Mathematics and Statistics Vol. 11(5), pp. 778 - 785
DOI: 10.13189/ms.2023.110503
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A Joint Chance Constrained Programming with Bivariate Dagum Distribution

Khalid M. El-khabeary ^*, Afaf El-Dash , Nada M. Hafez , Samah M. Abo-El-hadid
Department of Mathematics, Insurance and Applied Statistics, Helwan University, Egypt

ABSTRACT

A Joint chance-constrained programming (JCCP) technique is regarded as one of the most useful applicable techniques of stochastic programming techniques. It is more suitable for solving uncertain real problems, especially in economics and social problems, where some of model parameters are positive dependent random variables and follow well-known probability distributions. In this paper, we take into account a linear JCCP problem where some right-hand side random parameters are dependent and follow the Dagum distributions. So, firstly we derive a bivariate Dagum distribution with seven parameters with marginals following the Dagum distribution with three parameters. This proposed bivariate Dagum distribution is based on the Farlie-Gumbel-Morgensten copula (as presented in theorem (2.1)). Secondly, the proposed bivariate distribution is used in the context of JCCP technique to transform a linear JCCP model into an exact equivalent deterministic nonlinear programming model through theorem (3.1). Thirdly, through theorem (3.2), we prove that the obtained exact equivalent deterministic nonlinear programming model is a convex model, hence any nonlinear programming method can be used to solve it and find the global optimal solution. Finally, in order to demonstrate how to convert a linear JCCP model into an equivalent deterministic nonlinear programming model and solve it using the cutting plane method, a numerical example is included.

KEYWORDS
Farlie-Gumbel-Morgensten Copula, Chance Constrained Programming (CCP), JCCP, Bivariate Dagum Distribution, Multivariate Distributions, Equivalent Deterministic Model, Convex Model, Cutting Plane Method, Global Solution

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Khalid M. El-khabeary , Afaf El-Dash , Nada M. Hafez , Samah M. Abo-El-hadid , "A Joint Chance Constrained Programming with Bivariate Dagum Distribution," Mathematics and Statistics, Vol. 11, No. 5, pp. 778 - 785, 2023. DOI: 10.13189/ms.2023.110503.

(b). APA Format:
Khalid M. El-khabeary , Afaf El-Dash , Nada M. Hafez , Samah M. Abo-El-hadid (2023). A Joint Chance Constrained Programming with Bivariate Dagum Distribution. Mathematics and Statistics, 11(5), 778 - 785. DOI: 10.13189/ms.2023.110503.