Polish Journal of Management Studies
 ISSN 2081-7452
Go to content

Main menu:


Abstracts > Vol 8

Kazemi M., Shooshtarian Z.

Abstract: One of the  most  areas of  research  in recent years,  is decision making  methodologies under  conflicting  multi-objective. Due to this,  several techniques have been developed. Among them, Surrogate  Worth Trade Off   (SWT) method  is interested to solve the  multi-objective  problem  by analysts and   researchers. This paper  intends to review and  application  of  Surrogate  Worth Trade Off technique. The SWT method is one approach that provides an interference between the decision makers preferences and the mathematical models associated with the non-dominated solutions. In the final part of this work  a method  is  proposed  in order to use SWT technique with multiple  decision makers.

Keywords: Surrogate  worth  Function, Trade-Off  Function, Multi-objective , Group Decision Making


In recent years , decision  makers and  analysts  face to  many problems with more than one objective .There is no single accepted approach to solve the multi-objective  optimization  problems  .Because  of the conflicting nature of objective functions, using one  objective method to solve the multi- objective , lead us to situation where the optimization of one of these, may adversely affect the optimization of others. Due to this, decision making methodologies under  conflicting  multiple objectives have been developed . Multiple objectives decision making (MODM) methods are often used to solve the problems with   conflict objectives and large set of alternative.
Among   these  methods , Surrogate Worth Trade
Off (SWT)method   has been used  in the several  areas of research. This method  proposed by  Haimes , Hall and  Freedom in 1975 for decision making in water resource systems. The  original version  of SWT is not interactive .Shimizu  and  others [17] proposed an interactive version of the SWT method .
The general philosophy taken in the interactive approach is that the multi-objective decision making process should follow the  three steps procedure[15]:

  • Generate  Pareto optimal solution.

  • Obtain meaningful information to interact with the decision maker.

  • use information obtained in step 2 to interact with DM and select the final solution based on the DM preference response.

The “SWT “ method  uses the  ε constrain problem as a means of generating Pareto solutions. Objective trade- offs , whose values can be easily obtained from the values of some strictly positive multipliers from step 1 are used as the information carrier in step 2.And in step 3 , the DM responds by expressing his degree of preference  over the prescribed  trade offs by assigning numerical values to each surrogate worth function[16].
SWT emphasizes generation of a range of solutions and trade-offs to be presented to the decision maker for consideration. The main purpose of this method is to produce the set of effective solutions and the analyst helps  DM choose  the  best compromise or most preferred solution.
SWT  method  could be applied to both discrete and continuous decision-problem scenarios .In continuous problems , a predefined set of alternatives  is not available, but  discrete problem  is characterized by a  predefined set of alternatives.This method allows  a  decision maker to select the best possible options from a larger number of all available alternatives.

more in full version


In recent years, organizations  face to multi-objective decision making  due to  variable , dynamic  and   complex  environment. There is no single accepted approach to solve the multi-objective  optimization  problems .Because of this, several techniques have been developed. One of these techniques , is Surrogate  Worth Trade – Off   (SWT) method  that is interested to solve the  multi-objective  problem  by analysts and   researchers . SWT  method  proposed by  Haimes , Hall and  Freedom in 1975 for decision making in water resource systems .It is an interactive approach that includes 3 steps ,such as; Generate  Pareto optimal solution , Obtain meaningful information to interact with the decision maker and use information obtained in step 2 to interact with DM and select the final solution based on the DM preference response.
Surrogate worth trade off method is used to solve the problem in different situations and  several areas of studies by analysts and researchers. SWT method is   applied  to solve the static two-objective problems, static n-objective problems, dynamic two-objective problems  and dynamic n-objective problems .
This paper, intends to  describe the SWT method ,review of  literature, applications and extension  of this method  to solve the multi-objective problems with  group  decision making.


