Goal programming is a branch of
multiobjective optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with ...
, which in turn is a branch of
multi-criteria decision analysis (MCDA). 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. Deviations are measured from these goals both above and below the target. Unwanted deviations from this set of target values are then minimised in an achievement function. This can be a
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
or a
weighted sum
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is ...
dependent on the goal programming variant used. As satisfaction of the target is deemed to satisfy the decision maker(s), an underlying
satisficing
Satisficing is a decision-making strategy or cognitive heuristic that entails searching through the available alternatives until an acceptability threshold is met. The term ''satisficing'', a portmanteau of ''satisfy'' and ''suffice'', was introduc ...
philosophy is assumed. Goal programming is used to perform three types of analysis:
# Determine the required resources to achieve a desired set of objectives.
# Determine the degree of attainment of the goals with the available resources.
# Providing the best satisfying solution under a varying amount of resources and priorities of the goals.
History
Goal programming was first used by Charnes,
Cooper and Ferguson in 1955, although the actual name first appeared in a 1961 text by Charnes and Cooper. Seminal works by Lee, Ignizio,
[JP Ignizio (1976) Goal programming and extensions, Lexington Books, Lexington, MA.] Ignizio and Cavalier, and
Romero[C Romero (1991) Handbook of critical issues in goal programming, Pergamon Press, Oxford.] followed. Schniederjans gives in a bibliography of a large number of pre-1995 articles relating to goal programming, and Jones and Tamiz give an annotated bibliography of the period 1990-2000.
[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] A recent textbook by Jones and Tamiz .
[Jones DF, Tamiz M (2010) Practical Goal Programming, Springer Books.] gives a comprehensive overview of the state-of-the-art in goal programming.
The first engineering application of goal programming, due to Ignizio in 1962, was the design and placement of the antennas employed on the second stage of the
Saturn V
Saturn V is a retired American super heavy-lift launch vehicle developed by NASA under the Apollo program for human exploration of the Moon. The rocket was human-rated, with three stages, and powered with liquid fuel. It was flown from 196 ...
. This was used to launch the Apollo space capsule that landed the first men on the moon.
Variants
The initial goal programming formulations ordered the unwanted deviations into a number of priority levels, with the minimisation of a deviation in a higher priority level being infinitely more important than any deviations in lower priority levels. This is known as ''
lexicographic
Lexicography is the study of lexicons, and is divided into two separate academic disciplines. It is the art of compiling dictionaries.
* Practical lexicography is the art or craft of compiling, writing and editing dictionaries.
* Theoretica ...
'' or pre-emptive goal programming. Ignizio
gives an algorithm showing how a lexicographic goal programme can be solved as a series of linear programmes. Lexicographic goal programming is used when there exists a clear priority ordering amongst the goals to be achieved.
If the decision maker is more interested in direct comparisons of the objectives then ''weighted'' or non-pre-emptive goal programming should be used. In this case, all the unwanted deviations are multiplied by weights, reflecting their relative importance, and added together as a single sum to form the achievement function. Deviations measured in different units cannot be summed directly due to the phenomenon of
incommensurability.
Hence each unwanted deviation is multiplied by a normalisation constant to allow direct comparison. Popular choices for normalisation constants are the goal target value of the corresponding objective (hence turning all deviations into percentages) or the range of the corresponding objective (between the best and the worst possible values, hence mapping all deviations onto a zero-one range).
For decision makers more interested in obtaining a balance between the competing objectives, ''Chebyshev'' goal programming is used. Introduced by Flavell in 1976, this variant seeks to minimise the maximum unwanted deviation, rather than the sum of deviations. This utilises the
Chebyshev distance metric.
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 not
Pareto efficient. This violates a fundamental concept of
decision theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
, that no rational decision maker will knowingly choose a solution that is not Pareto efficient. However, techniques are available
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 suggesting the use of the
analytic hierarchy process
In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. It was developed by Thomas ...
or interactive methods for this purpose. Also, the weights of the objective functions can be calculated based on their preference using the
ordinal priority approach.
See also
*
Decision-making software Decision-making software (DM software) is software for computer applications that help individuals and organisations make choices and take decisions, typically by ranking, prioritizing or choosing from a number of options.
An early example of DM so ...
External links
LiPS— Free easy-to-use GUI program intended for solving linear, integer and goal programming problems.
LINSOLVE- Free Windows command-line window linear programming and linear goal programming]
References
{{DEFAULTSORT:Goal Programming
Mathematical optimization
Multiple-criteria decision analysis
Goal
de:Entscheidung unter Sicherheit#Zielprogrammierung