Fault tolerant combinatorial auctions for tasks having time and precedence constraints with bonuses and penalties

A system for conducting an auction comprising:

• a processor operative to:
• obtain a task and a valuation therefor submitted by a buyer, said task being defined by a plurality of sub-tasks, a set of precedence relationships specified between the sub-tasks, a designated start time for the task and a designated end time for the task corresponding to an interval in which the task is to be completed;
• obtain one or more bids associated with the task from one or more suppliers, each supplier submitting one or more of the bids and each bid identifying (i) a set of the sub-tasks for which the bid is being submitted, (ii) a proposed price for each individual sub-task in the identified set thereof and (iii) for each particular sub-task in the identified set, a schedule including a proposed start time range in which the supplier submitting the bid proposes to begin the particular sub-task in the identified set and a duration in which the supplier submitting the bid proposes to complete the particular sub-task;
• determine a probability of each supplier successfully completing each sub-task for which they submitted a bid;
• and
• identify one or more winning bids from the obtained bids based on the proposed prices of the bids, the determined success probabilities and the proposed schedules of the bids, said winning bids satisfying constraints of the task.