[1]. Brizzi  A., Bavo  C., Marannino P., The Surrogate Worth  Trade -Off  Analysis for Power System Operation in Electricity Markets, Power Engineering Society Summer Meeting,IEEE.Volume.2,PP.1034-1039, 2010  
[2]. Chen Y., Liao W., Yong Y.R., Shen K.Y., Wang S.CH., Chang  Y.C., The Interactive Surrogate Worth Trade – Off Method for Multi- Objective Decision Making in Reactive Power Sources Planning, IEEE XPLORI, International Conference on Power System Technology, 2002
[3]. Choedhury M., Tan P., A multi-Objective Decision – Making  Framework  for Transportation Investments, Journal of Transportation research Forum,Volume.43,No.1,PP.82-91, 2004
[4]. Debeljak   G.J., Haimes  Y.Y.,  Leach  M., Integrated  the Surrogate Worth Trade off  method and  analytic hierarchy  Process, Socio-Economic Planning sciences,Volume.20,Issue.6,PP.375-384, 1986
[5]. Dhilon  J.S.,  Kothari  D.P., The Surrogate Worth Trade-Off Approach for Multi-objective Thermal Power Dispatch problem, Electric Power Systems Research,Volume .56,Issue.2,PP.103-110, 2000
[6]. Ghaleh Khondabi  I.,  Fallah Tafti A., Fuzzy group decision making using SWT method, International Journal of Computer Science and Engineering , Volum.2,No.8,PP.2602-2608, 2010
[7]. Hall  W.A.,  Haimes  Y.Y., The Surrogate Worth Trade – Off Method With multiple decision- makers, Springer Science and Business  ,Lecture Notes in Economics and Mathematical System ,Volume.123,PP.207-233, 1976
[8]. Haimes  Y.Y., Hall  W.A.,  Freedom  H.T., Multi-Objective  in Water Resources  Systems: The Surrogate Worth Trade – Off  Method, Elsevier Scientific Publishing Company ,Amesterdam, 1975
[9]. Iwasawa  A., Kohtake  N., Minato  N.,  Crossley  W., Investigating the surrogate  worth  trade off   method  to facilitate technology selection for new system, Third International Engineering Systems Symposium, 18-20 June, 2012
[10]. Marsden  A.L.,  Wange M.,  Dennis J.E.,  Moin P., Optimal  Aero-acoustic Shape Design Using the Surrogate Management  Framework, Optimization and Engineering,Volume.5. Pp.235-262, 2004
[11]. Nangia  N., Jain N.K.,  Wadhawa  C.L., Surrogate Worth Trade – Off Technique  for  Multi- Objective Optimal Power Flows, IEE , Proc-Genev, Volume.144,No.6, 1997
[12]. Perić  T., Babić  Z., Determining Optimal Production Plan by Revised Surrogate Worth Trade – Off Method, World  Academy of Science, Engineering and Technology,  Volume.23,PP.324-333, 2008
[13]. Richi  M., Sharma  M.K,, Multi- Objective Decision Making  Framework For Transportation Investments ,Using Surrogate Worth Trade – Off Method, Thesis,  Thapar  University, Punjab, 2010
[14]. Singh  L.,  Dhilon  J.S., Fuzzy Satisfying Interactive  Multi-objective Thermal Power Dispatch: SWT Approach, Journal of Systems Science and Systems  Engineering, 16(1) ,PP.88-106, 2007
[15]. Sakawa   M., Optimal Reliability – Design of a Series – Parallel System by a Large-Scale Multi-objective Optimization Method, IEEE ,Volume .R-30,Issue.2,PP.173-174, 1981
[16]. Sakawa   M., Interactive  Multi-objective  Decision Making  by the  Sequential  Proxy Optimization Technique, European Journal of Operational Research, Volume. 9 , Issue.4,PP.346-396, 1982
[17]. Shimizu  K.,  Kawabe  H.,  Aiyoshi   E., A Theory for Interactive P-reference Optimization and its Algorithm-Generalized SWT method, The Transactions of the Institute of Electronics and Communication Engineering  of Japan , Vol.J61-A,No.11,PP.1075-1082, 1978
[18]. Szopa  R.,  Marczy  B., Optimization of Production Problems Using Mathematical Programming, Polish Journal of Management Studies,Vol.4 , PP.231-238, 2011
[19]. Zhang  Z.H., Kwok J.T., Yeung  D.Y., Surrogate Maximization /Minimization Algorithms  and Extension, Springer Science, Mach Learn, 96, PP.1-33, 2007



Jednym z najbardziej ważnych obszarów badań w ciągu ostatnich lat, jest metodologia podejmowania decyzji w przypadku wielu sprzecznych celów. W związku z tym, opracowano kilka technik. Wśród nich występuje metoda Surrogate Worth Trade-off – która koncentruje się na rozwiązaniu złożonego przez wielu naukowców i analityków. Niniejszy artykuł ma na celu przegląd i sposób stosowania tej metody. Metoda SWT to podejście, które zapewnia zakłócenia między preferencjami decydenta i modeli matematycznych związanych z niedominującymi rozwiązaniami. W końcowej części artykułu, zaproponowana została metoda w celu wykorzystania SWT przy podejmowaniu wielu decyzji.

Słowa kluczowe: Funkcjonowanie Surrogate Worth, funkcje trade-off, cele wielorakie, grupa decydentów

SURROGATE WORTH折衷方法的回顧,應用與推廣


Back to content | Back to main menu