Goal programmingGoal programming is a branch of multiobjective optimization, which in turn is a branch of multi-criteria

decision analysis (MCDA), also known as multiple-criteria decision making (MCDM). This is an

optimization programme. It can be thought of as an extension or generalisation of linear programming to

handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target

value to be achieved. Unwanted deviations from this set of target values are then minimised in an

achievement function. This can be a vector or a weighted sum dependent on the goal programming

variant used. As satisfaction of the target is deemed to satisfy the decision maker(s), an

underlying satisficing philosophy is assumed. Goal programming is used to perform three types of

analysis:

1. Determine the required resources to achieve a desired set of objectives.

2. Determine the degree of attainment of the goals with the available resources.

3. Providing the best satisfying solution under a varying amount of resources and priorities of the

goals.

Strengths and weaknesses

A major strength of goal programming is its simplicity and ease of use. This accounts for the large number

of goal programming applications in many and diverse fields. Linear Goal programmes can be solved

using linear programming software as either a single linear programme, or in the case of the lexicographic

variant, a series of connected linear programmes.

Goal programming can hence handle relatively large numbers of variables, constraints and objectives. A

debated weakness is the ability of goal programming to produce solutions that are notPareto efficient.

This violates a fundamental concept of decision theory, that is no rational decision maker will knowingly

choose a solution that is not Pareto efficient. However, techniques are available [6][11][12] to detect when this

occurs and project the solution onto the Pareto efficient solution in an appropriate manner.

The setting of appropriate weights in the goal programming model is another area that has caused

debate, with some authors [13] suggesting the use of the Analytic Hierarchy Process or interactive

methods [14] for this purpose.

References

1. A Charnes, WW Cooper, R Ferguson (1955) Optimal estimation of executive compensation by linear

programming, Management Science, 1, 138-151.

2. A Charnes, WW Cooper (1961) Management models and industrial applications of linear programming,

Wiley, New York

3. SM Lee (1972) Goal programming for decision analysis, Auerback, Philadelphia

4. ^  JP Ignizio (1976) Goal programming and extensions, Lexington Books, Lexington, MA.

5. JP Ignizio, TM Cavalier (1994) Linear programming, Prentice Hall.

6. C Romero (1991) Handbook of critical issues in goal programming, Pergamon Press, Oxford.

7. MJ Scniederjans (1995) Goal programming methodology and applications, Kluwer publishers, Boston.

8. DF Jones, M Tamiz (2002) Goal programming in the period 1990-2000, in Multiple Criteria Optimization:

State of the art annotated bibliographic surveys, M. Ehrgott and X.Gandibleux (Eds.), 129-170. Kluwer

9. Jones DF, Tamiz M (2010) Practical Goal Programming, Springer Books.

10. RB Flavell (1976) A new goal programming formulation, Omega, 4, 731-732.

11. EL Hannan (1980) Non-dominance in goal programming, INFOR, 18, 300-309

12. M Tamiz, SK Mirrazavi, DF Jones (1999) Extensions of Pareto efficiency analysis to integer goal

programming, Omega, 27, 179-188.

13. SI Gass (1987) A process for determining priorities and weights for large scale linear goal programmes,

Journal of the Operational Research Society, 37, 779-785.

14. BJ White (1996) Developing Products and Their Rhetoric from a Single Hierarchical Model, 1996

Proceedings of the Annual Conference of the Society for Technical Communication, 43, 223-224.