A Goal Programming model of the reference point method

Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.

[1]  H. Simon,et al.  Models of Man. , 1957 .

[2]  William J. Baumol.  Management models and industrial applications of linear programming, Volume I, by Abraham Charnes and William W. Cooper. John Wiley and Sons, New York, 1961. xxiii + 467 pp. $11.75 , 1962 .

[3]  D. A. Conway.  Management Goals and Accounting for Control , 1966 .

[4]  Roger M. Y. Ho,et al.  Goal programming and extensions , 1976 .

[5]  Manfred Grauer,et al.  DIDASS — Theory, Implementation and Experiences , 1984 .

[6]  A. Wierzbicki.  On the completeness and constructiveness of parametric characterizations to vector optimization problems , 1986 .

[7]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[8]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[9]  D. J. White,et al.  A Bibliography on the Applications of Mathematical Programming Multiple-objective Methods , 1990 .

[10]  Roy J. Clinton,et al.  Interactive Optimization Aspects of Electronic Spreadsheet Models for Design and Planning , 1991 .

[11]  K. Jörnsten,et al.  A Critical Comment on Integer Goal Programming , 1988 .

[12]  James P. Ignizio,et al.  Linear Programming in Single- and Multiple-Objective Systems , 1984 .

[13]  Sang M. Lee,et al.  Goal programming for decision analysis , 1972 .

[14]  James P. Ignizio.  On the Merits and Demerits of Integer Goal Programming , 1989 .

[15]  A. Wierzbicki.  A Mathematical Basis for Satisficing Decision Making , 1982 .

[16]  Andrzej P. Wierzbicki,et al.  Aspiration Based Decision Support Systems: Theory, Software and Applications , 1989 .

[17]  S. M. Junaid Zaidi,et al.  Linear Programming in Single and Multiple Objective Systems , 1982 .

[18]  Milan Zelany,et al.  A concept of compromise solutions and the method of the displaced ideal , 1974, Comput. Oper. Res..

[19]  L. R. Amey.  Management Goals and Accounting for Control , 1966 .