A Methodology for Tracing the Rank Invariance Region in Multi-Criterion Selection Problems: Application to Negative Emission Technologies

  • Raymond R. TanEmail author
  • Elvin Michael R. Almario
  • Kathleen B. Aviso
  • Jose B. CruzJr
  • Michael Angelo B. Promentilla
Short Communication


It has been previously established that, for multi-criterion selection problems, over a finite set of options, solved via simple additive weighting, there exists a set of weights for which the optimal alternative remains the best choice. This invariance region in the n-dimensional hyperspace defined by the problem criteria contains the set of all weights for which the optimal solution is robust to preference changes. When the set of options is a continuum, there are no known invariance regions reported in the literature. In this work, we develop a procedure to characterize and trace this invariance region when the number of options is finite. The methodology is demonstrated on a case study involving a selection of negative emission technologies based on carbon sequestration potential, water footprint, energy demand, and cost.


Multiple-attribute decision-making (MADM) Simple additive weighting (SAW) Sensitivity analysis Rank invariance in MADM over a finite set Negative emissions technologies (NETs) 



The support of the Philippine Commission on Higher Education (CHED) via the Philippine Higher Education Research Network (PHERNet) Sustainability Studies Program at De La Salle University is gratefully acknowledged. The support of a NAST Research Fellowship is acknowledged by Jose B. Cruz, Jr. We also wish to thank Mark Wiley of the LINDO Systems, Inc. for providing us with software code for tracing the vertices of convex polytopes.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.National Academy of Science and TechnologyTaguigPhilippines
  2. 2.Chemical Engineering DepartmentDe La Salle UniversityManilaPhilippines
  3. 3.Cruz & AssociatesSilangPhilippines

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