Romero 2001 in which a harvest schedule holding some desirable properties from the habitat diversity viewpoint was determined.
• In this paper, the trade-off curve between the proposed measure of habitat diversity and financial returns from harvested timber is determined. Then, a zero-one goal
programming model that integrates the mentioned habitat diversity index and the economic criterion in conjunction with other relevant forest management criteria such
as volume control over the planning horizon and ending forest volume inventory is formulated. From this model, several best compromise or satisfying harvest schedules
are obtained and interpreted in utility terms.
III. Research Procedure
A. Goal Programming 1. Definition
• Goal Programming is a fancy name for a very simple idea: the line between objectives and constraints is not completely solid. In particular, when there are a number of
objectives, it is normally a good idea to treat some or all of them as constraints instead of objectives Trick, 1996.
• Goal Programming is a procedure based on linear programming that allows several goals to be considered instead of just one single objective. Goal programming is a
branch of multiple objective programming
, which in turn is a branch of multi-criteria
decision analysis MCDA, also known as multiple-criteria decision making MCDM. It
can be thought of as an extension or generalization 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 minimized 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 makers, an underlying
satisfying philosophy is
assumed Wikipedia encyclopedia, 2006
2. History
• Goal programming was first used by Charnes, et al. 1955, although the actual name first appear in a 1961 Charnes and Cooper, 1961. Seminal works by Lee 1972,
Ignizio 1976, Ignizio and Cavalier 1994, and Romero 1991 followed. Scniederjans 1995 gives in a bibliography of a large number of pre 1995 articles relating to goal
programming and Jones and Tamiz 2002 give an annotated bibliography of the period 1990-2000.
• 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 .
This was used to launch the Apollo space capsule which landed the first men on the moon.
3. Variants
• The original goal programming formulations ordered the unwanted deviations into a number of priority levels, with the minimization of a deviation in a higher priority level
being of infinitely more importance than any deviations in lower priority levels. This is known as lexicographic or pre-emptive goal programming. Ignizio 1976 gives an
algorithm showing how a lexicographic goal programme can be solved as a series of linear programmes.
• It is important to recognize that deviations measured in different units cannot be summed directly due to the phenomenon of incommensurability. Hence each unwanted
deviation is multiplied by a normalization constant to allow direct comparison. Popular choices for normalization constants are the goal target value of the corresponding
objective hence turning all deviations into percentages or the range of the
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corresponding objective between the best and the worst possible values, hence mapping all deviations onto a zero-one range Onal, 1997.
• For decision makers more interested in obtaining a balance between the competing objectives, Chebyshev goal programming should be used. Introduced by Flavell 1976,
this variant seeks to minimize the maximum unwanted deviation, rather than the sum of deviations. This utilizes the
Chebyshev distance metric, which emphasizes justice and
balance rather than ruthless optimization.
4. Procedure for the development of a goal programming model
