# Uncertain programming models for fixed charge multi-item solid transportation problem

## Abstract

This paper investigates the fixed charge multi-item solid transportation problem, in which the fixed charges, direct costs, transportation capacities, supply and demand are uncertain variables. Based on the uncertainty theory, expected value programming model and chance-constrained programming model for fixed charge multi-item solid transportation problem are constructed, respectively. We can obtain the optimal solution of two models via solving the relevant deterministic models. Finally, a numerical experiment is implemented to illustrate the application of the models.

## Keywords

Transportation problem Uncertainty programming Uncertain variable## Notes

### Acknowledgements

This work was supported by the Natural Science Foundation of China (No. 11626234), the Hubei Provincial Natural Science Foundation (No. 2016CFB308), the Higher Educational Science and Technology Program Foundation of Shandong Province (No. J13LI10), and the Foundation of Liaocheng University (No. 318011303).

### Compliance with ethical standards

### Conflicts of interest

The authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

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