supply chain management, hierarchical model, network model, multiple criteria analysis, decision support, expert assessments, pairwise comparison matrix, sensitivity of the solution, stability of the solution


Background. Predicting future sales is necessary to control the flow of goods in supply chains (SC), which is why firms perform forecasting of consumer demand. To study the reliability of the solution, the sensitivity analysis (SA) of the results to changes in the original data is performed. Network decision support (DS) models usually contain a very large number of elements and connections between them, which makes it difficult to perform SA.

Objective. The aim of the paper is to assess the sensitivity of the solution, given in the form of the element ranking of the network DS model, to inaccuracies and contradictions in elements of expert pairwise comparison matrices (PCMs), as well as to changes in individual elements of the supermatrix of the network DS model. To assess the priority of different types of information in the SC management system and to assess the sensitivity of the decision to obtain a more accurate forecast of consumer demand.

Methods. Evaluation of DS models to prioritize information needs in the SC management system is carried out based on a developed method of network analysis. The method for assessing the sensitivity of the decision, proposed for the hierarchical DS model, includes finding stable elements of each level of the hierarchy and assessing the degree of sensitivity of global ranking of elements. The sensitivity of a solution based on a network DS model includes an assessment of the stability of local rankings, finding the matrix elements that most affect the change in consistency and change in the local ranking, as well as the sensitivity to changes in individual elements of the model supermatrix.

Results. The method of complex assessment of sensitivity has been further developed, the stages of assessing the stability of local ranking of elements of the network DS model and the resilience of the pairwise comparison matrix elements to changes in the permissible inconsistency have been improved. A method for SA of results based on the network DS model to changes in individual elements of the supermatrix using machine learning tools is generalized.

Conclusions. In the SC management problem, the elements of the expert PCM are found, which to the greatest extent affect the change in consistency and change in the rankings of decision alternatives. The stable elements of the matrix and elements for revision by an expert were calculated in order to increase the reliability of the solution to the SC management problem based on the hierarchical and network DS models.


N.I. Nedashkovskaya, “Supply chain management based on hierarchical decision support model”, KPI Sci. News, vol. 4, pp. 24–34, 2019. doi: 10.20535/kpi-sn.2019.4.180735

N.D. Pankratova and N.I. Nedashkovskaya, “Complex sensitivity analysis of solution based on the analytic hierarchy process”, Syst. Res. Inform. Technol., no. 3, pp. 7–25, 2006.

N.I. Nedashkovskaya, “Stability evaluation of local weights of decision alternatives based on pairwise comparison method”, Syst. Res. Inform. Technol., no. 4, pp. 14–22, 2016.

N.D. Pankratova and N.I. Nedashkovskaya, “Sensitivity analysis of a decision-making problem using the Analytic Hierarchy Process”, Inform. Theor. Appl., vol. 23, no. 3, pp. 232–251, 2016.

N.D. Pankratova and N.I. Nedashkovskaya, “Spectral coefficient of consistency of fuzzy expert information and estimation of its sensitivity to fuzzy scales when solving foresight problems”, Inform. Technol. Knowl., vol. 6, no. 4, pp. 316–329, 2012.

N.D. Pankratova and N.I. Nedashkovskaya, “Estimation of sensitivity of the DS/AHP method while solving foresight problems with incomplete data”, Intell. Control. Automat., vol. 4, no. 1, pp. 80–86, 2013. doi: 10.4236/ica.2013.41011

E. Triantaphyllou and A. Sánchez, “A sensitivity analysis approach for some deterministic multi-criteria decision-making methods”, Decision Sc., vol. 28, pp. 151–194, 1997. doi: 10.1111/j.1540-5915.1997.tb01306.x

J.Aguarón and J.M. Moreno-Jiménez, “Local stability intervals in the analytic hierarchy process”, Eur. J. Oper. Res., vol. 125, no. 1, pp. 114–133, 2000. doi: 10.1016/S0377-2217(99)00204-0

J.Aguarón et al., “Consistency stability intervals for a judgement in AHP decision support systems”, Eur. J. Oper. Res., vol. 145, no. 2, pp. 382–393, 2003. doi: 10.1016/S0377-2217(02)00544-1

T.L. Saaty and M. Sagir, “An essay on rank preservation and reversal”, Math. Comp. Model., vol. 49, pp. 1230–1243, 2009. doi: 10.1016/j.mcm.2008.08.001

V. Tsyganok et al., “Usage of multicriteria decision‐making support arsenal for strategic planning in environmental protection sphere”, J. Multi‐Criteria Decision Analysis, vol. 24, no. 5-6, pp. 227–238, 2017. doi: 10.1002/mcda.1616

S. Kadenko, “Defining relative weights of data sources during aggregation of pair-wise comparisons”, in Select. Papers of the XVII Int. Sci. Pract. Conf. Information Technologies and Security, 2017, pp. 47–55.

T. Sowlati et al., “Developing a mathematical programming model for sensitivity analysis in analytic hierarchy process”, Int. J. Math. Oper. Res., vol. 2, no. 3, pp. 290–301, 2010. doi: 10.1504/IJMOR.2010.032719

M. Ivanco et al., “Sensitivity analysis method to address user disparities in the analytic hierarchy process”, Expert Syst. Applicat., vol. 90, pp. 111–126, 2017. doi: 10.1016/j.eswa.2017.08.003

J.H. May et al., “A new methodology for sensitivity and stability analysis of analytic network models”, Eur. J. Oper. Res., vol. 224, no. 1, pp. 180–188, 2013. doi: 10.1016/j.ejor.2012.07.035

T.L. Saaty, The Analytic Hierarchy Process. New York: McGraw Hill, 1980.

T.L. Saaty and L.G. Vargas, Models, Methods, Concepts & Applications of the Analytic Hierarchy Process. Springer, 2012.

doi: 10.1007/978-1-4614-3597-6

T.L. Saaty, The Analytic Network Process: Decision Making with Dependence and Feedback. Pittsburgh, PA: RWS Publications, 2001.

S. Kheybari et al., “Analytic network process: An overview of applications”, Appl. Math. Comput., vol. 367, 2020. doi: 10.1016/j.amc.2019.124780

Y. Chen et al., “Analytic network process: Academic insights and perspectives analysis”, J. Cleaner Prod., vol. 235, pp. 1276–1294, 2019. doi: 10.1016/j.jclepro.2019.07.016

N.I. Nedashkovskaya, “A system approach to decision support based on hierarchical and network models”, Syst. Res. Inform. Technol, no. 1, pp. 7–18, 2018. doi: 10.20535/SRIT.2308-8893.2018.1.01.