Abstract: In a combinatorial exchange, rules can be input for processing bids and a desired exchange objective can be defined. A subset of the rules can be used to determine if an allocation of the bids exists that is optimal for the type of exchange being conducted. If the desired exchange objective is not satisfied, new allocations can be determined using different subsets of rules each time until the desired exchange objective is satisfied. At least one of the bids can include a reference ratio; a discount; a price associated with a quantity Q1 of a first item; a price associated with a quantity Q2 of a second item; and a rule that causes said discount to be applied to an average price of Q1 and an average price of Q2 for each instance of the allocated quantity Q1 over the allocated quantity Q2 that equals the reference ratio.

Abstract: In a combinatorial exchange, a set of rules can be input for processing of bids received in connection with the exchange. At least one bid can be received from each of a plurality of exchange participants and a desired exchange objective can be defined. A determination can be made as a function of a subset of the rules if an allocation of the bids exists that is optimal for the type of exchange being conducted. If the desired exchange objective is not satisfied, the step of determining an allocation is repeated utilizing a different subset of rules each time until the desired exchange objective is satisfied. It can be determined if the exchange is overconstrained and, if so, rules can be relaxed. Also or alternatively, the demand for a quantity of an item can be increased or decreased based on the average cost of the item.

Abstract: In a combinatorial exchange, rules can be input for processing bids and a desired exchange objective can be defined. A subset of the rules can be used to determine if an allocation of the bids exists that is optimal for the type of exchange being conducted. If the desired exchange objective is not satisfied, new allocations can be determined using different subsets of rules each time until the desired exchange objective is satisfied. Trigger bid groups and/or rules associated with trigger values can be used to determine whether to apply modification or discounts to bids. Item and bid groups can be partitioned into groups for the purpose of smoothing requirements. Trigger bid groups, rules associated with trigger values, item groups, and bid groups can be used for adjusting or constraining bids based on triggers, logical connectives, and adjustments.

Abstract: A method of processing an exchange includes providing a solver/analyzer for determining a solution that includes at least one of a winning allocation and feasible allocations. At least one bid is received at the solver/analyzer, with each bid including at least one item and an associated price. Exchange description data (EDD) is associated with the at least one bid. The EDD is also received at the solver/analyzer. The processing of the at least one bid is modified in accordance with the at least one feature included in the EDD.

Abstract: In a combinatorial exchange, a set of rules can be input for processing of bids received in connection with the exchange. At least one bid can be received from each of a plurality of exchange participants and a desired exchange objective can be defined. A determination can be made as a function of a subset of the rules if an allocation of the bids exists that is optimal for the type of exchange being conducted. If the desired exchange objective is not satisfied, the step of determining an allocation is repeated utilizing a different subset of rules each time until the desired exchange objective is satisfied.

Abstract: In a method of determining an optimal allocation in a combinatorial auction, a plurality of bids is received. Each bid includes a plurality of sub bids. Each sub bid includes either one good and a price associated with the good or a logical operator logically connecting at least two child sub bids and a price associated with the logical operator. For each sub bid, the price associated with the good or the logical operator is either an explicit price that is included with the sub bid or is assigned a value of zero when the sub bid does not include an explicit price. An objective is defined for the plurality of bids. For each bid, a plurality of mathematical relationships collectively representing the bid without logical operators is defined. The received bids are processed to achieve the objective subject to the mathematical relationships.

Abstract: In a live, expressive combinatorial exchange, each of a plurality of bidders can submit a bid. Based on the submitted bids, an allocation of the bids is determined that is optimal for the type of exchange being conducted. At least a portion of each bid of the allocation is displayed to each bidder of a first subset of the bidders that has at least one bid that is not included in the allocation. Each bidder of a subset of the first subset of bidders can then amend one or more of their existing bids or submit a new bid that is considered the next time the allocation is determined. The process of feeding back at least a portion of each bid of the allocation, submitting new bids or amendments to existing bids, and determining a new allocation based on all of the submitted bids continues until a predetermined condition is satisfied.

Abstract: A method for enabling optimizing software to determine an optimal allocation in a combinatorial auction includes (a) receiving a plurality of bids each of which includes a plurality of sub bids, wherein each sub bid is comprised of one of (1) one good and an associated price and (2) a logical operator logically connecting at least two child sub bids and a price associated with the logical operator; (b) defining an objective for the plurality of bids; (c) defining for each bid a plurality of mathematical relationships without logical operators that collectively represent the bid; and (d) causing the optimizing software to process the received bids to achieve the objective subject to the mathematical relationships. The method can be embodied in instructions stored on a computer-readable medium. When executed by a processor, the instructions can cause the processor to perform the method.

Abstract: In a combinatorial auction, a plurality of bids is received each having a plurality of sub bids and Boolean operators logically connecting each pair of sub bids. A current allocation is determined by allocating goods to at least one of the bids and a best allocation is initialized with the current allocation. A neighboring allocation is constructed by reallocating within the current allocation at least one good from at least one bid to another bid. The best allocation is updated with the neighboring allocation when the value of the neighboring allocation is greater than the current value of the best allocation.

Abstract: In an apparatus and method of solving a combinatorial exchange, a plurality of candidate allocations of input bids is determined from input bids and a set of bid vectors is formed from the input bids. A probability value, representing how likely the bids of a bid vector will comprise the bids from which a final allocation is determined, is associated with each bid vector. A mapping is then determined between each bid vector and at least one of the candidate allocations based on a set of objectives and a set of constraints. A candidate allocation is selected as a final allocation based on a comparison of another set of bids that define an exchange event bid vector with at least one of the bid vectors.

