TOPSIS Based Approach to Scoring Negotiating Offers in Negotiation Support Systems

Tomasz Wachowicz 0 Pawe Baszczyk 0 0 P. Baszczyk Institute of Mathematics, University of Silesia , ul. Bankowa 14, 40-007 Katowice, Poland In this paper we analyze the possibility of applying the technique for order preferences by similarity to ideal solution (TOPSIS) to building the scoring system for negotiating offers. TOPSIS is a multiple criteria decision making method that is based on measuring distances between alternatives under consideration and two bipolar reference alternatives, a positive and negative ideal. Thus the criteria used for the evaluation of alternatives should be described using strong scales. However, in the negotiation, the issues are very often described qualitatively, which results in ordinal or even nominal variables that must be taken into consideration in offers' evaluation process. What is more, TOPSIS may be applied to solving the discrete decision problems while the negotiation space may be defined by the means of continuous variables too. In this paper we try to modify the TOPSIS algorithm to make it applicable to negotiation support and, moreover, discuss the following methodological issues: using TOPSIS for a negotiation problem with continuous negotiation space; selecting the distance measure for adequate representation of negotiator's preferences and measuring distances for qualitative issues. Finally, we propose a simple additional mechanism that allows for building the TOPSIS-based scoring system for negotiating offers and does not involve negotiators in time consuming and tiresome preference elicitation process. This mechanism requires from negotiators to construct examples of offers that represent some categories of quality and then by using a goal programming approach it infers all the parameters required by the TOPSIS algorithm. We also - show a simple prototype software tool that applies the TOPSIS modified algorithm and may be used in electronic negotiation support. 1 Introduction The last few decades have changed a perspective from which negotiations are perceived. On the one hand, lots of formal tools for negotiation support are being proposed since a new scientific discipline called the negotiation analysis has been developed (Raiffa 1982). These formal models and procedures are implemented as software solutions in a form of negotiation support systems. Some of these models have been implemented to support real world negotiation problems, such as RAINS (Hordijk 1991) used in resolving the dispute between the European countries negotiating air pollution limits, or the Deep Ocean Mining Model used in the United Nations UNCLOS III negotiations (Sebenius 1992) on the rights to exploit the natural resources from beneath of the sea bed and sharing the profits yielded from the exploitation. Recently, the basic supportive ideas derived from SmartSettle system (Thiessen and Soberg 2003) have been used for supporting First Nations Negotiation in Canada (Thiessen and Shakun 2009). On the other hand, the Internet expansion and e-commerce development cause that the vast majority of the business processes, including the negotiations, are conducted by means of computers and the Web, using both simple communication software such as electronic mail clients and instant messaging systems, and more sophisticated negotiation support systems or electronic negotiation systems. The last two usually support not only the communication process between parties but also accomplish some proactive functions such as individual decision support, negotiation protocol structuring, compromise searching, postoptimization analysis etc. (Kersten and Lai 2007). These systems are used for both solving real world problems and for training or teaching negotiations, such as FamillyWinner (Bellucci and Zeleznikow 2006), applied in a negotiation between divorcing couples in Australia and helping them to divide the family assets in the most fair way, Inspire (Kersten and Noronha 1999) used recently for an international research project on how negotiators behave in electronic negotiations (Paradis et al. 2010) or Negoisst (Schoop et al. 2003). For accomplishing their decision support function NSSs need to apply formal models, which allow for analyzing negotiators preferences, determining a scoring system for negotiating offers and then using this system for building negotiators own proposals and analyzing his partners counteroffers. Usually a simple additive weighting model, SAW (Keeney and Raiffa 1976) is used in negotiators preference analysis (like in Inspire, Negoisst and SmartSettle systems), but the results of some research show, that the NSSs users very often misinterpret utilities scores used in SAW (Wachowicz and Kersten 2009). Other models are also applied into NSSs, based on different analytical approach, like the AHP (Mustajoki and Hamalainen 2000) or ELECTRE based ones (Wachowicz 2010). But all these solutions require negotiators to have at least the basic mathematical and decision making knowledge and the skills of abstract thinking, and very often involve them in a tiresome process of eliciting their preferences. In this study we propose a new tool for analyzing negotiators preferences and building the scoring system for negotiating offers that is based on the technique for order preferences by similarity to ideal solution (TOPSIS) (Hwang and Yoon 1981) and may be applied to negotiation support in a form of a simple software tool. Thanks to the application of some statistical methods into the process of preference analysis, the workload and time the negotiators have to devote for building their own scoring systems in the pre-negotiation phase are reduced. The original TOPSIS method operates on the set of predefined alternatives, i.e. it requires a decision (negotiation) problem to be formulated in a discrete form. However, in negotiations many issues are defined quantitatively (such as price, time of delivery etc.) and have a continuous character. It is easier to define them as the ranges of feasible values rather than the predefined salient options. Therefore, we propose our own modification of TOPSIS that makes it applicable to a negotiation problem containing continuous issues. Furthermore, TOPSIS assumes that the criteria under consideration are expressed on the strong scales, such as the ratio or interval ones. However, in negotiations some issues may be also described qualitatively or verbally, which results in the ordinal or even nominal variables, that must be taken into consideration in the evaluation process of offers. To solve this problem we propose a simple solution derived from Kaufman and Rousseeuw (1990) research work. Furthermore, we discuss the problem of using various distance measures and metrics in the TOPSIS scoring algorithm to determine the one-dimensional (single-issue) distance that reflects negotiators preferences in the best possible way. Then we propose a goal-programming based approach that allows negotiators to b (...truncated)