Improving agent-based negotiation efficiency in construction supply chains: A relative entropy method Xiaolong Xue a , Qiping Shen b , Heng Li b, ⁎, William J. O'Brien c , Zhaomin Ren d a Department of Construction and Real Estate, School of Management, Harbin Institute of Technology, Harbin 150001, China b Department of Building and Real Estate, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China c Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, USA d Division of Built Environment, Faculty of Advanced Technology, University of Glamorgan, UK abstract article info Article history: Accepted 6 May 2009 Keywords: Agent-based negotiation Negotiation efficiency Relative entropy Construction supply chain This research presents a relative entropy method for improving agent-based negotiation efficiency (REANE) in a construction supply chain. REANE provides a path forward to help negotiators reach an acceptable solution when other methods fail; the key insight is the use of relative entropy to measure the relative degree of consensus among parties and hence minimize necessary compromises. An illustrative example is presented to show the application of REANE. The REANE method aggregates the preference information of negotiators in CSC twice. First, a compromise group preference order is ascertained using preference information, which is newly provided by negotiators, and compromise preference information (formed previously in the agent-based auto-negotiation process). Second, group preferences are aggregated by employing a relative entropy model, which is established based on entropy theory, while, considering the multiple attributes of negotiation in a construction supply chain. The method of REANE fulfills the necessary requirement of group decision-making, i.e., maximizing the preference consistency of decision-making groups and minimizing the utility gaps between every negotiator's preference and the group's preference. © 2009 Elsevier B.V. All rights reserved. 1. Introduction In traditional business transactions (e.g., construction), negotia- tion has long been recognized as a time-consuming process, although various intelligent (e.g., agent-based) negotiation support systems have been developed to improve negotiation efficiency [2,5,12,13]. This is because all partners (decision makers) involved look to pursue their own benefits with conflicting goals; agents can represent the partners' interests in an automatic negotiation [1]. However, there are various factors which negatively affect efficient negotiation, such as the diversity of background of the negotiating partners, complex interactions, inadequate negotiation knowledge of opponents, dynamics of business environments, and asymmetric information between negotiating partners [2]. In order to increase the efficiency of agent-based negotiations, this research presents a relative entropy method for improving agent- based negotiation efficiency (REANE) in a construction supply chain (CSC). Efficiency can be seen as the ability to do the right things quickly with less resources or efforts [31]. The criterion of efficiency requires that “results be maximized with limited resources” [43]. This research defines negotiation efficiency as the ability of negotiators to search for solutions in different negotiation situations in terms of time and minimal use of resources. This research may be seen as an extension of our previous research [11], which contributed an agent- based framework for CSC coordination. To extend our previous work, the aim of this research (the method of REANE) is to find accepted solutions by all negotiators to meet the requirements of stable CSC operations when prior negotiations fail or automatic search processes are terminated, i.e. there are utility gaps among the solutions, but negotiators agree to stop negotiations and return to find a final solution from former solutions, which are generated by autonomous agents in previously automated negotiation processes. The rest of this paper is organized as follows. Section 2 reviews literatures on negotiation in CSCs, agent-based negotiation, and applications of the theory of relative entropy in decision making. The general process of steps in the relative entropy method of REANE is presented in Section 3. Section 4 introduces REANE in detail. An illustrative example of the relative entropy method is given in Section 5 to depict the application process. Section 6 summarizes and discusses the applicability and limitations of REANE. Conclusions are presented in Section 7 . 2. Literature review Negotiation is an important collaborative decision-making and coordination behavior in a CSC, which can take place at any stage and Automation in Construction 18 (2009) 975–982 ⁎ Corresponding author. E-mail addresses: xlxue@hit.edu.cn (X. Xue), bsqpshen@polyu.edu.hk (Q. Shen), bshengli@polyu.edu.hk (H. Li), wjob@mail.utexas.edu (W.J. O'Brien), zren@glam.ac.uk (Z. Ren). 0926-5805/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2009.05.002 Contents lists available at ScienceDirect Automation in Construction journal homepage: www.elsevier.com/locate/autcon