# A solid transportation model with product blending and parameters as rough variables

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## Abstract

In this paper, we formulate a practical solid transportation problem with product blending which is a common issue in many operational and planning models in the chemical, petroleum, gasoline and process industries. In the problem formulation, we consider that raw materials from different sources with different quality (or purity) levels are to be transported to some destinations so that the materials received at each destination can be blended together into the final product to meet minimum quality requirement of that destination. The parameters such as transportation costs, availabilities, demands are considered as rough variables in designing the model. We construct a rough chance-constrained programming (RCCP) model for the problem with rough parameters based on trust measure. This RCCP model is then transformed into deterministic form to solve the problem. Numerical example is presented to illustrate the problem model and solution strategy. The results are obtained using the standard optimization solver LINGO.

### Keywords

Solid transportation problem Blending Rough variable Trust measure Chance-constrained programming## Notes

### Acknowledgments

Pradip Kundu sincerely acknowledges the support received from IISER Kolkata to carry out this research work.

### Compliance with ethical standards

### Conflict of interest

None.

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