Abstract
Many countries produce significant quantities of nuclear waste which will have to be permanently and safely placed in a repository. We develop a mixed integer program that determines where to place each waste package of a specific waste type in a given time period with the goal of minimizing heat load concentration within a repository. Operational constraints include: (1) heat load limitations, (2) location and time at which waste packages can be placed, and (3) the number of waste packages that must be placed based on type and time period. Although applicable to other settings, we use the Yucca Mountain repository in Nevada as a case study. Each of the three objectives used for minimizing heat load concentration improves upon existing greedy and sequential filling methods. Existing filling methods give at least a 17 % to an 873 % higher, i.e., worse, heat load concentration in the repository with respect to these objectives than do optimal methods. Enhancements, i.e., symmetry reduction constraints, perturbations, and heuristics, increase the size of solvable problem instances. This research can be applied to any deep geologic repository planned for operation around the world with slight modifications to incorporate site-specific objectives and constraints.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alumur, S., & Kara, B. Y. (2007). A new model for the hazardous waste location-routing problem. Computers & Operations Research, 34(5), 1406–1423.
AMPL Optimization LLC. (2013). AMPL Version 20130109.
Angilella, S., Bottero, M., Corrente, S., Ferretti, V., Greco, S., & Lami, I. M. (2015). Non additive robust ordinal regression for urban and territorial planning: An application for siting an urban waste landfill. Annals of Operations Research,. doi:10.1007/s10479-015-1787-7.
Brown, G., Keegan, J., Vigus, B., & Wood, K. (2001). The Kellogg company optimizes production, inventory, and distribution. Interfaces, 31(6), 1–15.
Chicoisne, R., Espinoza, D., Goycoolea, M., Moreno, E., & Rubio, E. (2012). A new algorithm for the open-pit mine production scheduling problem. Operations Research, 60(3), 517–528.
Crowe, B. Y., Rawlinson, S., Black, P., Carilli, J., & Disanza, F. (2002). Application of probabilistic performance assessment modeling for optimization of maintenance studies for low-level radioactive waste disposal sites at the Nevada Test Site. In Proceedings waste management ’02 Tucson, Arizona, Paper 364.
Erkut, E., & Neuman, S. (1992). A multiobjective model for locating undesirable facilities. Annals of Operations Research, 40(1), 209–227.
Espinoza, D., Goycoolea, M., Moreno, E., & Newman, A. (2013). MineLib: A library of open pit mining problems. Annals of Operations Research, 206(1), 93–114.
Ewing, R. C., & Macfarlane, A. (2002). Nuclear waste: Yucca Mountain. Science, 296(5568), 659–660.
Filbert, W., Bollingerfehr, W., Wehrmann, J., & Graf, R. (2008). Optimization of emplacement technology for spent fuel. In Proceedings EAFORM.
Fourer, R., Gay, D., & Kernighan, B. (2003). AMPL—A modeling language for mathematical programming. Pacific Grove, CA: Thomson Brooks/Cole.
Geoffrion, A. M., & Nauss, R. (1977). Exceptional paper-parametric and postoptimality analysis in integer linear programming. Management Science, 23(5), 453–466.
Ghose, M., Dikshit, A. K., & Sharma, S. (2006). A GIS based transportation model for solid waste disposal—a case study on Asansol municipality. Waste Management, 26(11), 1287–1293.
Giannikos, I. (1998). A multiobjective programming model for locating treatment sites and routing hazardous wastes. European Journal of Operational Research, 104(2), 333–342.
Hutchinson, W. (1983). A linear program for assessing the assignment and scheduling of radioactive wastes for disposal to sea, Technical Report. Bedford: Hunting Engineering Ltd.
IBM ILOG AMPL. (2010). Version 12.2 User’s Guide: Standard (Command-line) Version Including CPLEX Directives.
International Business Machines. (2014). CPLEX Version 12.6.0.1.
Jin, D. (1994). Multimedia waste disposal optimization under uncertainty with an ocean option. Marine Resource Economics, 9(2), 119–139.