Abstract: A desirable allocation of bids in a combinatorial exchange can be selected by determining a first candidate allocation of the bids and a first value of a minimax regret, related to the difference in utility between the adversarial allocation and the candidate allocation, as a function of a first adversarial allocation of the bids. Based on the first candidate allocation, a second adversarial allocation of the bids and a first value of a maximum regret related to the difference in utility between the new adversarial allocation and the utility of the candidate allocation can be determined. When the value of the maximum regret is greater than the value of the minimax regret, the candidate allocation can be designated as the desirable allocation.

Abstract: Each bid received via a computer network is an offer for the right to cause at least one advert associated with the bid to be output to at least one device that is part of the computer network or in communication with the computer network in response to the bid being allocated one or more user events. At a time t, at least one rule or decision variable for allocating user events to bids is determined based on bids received before time t and an estimate of bids, user events or user activity occurring after time t. Based on information or data regarding a user event received from one of the devices after time t, the user event is allocated to at least one bid based on the at least one rule or decision variable and the at least one word, term, phrase or string of characters of the bid.

Abstract: In an allocation of subscribers to one or more wireless carrier rate plans, a number of wireless voice and/or data carrier rate plans is selected and each subscriber's historical wireless time usage for each of a number of foregone time intervals is determined. For each combination of subscriber and rate plan a first expression is defined that includes a unique variable and a cost associated with assigning the subscriber to the rate plan for at least one of the time intervals. Constraints that collectively ensure that subscribers are allocated to a specified minimum or maximum number of rate plans, or restrict a subscriber to be allocated to just one rate plan are determined. The expressions and constraints are processed by an optimal solution solver running on a computer to determine an optimal assignment of subscribers to at least one rate plan.

Abstract: In a multi-unit combinatorial auction, reverse auction, or exchange, a number of bids can be received, with each bid including one or more items and for each item a desired quantity thereof. Each bid also includes a price. A number of unique combinations of bids can be formed from the received bids, and the one combination of bids which represents the best value in terms of an auction setting, a reverse auction setting and/or an exchange setting can be determined. Thereafter, the bids forming this combination can be declared the winning bids of the auction, reverse auction or exchange.

Abstract: In a multi-unit combinatorial auction, reverse auction, or exchange, a number of bids can be received, with each bid including one or more items and for each item a desired quantity thereof. Each bid also includes a price. A number of unique combinations of bids can be formed from the received bids, and the one combination of bids which represents the best value in terms of an auction setting, a reverse auction setting and/or an exchange setting can be determined. Thereafter, the bids forming this combination can be declared the winning bids of the auction, reverse auction or exchange.

Abstract: In an on-line ad auction, bids for the right to display at least one advert on a display of a computer of a computer network in response to the bid being allocated a query received from the computer are received via a computer network. At a time t, at least one rule or decision variable for allocating queries to bids is determined based on the bids received before time t and an estimate of at least one of: an estimate of queries to be received after time t; an estimate of events to occur in response to the display of adverts after time t; and/or an estimate of bids to be received after time t. After time t, a query received from the computer is allocated to at least one of the received bids based on the at least one rule or decision variable.

Abstract: A method of selecting a winning allocation of bids in a combinatorial auction includes receiving a plurality of bids and designating a subset of the received bids as a current allocation having no overlap in the items of its bids. For each bid not part of the current allocation, a neighboring allocation is determined by combining the bid with the current allocation and deleting from such combination any bid of the current allocation having an item that overlaps an item of the bid combined with the current allocation. A heuristic is determined for each neighboring allocation and one of the neighboring allocations is selected stochastically or based on its heuristic. If this one neighboring allocation is greater than the value of the best allocation, the current allocation is substituted for the best allocation.

Abstract: A desirable allocation of bids in a combinatorial exchange can be selected by determining a first candidate allocation of the bids and a first value of a minimax regret, related to the difference in utility between the adversarial allocation and the candidate allocation, as a function of a first adversarial allocation of the bids. Based on the first candidate allocation, a second adversarial allocation of the bids and a first value of a maximum regret related to the difference in utility between the new adversarial allocation and the utility of the candidate allocation can be determined. When the value of the maximum regret is greater than the value of the minimax regret, the candidate allocation can be designated as the desirable allocation.

Abstract: In a combinatorial exchange, a set of rules can be input for processing of bids received in connection with the exchange. At least one bid can be received from each of a plurality of exchange participants and a desired exchange objective can be defined. A determination can be made as a function of a subset of the rules if an allocation of the bids exists that is optimal for the type of exchange being conducted. If the desired exchange objective is not satisfied, the step of determining an allocation is repeated utilizing a different subset of rules each time until the desired exchange objective is satisfied.

Abstract: In a live, expressive combinatorial exchange, each of a plurality of bidders can submit a bid. Based on the submitted bids, an allocation of the bids is determined that is optimal for the type of exchange being conducted. At least a portion of each bid of the allocation is displayed to each bidder of a first subset of the bidders that has at least one bid that is not included in the allocation. Each bidder of a subset of the first subset of bidders can then amend one or more of their existing bids or submit a new bid that is considered the next time the allocation is determined. The process of feeding back at least a portion of each bid of the allocation, submitting new bids or amendments to existing bids, and determining a new allocation based on all of the submitted bids continues until a predetermined condition is satisfied.