This paper reports on the design and comparison of two economically-inspired mechanisms for task allocation in environments where sellers have finite production capacities and a cost structure composed of a fixed overhead cost and a constant marginal cost. Such mechanisms are required when a system consists of multiple self-interested stakeholders that each possess private information that is relevant to solving a system-wide problem. Against this background, we first develop a computationally tractable centralised mechanism that finds the set of producers that have the lowest total cost in providing a certain demand (i.e. it is efficient). We achieve this by extending the standard Vickrey-Clarke-Groves mechanism to allow for multi-attribute bids and by introducing a novel penalty scheme such that producers are incentivised to truthfully report their capacities and their costs. Furthermore our extended mechanism is able to handle sellers’ uncertainty about their production capacity and ensures that individual agents find it profitable to participate in the mechanism. However, since this first mechanism is centralised, we also develop a complementary decentralised mechanism based around the continuous double auction. Again because of the characteristics of our domain, we need to extend the standard form of this protocol by introducing a novel clearing rule based around an order book. With this modified protocol, we empirically demonstrate (with simple trading strategies) that the mechanism achieves high efficiency. In particular, despite this simplicity, the traders can still derive a profit from the market which makes our mechanism attractive since these results are a likely lower bound on their expected returns.