in sustainable supply chain under uncertainty. In: Proceedings of the International Annual Conference of the American Society for Engineering Management, pp. 1–7. American Society for Engineering Management (ASEM), Huntsville (2017)

    Google Scholar 

  22. Golroudbary, S.R., Zahraee, S.M.: System dynamics model for optimizing the recycling and collection of waste material in a closed-loop supply chain. Simul. Model. Pract. Theory 53, 88–102 (2015)

    Article  Google Scholar 

  23. Haddadsisakht, A., Ryan, S.M.: Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax. Int. J. Prod. Econ. 195, 118–131 (2018)

    Google Scholar 

  24. Hooshmand, F., MirHassani, S.A.: Reduction of nonanticipativity constraints in multistage stochastic programming problems with endogenous and exogenous uncertainty. Math. Methods Oper. Res. 87(1), 1–18 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kazemian, I., Aref, S.: Multi-echelon supply chain flexibility enhancement through detecting bottlenecks. Glob. J. Flex. Syst. Manag. 17(4), 357–372 (2016)

    Article  Google Scholar 

  26. Kilian, L., Lütkepohl, H.: Structural Vector Autoregressive Analysis. Cambridge University Press, Cambridge (2017)

    Google Scholar 

  27. Kovtun, V., Giloni, A., Hurvich, C.: Aggregated information in supply chains (2018)

    Google Scholar 

  28. Laumanns, M., Woerner, S.: Multi-echelon supply chain optimization: methods and application examples. In: Optimization and Decision Support Systems for Supply Chains, pp. 131–138. Springer, Cham (2017)

    Google Scholar 

  29. Li, S., Luo, Q., Hampshire, R.: Design of multimodal network for mobility-as-a-service: first/last mile free floating bikes and on-demand transit (2017)

    Google Scholar 

  30. Özceylan, E., Paksoy, T.: A mixed integer programming model for a closed-loop supply-chain network. Int. J. Prod. Res. 51(3), 718–734 (2013)

    Article  Google Scholar 

  31. Pagnano, M., Cushner, F.D., Hansen, A., Scuderi, G.R., Scott, W.N.: Blood management in two-stage revision knee arthroplasty for deep prosthetic infection. Clin. Orthop. Relat. Res. 367, 238–242 (1999)

    Google Scholar 

  32. Parlar, M., Perry, D.: Inventory models of future supply uncertainty with single and multiple suppliers. Nav. Res. Logist. (NRL) 43(2), 191–210 (1996)

    Article  MATH  Google Scholar 

  33. Pirhooshyaran, M., Niaki, S.T.A.: A double-max MEWMA scheme for simultaneous monitoring and fault isolation of multivariate multistage auto-correlated processes based on novel reduced-dimension statistics. J. Process. Control. 29, 11–22 (2015)

    Article  Google Scholar 

  34. Pishvaee, M.S., Jolai, F., Razmi, J.: A stochastic optimization model for integrated forward/reverse logistics network design. J. Manuf. Syst. 28(4), 107–114 (2009)

    Google Scholar 

  35. Raviv, T., Kolka, O.: Optimal inventory management of a bike-sharing station. IIE Trans. 45(10), 1077–1093 (2013)

    Article  Google Scholar 

  36. Rezaee, A., Dehghanian, F., Fahimnia, B., Beamon, B.: Green supply chain network design with stochastic demand and carbon price. Ann. Oper. Res. 250(2), 463–485 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  37. Schuijbroek, J., Hampshire, R.C., Van Hoeve, W.-J.: Inventory rebalancing and vehicle routing in bike sharing systems. Eur. J. Oper. Res. 257(3), 992–1004 (2017)

    Google Scholar 

  38. Shankar, R., Bhattacharyya, S., Choudhary, A.: A decision model for a strategic closed-loop supply chain to reclaim end-of-life vehicles. Int. J. Prod. Econ. 195, 273–286 (2018)

    Article  Google Scholar 

  39. Shapiro, A., Philpott, A.: A tutorial on stochastic programming. Manuscript. www2.isye.gatech.edu/ashapiro/publications.html (2007)

  40. Sinha, R.K.: Hip Replacement: Current Trends and Controversies. CRC Press, Boca Raton (2002)

    Google Scholar 

  41. Snyder, L.V.: Facility location under uncertainty: a review. IIE Trans. 38(7), 547–564 (2006)

    Google Scholar 

  42. Snyder, L.V., Daskin, M.S.: Stochastic p-robust location problems. IIE Trans. 38(11), 971–985 (2006)

    Google Scholar 

  43. Snyder, L.V., Shen, Z.-J.M.: Fundamentals of Supply Chain Theory. Wiley, New York (2011)

    Google Scholar 

  44. Soleimani, H., Govindan, K.: Reverse logistics network design and planning utilizing conditional value at risk. Eur. J. Oper. Res. 237(2), 487–497 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  45. Spahn, D.R.: Anemia and patient blood management in hip and knee surgerya systematic review of the literature. Anesth. J. Am. Soc. Anesth. 113(2), 482–495 (2010)

    Google Scholar 

  46. Spiliotopoulou, E., Donohue, K., Gürbüz, M.Ç., Heese, H.S.: Managing and reallocating inventory across two markets with local information. Eur. J. Oper. Res. 266(2), 531–542 (2018)

    Google Scholar 

  47. Srivastava, S.K.: Network design for reverse logistics. Omega 36(4), 535–548 (2008)

    Google Scholar 

  48. Wiesemann, W., Kuhn, D., Sim, M.: Distributionally robust convex optimization. Oper. Res. 62(6), 1358–1376 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  49. Yi, P., Huang, M., Guo, L., Shi, T.: A retailer oriented closed-loop supply chain network design for end of life construction machinery remanufacturing. J. Clean. Prod. 124, 191–203 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mohler Lab, Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Ave., Bethlehem, PA, 18015, USA

    Mohammad Pirhooshyaran & Lawrence V. Snyder

Authors
  1. Mohammad Pirhooshyaran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lawrence V. Snyder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Pirhooshyaran .

Editor information

Editors and Affiliations

  1. Dept of Industrial & Systems Engineering, Lehigh University, Bethlehem, PA, USA

    János D. Pintér

  2. Dept of Industrial & Systems Engineering, Lehigh University, Bethlehem, PA, USA

    Tamás Terlaky

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Pirhooshyaran, M., Snyder, L.V. (2019). Optimization of Inventory and Distribution for Hip and Knee Joint Replacements via Multistage Stochastic Programming. In: Pintér, J.D., Terlaky, T. (eds) Modeling and Optimization: Theory and Applications. MOPTA 2017. Springer Proceedings in Mathematics & Statistics, vol 279. Springer, Cham. https://doi.org/10.1007/978-3-030-12119-8_7

Download citation

Publish with us

Policies and ethics

Search

Navigation