Solving Multi-Objective Probabilistic Factional Programming Problem
Berhanu Belay1, Srikumar Acharya2, Rajshree Mishra3
1Berhanu Belay, Department of Mathematics, School of Applied Sciences, KIIT Deemed University, Bhubaneshwar (Odisha), India.
2Srikumar Acharya, Department of Mathematics, School of Applied Sciences, KIIT Deemed University, Bhubaneshwar (Odisha), India.
3Rajshree Mishra, Department of Mathematics, School of Applied Sciences, KIIT Deemed University, Bhubaneshwar (Odisha), India.
Manuscript received on 28 September 2019 | Revised Manuscript received on 10 November 2019 | Manuscript Published on 22 November 2019 | PP: 897-903 | Volume-8 Issue-6S3 September 2019 | Retrieval Number: F11620986S319/19©BEIESP | DOI: 10.35940/ijeat.F1162.0986S319
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper presents the solution methodology of a multi-objective probabilistic fractional programming problem. In the proposed model the parameters in the constraints coefficient and the right-hand sides of the constraints follow continuous random variables having known distribution. Since the programming problem consists of random variables, multi-objective function and fractional objective function, it is lengthy, time-consuming and clumsy to solve the proposed programming problem using analytical methods. Stochastic simulation-based genetic algorithm approach is directly applied to solve multi-objective probabilistic non-linear fractional programming problem involving beta distribution and chi-square distribution. In the proposed method, it is not necessary to find the deterministic equivalent of a probabilistic programming problem and applying any traditional methods of fractional programming problem. The stochastic simulation-based genetic algorithm is coded by Code block C++ 16.01 compiler. A set of Pareto optimal solutions are generated for a multi objective probabilistic non-linear fractional programming problem. A numerical example and case study on inventory problem are presented to validate the proposed method.
Keywords: Continuous Distribution, Fractional Programming Problem, Multi-Objective Programming Problem, Probabilistic Programming Problem, Stochastic Simulation Based Genetic Algorithm.
Scope of the Article: Cryptography and Applied Mathematics