# Bullwhip and inventory variance in a closed loop supply chain

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## Abstract

A simple dynamic model of a hybrid manufacturing/remanufacturing system is investigated. In particular we study an infinite horizon, continuous time, APIOBPCS (Automatic Pipeline Inventory and Order Based Production Control System) model. We use Åström’s method to quantify variance ratios in the closed loop supply chain. Specifically we highlight the effect of a combined “in-use” and remanufacturing lead-time and the return rate on the inventory variance and bullwhip produced by the ordering policy. Our results clearly show that a larger return rate leads to less bullwhip and less inventory variance in the plant producing new components. Thus returns can be used to absorb demand fluctuations to some extent. Longer remanufacturing and “in-use” lead-times have less impact at reducing inventory variance and bullwhip than shorter lead-times. We find that, within our specified system, that inventory variance and bullwhip is always less in supply chains with returns than supply chains without returns. We conclude by separating out the remanufacturing lead-time from the “in-use” lead-time and investigating its impact on our findings. We find that short remanufacturing lead-times do not qualitatively change our results.

## Keywords

Manufacturing Remanufacturing Inventory variance Bullwhip Return rate Lead-time## References

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