Lambert, W., & Newman, A. (2014). Tailored Lagrangian Relaxation for the open pit block sequencing problem. Annals of Operations Research, 222(1), 419–438.
Lawrence Livermore National Laboratory. (2005). How one equation changed the world. https://str.llnl.gov/str/September05/Aufderheide.html.
Leao, S., Bishop, I., & Evans, D. (2001). Assessing the demand of solid waste disposal in urban region by urban dynamics modelling in a GIS environment. Resources, Conservation and Recycling, 33(4), 289–313.
Lerchs, H., & Grossmann, I. F. (1965). Optimum design of open pit mines. CIM Bulletin, 58, 47–54.
Lewis, E. E. (2008). Fundamentals of nuclear reactor physics. New York: Academic Press.
McCullough, G., Jr. (2014). The other senate nuclear option. The Wall Street Journal. http://www.wsj.com/articles/glenn-mccullough-midterms-yucca-mountain-and-the-other-senate-nuclear-option-1414366541
Mohr, C., & O’Brien, P. (1973). Decision mapping-tool for underground waste management. IAHS Publ no. III (pp. 731–737).
Nuclear Energy Institute. (2014). US State by State Used Fuel and Payments to the Nuclear Waste Fund. http://www.nei.org/Knowledge-Center/Nuclear-Statistics/On-Site-Storage-of-Nuclear-Waste/US-State-by-State-Used-Fuel-and-Payments-to-the-Nu.
Nuclear Regulatory Commission. (2008). Yucca Mountain Repository License Application: Safety Analysis Report, Technical report. DOE/RW-0573, Rev. 0, U.S. Department of Energy Office of Civilian Radioactive Waste Management.
Nuclear Regulatory Commission. (2014). Stages of the nuclear fuel cycle. http://www.nrc.gov/materials/fuel-cycle-fac/stages-fuel-cycle.html.
Pochet, Y., & Wolsey, L. A. (2006). Production planning by mixed integer programming. Berlin: Springer.
Posiva. (2015). Final Disposal Facility. http://www.posiva.fi/en/final_disposal/final_disposal_facility/repository#.Vl4Mxb8qLoM.
Rautman, C. A., Reid, R. A., & Ryder, E. E. (1993). Scheduling the disposal of nuclear waste material in a geologic repository using the transportation model. Operations Research, 41(3), 459–469.
Sherali, H. D., & Smith, J. C. (2001). Improving discrete model representations via symmetry considerations. Management Science, 47(10), 1396–1407.
SKB. (2014). SKB—Swedish Nuclear Fuel and Waste Management Co. http://www.skb.se/default____24417.aspx.
Taji, K., Levy, J. K., Hartmann, J., Bell, M. L., Anderson, R., Hobbs, B., et al. (2005). Identifying potential repositories for radioactive waste: Multiple criteria decision analysis and critical infrastructure systems. International Journal of Critical Infrastructures, 1(4), 404–422.
Tsoulfanidis, N. (2013). The nuclear fuel cycle. Lagange Park: American Nuclear Society.
Tung, D. V., & Pinnoi, A. (2000). Vehicle routing-scheduling for waste collection in Hanoi. European Journal of Operational Research, 125(3), 449–468.
World Nuclear Association. (2014). Radioactive Waste Management. http://www.world-nuclear.org/info/nuclear-fuel-cycle/nuclear-wastes/radioactive-waste-management/.
Yucca Mountain Project. (2009). Yucca Mountain, Nevada. http://www.ymp.gov.
Acknowledgments
We acknowledge the insights provided by Eduardo Moreno of Universidad Adolfo Ibañez and Daniel Espinoza of Universidad de Chile regarding the time-independent placement heuristic. We also acknowledge helpful comments provided by the anonymous reviewers on a previous draft of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Johnson, B., Newman, A. & King, J. Optimizing high-level nuclear waste disposal within a deep geologic repository. Ann Oper Res 253, 733–755 (2017). https://doi.org/10.1007/s10479-016-2194-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-016-2194-4