Albert PlaBeatriz López Javier Murillo Multi Criteria Operators for Multi-attribute Auctions...

Albert Pla Beatriz López Javier Murillo

Multi Criteria Operators for Multi-attribute Auctions

[email protected] of Girona


[email protected]

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


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


Example– Medical device maintenance service in a hospital

Fault Reparation

Internal technicians

Outsourcing technicians

Provider 1 Provider 2 Provider n

…?

Domain Auctions

Introduction


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


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


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


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))



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)


[5] Che. Y,K. Design competition through multidimensional auctions


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


[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


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)


[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


Auctions

Second price Multi-attribute auctions (MAA)

– To summarize…

Payment:



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



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.




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.


Domain for the time attribute



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




Examples– Product

– Weighted Sum


*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



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



Experimentation

Multi-Agent Business Process Simulation


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


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


Results

ExperimentationBe

nefit

s (€

)

Euclidean norm favours balanced bidders

Unbalanced Attributes Balanced Attributes


Results

ExperimentationBe

nefit

s (€

)

Cheaters obtain less benefits than honest bidders


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]


Introduction

DynamismDecentralization

Third Party OustourcingContingency Robustness

Customer OrientationProviders Privacy

Process Planing:+ Uncertainity+ Complexity

Business process

Many concurrent executions

Domain Auctions

Albert PlaBeatriz López Javier Murillo Multi Criteria Operators for Multi-attribute Auctions...

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