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Consider a three level supply chain consisting of a manufacturer, a wholesaler and a retailer. Suppose I wish to include a buyback contract to this network. Then am I right when I say that wholesaler buys unsold items from the retailer at a specific buyback price. Similar is the case between manufacturer and wholesaler. But what does a manufacturer do with unsold goods? Suppose the product is perishable say a food item.

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Per my friend the procurement guru, buyback contracts are apparently rare, whether between retailer and wholesaler or between wholesaler and manufacturer. In any case, the options for the party buying the inventory back are pretty much the same at any level: push it off on another customer (possibly at a discount); put it in inventory in hopes of future orders (apparently not too likely); or ship it to the nearest landfill.

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In terms of the theory of buyback contracts (i.e., the math), it doesn't matter what the party doing the "buying back" (the manufacturer, in your question) does with the goods. They can resell them, dispose of them, rework them, etc.

In fact, in practice, the other firm isn't always even required to physically send the units back, but only to provide evidence that they have been destroyed and can't be sold. For example, newspaper publishers sometimes allow resellers to cut off the banner (e.g., the part that says the name of the newspaper and the date) and send back that small strip of paper in order to get the buyback credit. This saves freight costs and disposal costs on the part of the publisher.

I suspect @prubin's friend is right that buyback contracts may be rare. However, I have seen first-hand a hotel cutting newspapers apart for this purpose, and I once worked in a deli that essentially had a buyback contract with its bagel provider. So, they do occur in practice, at least sometimes.

On the other hand, this question asks for real-world examples of supply chain contracts and got no responses.

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