##
**Revised multi-choice goal programming.**
*(English)*
Zbl 1167.90637

Summary: C.-T. Chang [Multi-choice goal programming, Omega, Int. J. Manage. Sci. 35, 389–396 (2007)] has recently proposed a new method namely multi-choice goal programming (MCGP) for multi-objective decision problems. The multi-choice goal programming allows the decision maker to set multi-choice aspiration levels for each goal to avoid underestimation of the decision. However, to express the multi-choice aspiration levels, multiplicative terms of binary variables are involved in their model. This leads to difficult implementation and it is not easily understood by industrial participants. In this paper, we propose an alternative method to formulate the multi-choice aspiration levels with two contributions: (1) the alternative approach does not involve multiplicative terms of binary variables, this leads to more efficient use of MCGP and is easily understood by industrial participants, and (2) the alternative approach represents a linear form of MCGP which can easily be solved by common linear programming packages, not requiring the use of integer programming packages. In addition, a new concept of constrained MCGP is introduced for constructing the relationships between goals in this paper. Finally, to demonstrate the usefulness of the proposed method, an illustrate example is included.

### MSC:

90C29 | Multi-objective and goal programming |

PDFBibTeX
XMLCite

\textit{C.-T. Chang}, Appl. Math. Modelling 32, No. 12, 2587--2595 (2008; Zbl 1167.90637)

Full Text:
DOI

### References:

[1] | Charnes, A.; Cooper, W. W., Management Model and Industrial Application of Linear Programming, vol. 1 (1961), Wiley: Wiley New York · Zbl 0107.37004 |

[2] | Lee, S. M., Goal Programming for Decision Analysis (1972), Auerbach: Auerbach Philadelphia, PA |

[3] | Ignizio, J. P., Introduction to Linear Goal Programming (1985), Sage: Sage Beverly, Hills, CA · Zbl 0662.90075 |

[4] | Tamiz, M.; Jones, D.; Romero, C., Goal programming for decision making: an overview of the current state-of-the-art, Eur. J. Oper. Res., 111, 567-581 (1998) · Zbl 0937.90048 |

[5] | Romero, C., Extended lexicographic goal programming: a unifying approach, Omege, 29, 63-71 (2001) |

[6] | Jones, D. F.; Tamiz, M., Goal programming in the period 1990-2000, (Ehrgott, M.; Gandibleux, X., Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys (2002), Kluwer), 129-170 · Zbl 1095.90594 |

[7] | Chang, C.-T., Multi-choice goal programming, Omega, The Inter. J. Manage. Sci., 35, 389-396 (2007) |

[8] | Chang, C.-T., An efficient linearization approach for mixed integer problems, Eur. J. Oper. Res., 123, 652-659 (2000) · Zbl 0982.90034 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.