Albert Pla Beatriz López Javier Murillo
Multi Criteria Operators for Multi-attribute Auctions
[email protected] of Girona
[email protected] of Girona
2/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012
Index Introduction
– Domain– Auctions
Auctions– Basic Concepts– Multi-Attribute Auctions
Multi-Criteria Methods in Multi-Attribute Auctions– Requirements– Examples
Experimentation
Conclusions
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Introduction
Special domains:– Production not known in advance– Production under demand
– Unknown resource status– Outsourced resources
– Resource allocation in real time• Managers expect low price, high speed and high quality
VS• Resource providers want to maximize benefits and occupation
Domain Auctions
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Example– Medical device maintenance service in a hospital
Fault Reparation
Internal technicians
Outsourcing technicians
Provider 1 Provider 2 Provider n
…?
Domain Auctions
Introduction
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Auctions:– Allocate resources in a competitive market– Optimize outcome of the participants
Resource Agent 1
Resource Agent 2
Workflow Agent A
Resource Type A
AUCTION!
Domain Auctions
Introduction
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Multi-Attribute Auctions:– Each bid is characterized by a set of attributes in addition
to price:• Time• Quality• Energy• …
– Attribute aggregation can be done using multi-criteria functions.
– How should be the multi-criteria aggregator?
Domain Auctions
Introduction
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Auctions
Auctions– Utility: is the measurement of the satisfaction received by the participants
of an auction. U (Bi)– Value: is the score or the price which participants assign to a certain bid. It
can be defined using an Evaluation Function V (Bi)– Winner determination problem (WDP) is the problem to compute the
winner bid that maximizes the auctioneer’s utility.– The payment mechanism is the process of deciding which is the price p and
payout for the auctioneers and the bidders. Desirable property:
– Incentive compatible mechanism: the auction mechanism must encourage bidders to reveal their real attributes. This means that bidders obtain a better profit by revealing their real attributes than by cheating. Example:Vickrey auction: The winner pays the price of the second-highest bid.
Simple Auctions Multi-attribute auctions
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Auctions
Multi-attribute auctions (MAA)
– Each Bid B is composed by its cost b and a set of attributes AT=(at1,…, atn). B=(b,AT)
– WDP: Find the optimal Bid according to cost b and attributes AT• Evaluation function V(bi,ATi) depends on the auctioneers goal• The winner is determined by:
argmax(V(bi,ATi))
Simple Auctions Multi-attribute auctions
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Auctions
Second price Multi-attribute auctions
– The winner pays the second highest-bid price. But…
What is a second price in MAA?
– The winner must provide the attributes in such a way that the evaluation is, at least, as good as in the second best bid:
V(b1v,AT1
v) ≥ V(b2,AT2)
Simple Auctions Multi-attribute auctions
[5] Che. Y,K. Design competition through multidimensional auctions
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Auctions
Second price Multi-attribute auctions
– If we assume that the winner will provide AT1 (AT1=AT1v) then the
payment is the following:V(p,AT1) = V(b2,AT2)p = V’(V(b2,AT2), AT1)
Where V’(x,AT) = b is the anti-function of V(b,AT) = x
Simple Auctions Multi-attribute auctions
[17] Pla et al. Multi-Attribute Auction Mechanism for Supporting Resource Allocation in Business Process Enactment
b1, AT1Best Bid AT1v
Delivered Item
b2, AT22nd Best Bid
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Auctions
Second price Multi-attribute auctions
– To prevent cheating on the attributes level, if a bidder provide a different attributes than AT1 (AT1≠AT1
v) the payment is:
V(p,AT1v) = V(b1,AT1)
p = V’(V(b1,AT1), AT1v)
Simple Auctions Multi-attribute auctions
[17] Pla et al. Multi-Attribute Auction Mechanism for Supporting Resource Allocation in Business Process Enactment
b1, AT1Best Bid AT1v
Delivered Item
b2, AT22nd Best Bid
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Auctions
Second price Multi-attribute auctions (MAA)
– To summarize…
Payment:
Simple Auctions Multi-attribute auctions
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Multi Criteria Methods in MAA
Multicriteria Function as Evaluation Function
– Requirements for a Multi Criteria Function to be used as evaluation function V(b,AT)
• Real Valued Function
• Monotonicity
• Bijection
Requirements Examples
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Multi Criteria Methods in MAA
Real Valued Function
– V(b,AT) must return a real number evaluation for each bid• The payment mechanism involves the score obtained by the second
best bid.
