# A Fractile Model for Stochastic Interval Linear Programming Problems

Document Type : Original Manuscript

Authors

Department of Mathematics, University of Mazandaran, Babolsar, Iran

10.22094/joie.2021.566423.1558

Abstract

In this paper, we first introduce a new category of mathematical programming where the problem coefficients are interval random variables. These problems include two different kinds of ambiguity in the problem coefficients which are being interval and being random. We use Fractile method to solve these problems. In this method, using the existing method, we change the interval problem coefficients to random mode and then we solve the random problem using Fractile method. Also, a numerical example is presented to show the effectiveness of this model. Finally, we emphasize that this approach can be useful for the model with multi-objective as a generalized model in the future study.

Graphical Abstract

Highlights

In this paper, we first introduce a new category of mathematical programming where the problem coefficients are interval random variables. These problems include two different kinds of ambiguity in the problem coefficients which are being interval and being random. We use Fractile method to solve these problems. In particular, a numerical example is presented to show the effectiveness of this model. The following results are achieved after the mentioned discussions.

We have considered linear programming problem with random interval coefficients. We have used an extension of fractile model of stochastic programming for solving it. we saw the mentioned approach is so practical to the real situations. In the proposed approach, we reduced the main model to two sub-problem for determining the optimistic and pessimistic optimal solution. In particular, we solved a numerical example to show the fractile model can prepare a solving process. The main discussion based on the taken results in numerical example part is as follows:

• In the discussed problem, two optimistic and pessimistic solutions were gained. The optimistic solution is achieved by considering the lower bound parameters available in problem constraints and as a result of the development of the feasible region.
• This solution would give a better optimum value to interval programming problem because it is chosen in a wider range in compare with the pessimistic solution.
• In stochastic interval programming, the result will ensure with the percentage of confidence because the parameters available in lower and upper bound of problem are random.

We also emphasize that this approach can be useful for the model with multi-objective as a generalized model in the future study.

Keywords

#### References

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