Albert PlaBeatriz López Javier Murillo Multi Criteria Operators for Multi-attribute Auctions University of Girona University of Girona Newronia

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

3/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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

4/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  Example – Medical device maintenance service in a hospital Fault Reparation Internal technicians Outsourcing technicians Provider 1Provider 2Provider n … ? Domain Auctions Introduction

5/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  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

6/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  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

7/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Auctions  Auctions – Utility: is the measurement of the satisfaction received by the participants of an auction.U (B i ) – Value: is the score or the price which participants assign to a certain bid. It can be defined using an Evaluation Function V (B i ) – 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

8/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Auctions  Multi-attribute auctions (MAA) – Each Bid B is composed by its cost b and a set of attributes AT=(at 1,…, at n ).B=(b,AT) – WDP: Find the optimal Bid according to cost b and attributes AT Evaluation function V(b i,AT i ) depends on the auctioneers goal The winner is determined by: argmax(V(b i,AT i )) Simple Auctions Multi-attribute auctions

9/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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(b 1 v,AT 1 v ) ≥ V(b 2,AT 2 ) Simple Auctions Multi-attribute auctions [5] Che. Y,K. Design competition through multidimensional auctions

10/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Auctions  Second price Multi-attribute auctions – If we assume that the winner will provide AT 1 (AT 1 =AT 1 v ) then the payment is the following: V(p,AT 1 ) = V(b 2,AT 2 ) p = V’(V(b 2,AT 2 ), AT 1 ) 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 b 1, AT 1 Best Bid AT 1 v Delivered Item b 2, AT 2 2 nd Best Bid

11/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Auctions  Second price Multi-attribute auctions – To prevent cheating on the attributes level, if a bidder provide a different attributes than AT 1 (AT 1 ≠AT 1 v ) the payment is: V(p,AT 1 v ) = V(b 1,AT 1 ) p = V’(V(b 1,AT 1 ), AT 1 v ) Simple Auctions Multi-attribute auctions [17] Pla et al. Multi-Attribute Auction Mechanism for Supporting Resource Allocation in Business Process Enactment b 1, AT 1 Best Bid AT 1 v Delivered Item b 2, AT 2 2 nd Best Bid

12/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Auctions  Second price Multi-attribute auctions (MAA) – To summarize… Payment: Simple Auctions Multi-attribute auctions

13/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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 RequirementsExamples

14/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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. RequirementsExamples

15/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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. RequirementsExamples Domain for the time attribute

16/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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 be V’(x,AT) = bwhere b can be just one value RequirementsExamples

17/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Multi Criteria Methods in MAA  Examples – Product – Weighted Sum RequirementsExamples *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

18/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Multi Criteria Methods in MAA  Weighted Sum of Functions – Attributes utility computed individually using a function f j (x) – Results are then aggregated using a weighted sum – Highly adaptable to the domain – All f j (x) must commit the requirements previously presented RequirementsExamples

19/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Experimentation  Multi-Agent Business Process Simulation

20/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 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 strategyCheating

21/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  Results Wf Mean Economic CostWf Mean Error ToleranceWF Mean Service time V(b,AT) V(b,AT) V(b,AT) € % minutes Experimentation

22/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  Results Experimentation Benefits (€) Euclidean norm favours balanced bidders Unbalanced Attributes Balanced Attributes

23/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  Results Experimentation Benefits (€) Cheaters obtain less benefits than honest bidders

24/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012  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 PlaBeatriz López Javier Murillo Multi Criteria Operators for Multi-attribute Auctions University of Girona University of Girona Newronia

26/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012

27/24MDAI2012 – Multi Criteria Operators for Multi-Atrribute Auctions21/11/2012 Introduction Dynamism Decentralization Third Party Oustourcing Contingency Robustness Customer Orientation Providers Privacy Process Planing: + Uncertainity + Complexity Business process Many concurrent executions Domain Auctions