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Journal of Information and Optimization Sciences

(Since 1980)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

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Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

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Journal of Information and Optimization Sciences
Open Access Original Articles

Chance constrained programming problem with shifted exponential random variables

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pp. 2205–2221Vol. 47Issue 6June 2026DOI: 10.47974/JIOS-2118XML
Received:
01 Nov 2025
Published Online:
06 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 theoryExponential distributionMinimum guarantee timeProbability density function (PDF)Fuzzy random variable (FRV)Fuzzy chance constrained programming (FCCP)

Subject Classifications

62F1590C1562N05

References

[1] A. Charnes and W. W. Cooper, “Chance-constrained programming,” Management Science, vol. 6, no. 1, pp. 73-79 (1959).
[2] B. L. Miller and H. M. Wagner, “Chance constrained programming with joint constraints,” Operations Research, vol. 13, no. 6, pp. 930-945 (1965).
[3] S. Nanda and K. Kar, “Convex fuzzy mappings,” Fuzzy Sets and Systems, vol. 48, no. 1, pp. 129-132 (1992).

[4] K. Iwamura and B. Liu, “Chance constrained integer programming models for capital budgeting in fuzzy environments,” Journal of the Operational Research Society, vol. 49, pp. 854-860 (1998).
[5] A. Nemirovski and A. Shapiro, “Convex approximations of chance constrained programs,” SIAM Journal on Optimization, vol. 17, no. 4, pp. 969-996 (2007).
[6] J. J. Buckley, Fuzzy Probability and Statistics. Heidelberg: Springer (2006).
[7] M. P. Biswal, N. P. Biswal, and D. Li, “Probabilistic linear programming problems with exponential random variables: A technical note,” European Journal of Operational Research, vol. 111, no. 3, pp. 589-597 (1998).
[8] J. K. Dash, G. Panda, and S. Nanda, “Chance constrained programming problem under different fuzzy distributions,” International Journal of Optimization Theory Methods and Applications, vol. 1, no. 1, pp. 58-71 (2009).
[9] S. Nanda, G. Panda, and J. K. Dash, “A new solution method for fuzzy chance constrained programming problem,” Fuzzy Optimization and Decision Making, vol. 5, no. 4, pp. 355-370 (2006).
[10] S. Nanda, G. Panda, and J. K. Dash, “A new methodology for crisp equivalent of fuzzy chance constrained programming problem,” Fuzzy Optimization and Decision Making, vol. 7, pp. 59-74 (2008).
[11] S. Nanda, G. Panda, and J. K. Dash, “Chance constrained programming with fuzzy inequality constraints,” Opsearch, vol. 45, no. 1, pp. 34-48 (2008).
[12] H. Katagiri, F. Kato, and K. Tanaka, “Interactive multiobjective fuzzy random linear programming: Maximization of possibility and probability,” European Journal of Operational Research, vol. 188, no. 2, pp. 530-539 (2008).
[13] S. K. Barik, “Probabilistic fuzzy goal programming problems involving Pareto distribution: Some additive approaches,” Fuzzy Information and Engineering, vol. 7, no. 2, pp. 227-244 (2015).
[14] G. Pantazis, F. Fele, and K. Margellos, “On the probabilistic feasibility of solutions in multi-agent optimization problems under uncertainty,” European Journal of Control, vol. 63, pp. 186-195 (2022).
[15] M. Mammarella, S. Grammatico, and F. Dabbene, “Chance-constrained sets approximation: A probabilistic scaling approach,” Automatica, vol. 137, p. 110108 (2022).
[16] M. Sakawa, K. Kato, and H. Katagiri, “An interactive fuzzy satisficing method for multiobjective linear programming problems with random variable coefficients through a probability maximization model,” Fuzzy Sets and Systems, vol. 146, no. 2, pp. 205-220 (2004).
[17] M. Sakawa and T. Matsui, “Interactive fuzzy programming for fuzzy random two-level linear programming problems through probability maximization with possibility,” Expert Systems with Applications, vol. 40, no. 7, pp. 2487-2492 (2013).
[18] G. Panda and J. K. Dash, “Nonlinear fuzzy chance constrained programming problem,” Opsearch, vol. 51, pp. 270-279 (2014).
[19] N. Ranarahu, J. K. Dash, and S. Acharya, “Multi-objective bilevel fuzzy probabilistic programming problem,” Opsearch, vol. 54, pp. 475-504 (2017).
[20] N. Ranarahu, J. K. Dash, and S. Acharya, “Multi-objective fuzzy quadratic probabilistic programming problem involving fuzzy Cauchy random variable,” International Journal of Operational Research, vol. 32, no. 4, pp. 495-513 (2018).
[21] J. K. Dash, S. Panda, and G. B. Panda, “A new method to solve fuzzy stochastic finance problem,” Journal of Economic Studies, vol. 49, no. 2, pp. 243-258 (2022).
[22] N. Ranarahu and J. K. Dash, “Computation of multi-objective two-stage fuzzy probabilistic programming problem,” Soft Computing, vol. 26, no. 1, pp. 271-282 (2022).
[23] R. Yadav and R. Singh, “A multi objective optimization in wireless sensor network using enhanced NSGA-3 algorithm,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 7, pp. 1925-1937 (2023), doi: 10.47974/JDMSC-1727.
[24] R. Agarwal, R. P. Chaturvedi, A. Mishra, S. Asthana, and M. Parashar, “An approach for determining the best solution for intutionistic fuzzy transportation problem,” Journal of Information and Optimization Sciences, vol. 45, no. 7, pp. 1867-1879 (2024), doi: 10.47974/JIOS-1739.
[25] S. Gautam, A. Khunteta, and D. Ghosh, “Adaptive optimization framework for multimodal software defect prediction using reinforcement learning,” Journal of Information and Optimization Sciences, vol. 46, no. 7, pp. 2351-2362 (2025), doi: 10.47974/JIOS-2162.
[26] M. Saleki, M. S. Fallahnezhad, D. Shishebori, and M. A. D. Tafti, “Multi-objective fuzzy optimization under uncertainty for investment portfolio selection in emerging financial markets,” Journal of Information and Optimization Sciences, vol. 47, no. 3, pp. 849-885 (2026), doi: 10.47974/JIOS-1574.

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