Consumer search, transshipment, and bargaining power in a supply chain

We study a decentralised supply chain with one manufacturer and two symmetric retailers who could transship their excess inventory between each other. Without transshipment, the retailer's unsatisfied customers search and buy the product at the other retailer with some probability. With transshipment, the retailer can transship the other retailer's excess inventory to fulfil its own unmet demand. However, a transshipment price is often charged by one retailer for transshipping goods to another. We show the retailer's profit is unimodal in the transshipment price, and the manufacturer's profit increases in the customer search probability. Although the retailer's preference over transshipment depends on the magnitude of search probability and transshipment price, the retailer may always prefer the transshipment no matter their magnitude. We then study the effect of bargaining power over the transshipment decision (whether to transship between retailers and at what transshipment price). Our analysis suggests that the manufacturer always prefers to control the transshipment price rather than to control whether to transship, while the retailer can prefer both. We also find that increasing bargaining power always benefits the manufacturer but could hurt the retailer. We finally check the robustness of our results by investigating the case with asymmetric retailers