In a double auction, each deal involves two agents - a buyer and a seller, so the "supply-chain" contains only a single link.
In a general supply-chain auction, each deal may involve many different agents, for example: a seller, a mediator, a transporter and a buyer.
Market-equilibrium outcome (efficient and budget-balanced) Two squeezers squeeze for -3; Two drinkers drink for +9; Social welfare 12+11-1-3-3-6 = +10; Budget is balanced.
(starting at juice market), VCG auction (truthful and efficient) two sellers (pickers) sell; their price is max(-8, -7)=-7.
Babaioff and Walsh[2] extend the above work to the case in which the supply-chain can be any acyclic graph.