=Paper=
{{Paper
|id=None
|storemode=property
|title=Using Saaty's Method in Contract Negotiations
|pdfUrl=https://ceur-ws.org/Vol-918/111110199.pdf
|volume=Vol-918
|dblpUrl=https://dblp.org/rec/conf/at/WasielewskaG12
}}
==Using Saaty's Method in Contract Negotiations==
https://ceur-ws.org/Vol-918/111110199.pdf
Using Saaty’s method in contract negotiations?
Katarzyna Wasielewska1 and Maria Ganzha1
Systems Research Institute Polish Academy of Sciences, Warsaw, Poland
maria.ganzha@ibspan.waw.pl
This note (motivated by the STSM at the Imperial College London), is de-
voted to combining ontologically demarcated information with the Analytical
Hierarchy Process (AHP; [4]) for assessment of offers during contract negoti-
ations. The AHP is widely used [1], while an attempt at combining it with
ontologies was reported in [3]. Here, the context for the AHP method is pro-
vided by the Agents in Grid project (AiG; [5]), aiming at development of an
agent-based infrastructure for resource management in the Grid where agents
negotiate (1) joining a team to earn money, or (2) finding a team to execute a
job, and ontologically described contracts result from autonomous negotiations.
Therefore, multicriterial (AHP-based) assessment of proposals may be used to
reach an agreement. Here, we consider how the AHP method can be used to
assess ontologically described contract proposals in the AiG use case.
Fig. 1: Part of the contract structure from AiG ontology
In the AiG ontology [2] a set of classes and properties describe a contract.
Since an ontology can be represented on a acyclic directed graph, one can de-
termine the structure of the decision hierarchy with the top node being “main
goal” (see, Figure 1). For the user (expert) with preferences regarding the con-
tract, we construct pairwise comparison matrices for each level in the hierarchy,
where the elements in the lower level are compared with respect to the element
immediately above them, e.g. lead time and the delay penalty are compared with
respect to the payment conditions. For comparisons we follow Saaty and assign
numerical values to expressions like: equally important etc. For the structure
from Figure 1, an expert has to consider matrices in the following tables.
In the AHP algorithm, weights of criteria are coefficients of normalized eigen-
vector corresponding to the maximal eigenvalue. Thus weight of the lead time
?
AT2012, 15-16 October 2012, Dubrovnik, Croatia. Copyright held by the author(s).
deadline payment jobExecution
Penalty Conditions Timeline delay
deadline leadTime Penalty
1
Penalty 1 3
3
payment leadTime 1 3
Conditions 3 1 5 delay
1
jobExecution Penalty 3
1
1 1
Timeline 3 5
1
is 0.75, delay penalty is 0.25, deadline penalty 0.2, payment conditions 0.68 and
job execution timeline 0.12. Next, for every alternative, an evaluation matrix is
created, estimating badness of an alternative for the user (expert) for a given
criteria; found in the next two tables.
Badness Badness
Criteria for expert 1 Criteria for expert 1
deadlinePenalty 1 deadlinePenalty 3
leadTime 3 leadTime -1
delayPenalty 5 delayPenalty 5
jobExecutionTimeline 1 jobExecutionTimeline 3
Results for alternatives 1-2 are 2.7 and 1.3 and alternative 1 is the winner.
We have demonstrated, how to utilize the AHP method to compare ontologically
described offers. A full graph of the ontological contract, would result in Saaty’s
hierarchy with more levels, and more elements on each level. Moreover, the
method should be able to deal with arbitrary large structures, and knowledge of
multiple experts captured as comparison matrices.
References
1. A. Labib A. Ishizaka. Review of the main developments in the analytic hierarchy
process. Expert Systems and Applications, 38(11):14336–14345, 2011.
2. M. Drozdowicz, K. Wasielewska, M. Ganzha, M. Paprzycki, N. Attaui, I. Lirkov,
R. Olejnik, D. Petcu, and C. Badica. Trends in parallel, distributed, grid and cloud
computing for engineering. chapter Ontology for Contract Negotiations in Agent-
based Grid Resource Management System. Saxe-Coburg Publications, Stirlingshire,
UK, 2011.
3. R.S. Sumi G. Kabir. An ontology-based intelligent system with AHP to support
supplier selection. Suranaree Journal of Science and Technology, 17(3):249–257,
2010.
4. Thomas L. Saaty. The analytic hierarchy process. Pittsburg, 1990. RWS Publica-
tions.
5. K. Wasielewska, M. Drozdowicz, M. Ganzha, M. Paprzycki, N. Attaui, D. Petcu,
C. Badica, R. Olejnik, and I. Lirkov. Trends in parallel, distributed, grid and cloud
computing for engineering. chapter Negotiations in an Agent-based Grid Resource
Brokering Systems. Saxe-Coburg Publications, Stirlingshire, UK, 2011.