Chance constrained programming problem with shifted exponential random variables

Sahoo, K. S.; Mahapatra, A. K.; Sahoo, A.; Dash, J. K.

doi:10.47974/JIOS-2118

Open Access Original Articles

Chance constrained programming problem with shifted exponential random variables

K. S. Sahookarpura97@gmail.comDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , ^*A. K. MahapatraCorresponding authorajayaiter@gmail.comDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , A. Sahooanuradha25anu@gmail.comDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , J. K. Dashjkdash@gmail.comDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile →

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pp. 2205–2221Vol. 47Issue 6June 2026DOI: 10.47974/JIOS-2118XML

Received:: 01 Nov 2025
Published Online:: 01 Jun 2026
Article type:: Original Articles
Language:: EN
Article no.:: JIOS-2118
Pages:: 2205–2221

Abstract

A solution technique is developed for Chance Constrained Programming (CCP) problems where the coefficients appearing in the objective function and constraints are assumed to follow a two-parameter exponential distribution. (f(x)=1/λ e^(–1/λ(x–μ)), xμ) is presented. Here the parameters μ and λ are called location and scale parameters of the exponential distribution. We call the location parameter μ as the minimum guarantee time and, λ is the mean time after the guarantee time is observed. This distribution is quite familiar in real life situations where the random variables X has a shift i.e., Xμ. For example in inventory systems the demand X is a random variable X satisfying a minimum quantity as the demand may not start with zero. So we aim to present a complete deterministic equivalent of the CCP where the coefficients follow a two parameter exponential distribution. Also, the CCP problem is derived in a mixed environment i.e., the coefficients are random whose parameters are fuzzy numbers. In both cases, the problem is converted to its deterministic equivalent. Here the Fuzzy Probability theory due to Buckley [6] is used. Also, a real-life situation is presented. The method is justified by numerical examples.

Keywords

Chance constrained programming (CCP)Fuzzy probability theory Exponential distribution Minimum guarantee time Probability density function (PDF)Fuzzy random variable (FRV)Fuzzy chance constrained programming (FCCP)

Subject Classifications

62F1590C1562N05

References

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