Multi Criteria Operators for Multi-attribute Auctions

1. Albert Pla Beatriz López Javier Murillo Multi Criteria Operators for Multi-attribute Auctions albert.pla@udg.edu University of Girona beatriz.lopez@udg.edu University of Girona javier.murillo@newronia.com Newronia

2. Index • Introduction • Domain • Auctions • Auctions • Basic Concepts • Multi-Attribute Auctions • Multi-Criteria Methods in Multi-Attribute Auctions • Requirements • Examples • Experimentation • Conclusions

3. Introduction Auctions Domain • 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

4. Introduction Auctions Domain • Example • Medical device maintenance service in a hospital Internal technicians Fault Reparation Outsourcing technicians ? … Provider 1 Provider 2 Provider n

5. Introduction Auctions Domain • Auctions: • Allocate resources in a competitive market • Optimize outcome of the participants WorkflowAgent A ResourceType A AUCTION! ResourceAgent 1 ResourceAgent 2

6. Introduction Auctions Domain • 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?

7. Auctions Simple Auctions Multi-attribute 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 FunctionV (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.

8. Auctions Simple Auctions Multi-attribute 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))

9. Auctions Simple Auctions Multi-attribute 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,AT1v) ≥ V(b2,AT2) [5] Che. Y,K. Design competition through multidimensional auctions

10. Auctions Simple Auctions Multi-attribute 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 b1, AT1 AT1v BestBid DeliveredItem b2, AT2 2ndBestBid [17] Pla et al. Multi-Attribute Auction Mechanism for Supporting Resource Allocation in Business Process Enactment

11. Auctions Simple Auctions Multi-attribute auctions • Second price Multi-attribute auctions • To prevent cheating on the attributes level, if a bidder provide a different attributes than AT1 (AT1≠AT1v) the payment is: V(p,AT1v) = V(b1,AT1) p = V’(V(b1,AT1), AT1v) b1, AT1 AT1v BestBid DeliveredItem b2, AT2 2ndBestBid [17] Pla et al. Multi-Attribute Auction Mechanism for Supporting Resource Allocation in Business Process Enactment

12. Auctions Simple Auctions Multi-attribute auctions • Second price Multi-attribute auctions (MAA) • To summarize… Payment:

13. Multi Criteria Methods in MAA Requirements Examples • 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

14. Multi Criteria Methods in MAA 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.

15. Multi Criteria Methods in MAA Requirements Examples • 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. Domainfor the time attribute

16. Multi Criteria Methods in MAA Requirements Examples • 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) = b where b can be just one value

17. Multi Criteria Methods in MAA Requirements Examples • Examples • Product • Weighted Sum • 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 *Assumingassuming that all attributes belong to the real numbers domain and are normalized

18. Multi Criteria Methods in MAA Requirements Examples • WeightedSum 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

19. Experimentation • Multi-Agent Business ProcessSimulation

20. 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) Truthfulbiddingstrategy Cheating BalancedAttributes UnbalancedAttributes

21. Experimentation • Results Wf Mean EconomicCost Wf Mean Error Tolerance WF Mean Service time % minutes € V(b,AT) V(b,AT) V(b,AT)

22. Experimentation • Results Euclideannormfavoursbalancedbidders Benefits (€) UnbalancedAttributes BalancedAttributes

23. Experimentation • Results Cheatersobtainlessbenefitsthanhonestbidders Benefits (€)

24. Conclusions • 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

25. Albert Pla Beatriz López Javier Murillo Multi Criteria Operators for Multi-attribute Auctions albert.pla@udg.edu University of Girona beatriz.lopez@udg.edu University of Girona javier.murillo@newronia.com Newronia

27. Introduction Auctions Domain Dynamism Decentralization Third Party Oustourcing Contingency Robustness Customer Orientation Providers Privacy Process Planing: + Uncertainity + Complexity Business process Many concurrent executions