Internal and external reference effects in a two-tier supply chain

We study a two-tier supply chain with a newsvendor retailer that has an internal reference effect related to its own profit as well as an external reference effect centered on the profit of the supplier. We show that the internal and external reference effects in isolation can have opposite effects on the wholesale price set by a supplier who has full knowledge on the retailer's ordering bias. The internal reference effect, which is driven by the relative disutility from ex-post inventory error, causes the supplier to increase the wholesale price, whereas the external effect, which results from disadvantageous profit inequity, causes the supplier to decrease the wholesale price. While the internal reference effect can achieve supply chain coordination for items with a low profit margin, the external reference effect improves efficiency for high profit margin products, but never achieves coordination. When the retailer's ordering behavior is influenced by both reference effects, then the interaction can improve efficiency and lead to an equilibrium where the supply chain is coordinated. We find that the relative impact of each reference effect is highly dependent upon the profit margin. We study these equilibria with full information as well as for a supplier who is naïve to the retailer's behavioral biases and compare these results to derive insights into the behavioral management of supply chains.