# Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing

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## Abstract

To reduce default risk, a retailer may offer a partial down-stream trade credit to its credit-risk customers who should pay a portion of their purchasing costs at the time of receiving items as a collateral deposit, and then receive a permissible trade credit on the rest of the outstanding amount. To reflect this fact, we consider an inventory model with linear time dependent demand under two levels of trade credit and allowable shortages. Depending on the relationship between up-stream and down-stream trade credit periods, several cases are considered and the necessary and sufficient conditions are derived for finding the optimal solution. We also present a simple algorithm to determine the optimal solution. Numerical examples are provided to illustrate the solution procedure. Sensitivity analysis of important model-parameters is performed and some relevant managerial implications are discussed.

## Keywords

Inventory Increasing demand Partial trade credit Shortages## Notes

### Acknowledgments

The authors are thankful to the honorable referees for their helpful comments and suggestions on the earlier version of the manuscript. The second author acknowledges the financial assistance provided by Jadavpur University under the State Govt. Fellowship Scheme.

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