From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series

Main Article Content

Raïmi Aboudou Essessinou
Guy Degla
Babacar Mbaye Ndiaye

Abstract

The quarterly disaggregation of an annual economic aggregate, by a mathematical method with a cyclical indicator, gives rise to a problem of minimization to make the quarterly economic aggregate smooth. This involves two indexes for the quarter and the year, which sometimes can make the resolution algorithm less efficient if the problem is large. In this paper we propose a method of indexing quarterly variables based on an isomorphic transformation of a two-index program into a one-index program, in order to minimize the cost of the algorithm of resolution. This method of continuous indexing of variables, applied to national accounts, shows that the algorithm with a single index is more efficient than the algorithm with two indexes when solving the optimization program of the quarterly disaggregation.

Keywords:
Isomorphism, indexing variables, optimization, algorithms performance, quarterly disaggregation.

Article Details

How to Cite
Essessinou, R. A., Degla, G., & Ndiaye, B. M. (2019). From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series. Journal of Advances in Mathematics and Computer Science, 34(1), 1-15. https://doi.org/10.9734/jamcs/2019/v34i1-230199
Section
Original Research Article

References

Shiva R. Iyera, et al. Energy disaggregation analysis of a supermarket chain using a facility-model. Energy and Buildings, Elsevier. 2015;97:65-76.
Available:https://doi.org/10.1016/j.enbuild.2015.03.053

Sangjin Han, et al. Network Support for Resource Disaggregation in Next-Generation Datacenters.
Available:https://people.csail.mit.edu/alizadeh/courses/6.888/papers/disagg.pdf

Essessinou RA. Modélisation et optimisation du problème de calage dans la trimestrialisation d’agrégats macroéconomiques. Mémoire de Master II, Option Recherche Opérationnelle. Institut de Mathématiques et de Sciences Physiques (IMSP). Université d’Abomey-Calavi (UAC) – Bénin; 2014. French.

International Monetary Fund: Quarterly National Accounts Manual. 2017 Edition. Pre-Publication. 2018;86-126.
Available:https://www.imf.org/external/pubs/ ft/qna/

Jorge Nocedal, Stephen J. Wright. Numerical optimization. Second Edition, Springer Series in Operation Research. 2000;388-389.

Guy E. Blelloch, Métriques de performance pour les algorithmes et programmes parallèles. French.
Available:http://www.lacim.uqam.ca/~chauve/Enseignement/ INF7440/A04/COURS7-8/GUY-metriques.pdf

Ji-Bo Wang, Jian-Jun Wang. Single-machine scheduling problems with precedence constraints and simple linear deterioration. Applied Mathematical Modelling. 2015;39:1172–1182. Elsevier.
Available:http://dx.doi.org/10.1016/j.apm.2014.07.028

Anthony Bonato, Shahin Kamali. Approximation algorithms for graph burning. International Conference on Theory and Applications of Models of Computation TAMC 2019: Theory and Applications of Models of Computation. Springer Nature Switzerland AG. 2019;74-92.

Jon Kleinberg. An approximation algorithm for the disjoint paths problem in even-degree planar graphs. Doctorate of Philosophy in Computer Sciences, Massachusetts Institute of Technologie; 1996.
Available:https://scholar.google.com/scholar

Jon Kleinberg. An approximation algorithm for the disjoint paths problem in even-degree planar graphs.
Available:https://www.cs.cornell.edu/home/kleinber/focs05-even.pdf

Gamst Mette, Jensen PN, Pisinger David, Plum Christian. Two and three-index formulations of the minimum cost multicommodity k-splittable flow problem. European Journal of Operational Research. 2010;202(1):82-89.
Available:https://doi.org/10.1016/j.ejor.2009.05.014

Anna Melchiori, Antonino Sgalambro. Optimizing emergency transportation through multicommodity quickest paths. 18th Euro Working Group on Transportation, EWGT. July 2015, Delft, The Netherlands. ELSEVIER. 2015;14-16.
Available:https://www.sciencedirect.com

Bernard Le Stum. Algèbre linéaire et bilinéaire, Version du 17 Février. 2017;15-18. French.

Saliou Toure. Algèbre, premier cycle MP1. Universités Francophones. UREF, EDICEF. 1991;197-199. French.

Ahuja Magnanti Orlin, Network Flow. Pearson New International Edition. 2014;59.