– Discards MCM which result in ranked lists or orders without a score.• If there is not a score or evaluation, the payment cannot be computed.
Requirements Examples
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Multi Criteria Methods in MAA
Monotoniciy
– If an attribute is improved, the score of the evaluation must also improve.
– Ensures that, for every possible value in the attribute domain, V(b,AT) will return a value.
– Only applied in the range of values an attribute can take.• E.g.: If an attribute can only take positive values (time duration), it
can be evaluated using its square.
Requirements Examples
Domain for the time attribute
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Multi Criteria Methods in MAA
Bijection
– In order to calculate the payment, V(b,AT) must have a bijective behavior regarding the price attribute.
– In other words, given:V(b,AT) = x
its antifunction will beV’(x,AT) = b where b can be just one
value
Requirements Examples
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Multi Criteria Methods in MAA
Examples– Product
– Weighted Sum
Requirements Examples
*Assuming assuming that all attributes belong to the real numbers domain and are normalized
– Mathematical Norms:• E.g. Euclidean norm– Favors bids with more balanced attributes– Attribute domain: positive numbers plus 0
• Not all the norms can be used: e.g. Chebyshev norm cannot be used as V(B) since it is not bijective
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Multi Criteria Methods in MAA
Weighted Sum of Functions
– Attributes utility computed individually using a function fj(x)– Results are then aggregated using a weighted sum– Highly adaptable to the domain– All fj(x) must commit the requirements previously presented
Requirements Examples
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Experimentation
Multi-Agent Business Process Simulation
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Experimentation
Simulation– 3 different concurrent Business Processes composed by 6 different tasks. – Each task has an estimated duration between 10 and 15 minutes and requires one resource of a
certain type (A to D) to be executed.
– There are 4 (A to D) types of resources provided by 8 Resource providers.– Each Resource Provider can perform 3 types of tasks with different qualifications (Type, time, error
tolerance)
– Repeated using Product, Weighted Sum and Euclidean Norm as Evaluation function (100 executions each)
Unbalanced Attributes Balanced Attributes
Truthful bidding strategy Cheating
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Results
Wf Mean Economic Cost Wf Mean Error Tolerance WF Mean Service time
V(b,AT) V(b,AT) V(b,AT)
€ %
min
utes
Experimentation
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Results
ExperimentationBe
nefit
s (€)
Euclidean norm favours balanced bidders
Unbalanced Attributes Balanced Attributes
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Results
ExperimentationBe
nefit
s (€)
Cheaters obtain less benefits than honest bidders
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This paper treated the problem of allocation resources in a decentralized environment where production agenda is unknwon: Multi Attribute Auctions (MAA)
Defined the properties of the MAA evaluation function:– Monotonicity– Real Valued function– Bijective (regarding the economic attribute)
Examples: Weighted sum, mathematical norms, weighted sum of functions…
Shown how the evaluation function conditions the behavior of the auction
Conclusions
Albert Pla Beatriz López Javier Murillo
Multi Criteria Operators for Multi-attribute Auctions
[email protected] of Girona
[email protected] of Girona
26/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012
27/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012
Introduction
DynamismDecentralization
Third Party OustourcingContingency Robustness
Customer OrientationProviders Privacy
Process Planing:+ Uncertainity+ Complexity
Business process
Many concurrent executions
Domain Auctions
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