Goal Programming

Goal Programming is a method for when you hold several criteria, each with a target (aspiration) level you want to reach, and you want alternatives ranked by their total deviation from these targets. Unlike TOPSIS's "find the one closest to the best," it asks "find the one that strays least from the targets." Its roots lie in Charnes, Cooper and Ferguson's 1955 study, which used linear programming to estimate executive compensation; the concept grew into a distinct family within multi-criteria decision analysis over the following decades. The output is a total deviation score for every alternative and the rank that score produces; the smallest deviation marks the best alternative.

Goal Programming's underlying idea is that a decision-maker aims, on each criterion, not for "the best conceivable" but for "an acceptable, realistic level." Think of a student preparing for exams. Rather than aiming for full marks in every subject, the student aims to pass each one and directs revision time towards whichever subjects fall short of that mark. Goal Programming works the same way: a target is set for each criterion, then alternatives are measured against where they stand relative to that target, and only falling short of it is penalised. The philosophical consequence of this approach is that it satisfices rather than optimises. Exceeding a target on one criterion brings no extra reward; only whether the target is reached or missed matters.

The method proceeds through five steps.

First, verifying the inputs. The decision table is checked for completeness, the criterion weights are checked to sum to 1, and the direction is confirmed for every criterion.

Second, setting a target for each criterion. For benefit criteria, the highest observed value in the table is taken as the target; for cost criteria, the lowest observed value is taken. These targets are the reference points against which alternatives are measured; the decision-maker may also enter their own targets instead.

Third, computing the deviations. For every alternative and every criterion, two-way deviation is computed: falling below the target and rising above it. For a benefit criterion, falling below the target is the undesirable deviation; for a cost criterion, rising above the target is the undesirable deviation. Only one of the two deviations can be non-zero.

Fourth, finding the weighted total deviation. Each alternative's undesirable deviations are multiplied by the relevant criterion's weight and summed. A small total shows that the alternative stays close to the targets overall.

Fifth, ranking. Alternatives are ordered from the smallest total deviation to the largest; the alternative with the smallest deviation sits closest to the targets.

The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

The total deviation score shows how far an alternative sits from the targets that have been set; it says nothing more than that. A score near zero shows that the alternative meets the target on almost every criterion. This does not mean the alternative is perfect, because the targets themselves are drawn from the best observed values in the table, and they shift when the table does. The gap between two alternatives' scores shows how differently far apart from the targets they fall; whether that gap matters depends on the weights.

An alternative that overshoots a target by a wide margin on one criterion earns no extra credit for it; Goal Programming penalises only falling short of the target. The report should separately state by how much an alternative exceeds the target on some criteria, because this information does not feed into the total score.

Thus instead of writing:

"Goal Programming found the best alternative"

the report should read:

"Against these targets, the alternative with the least total deviation is this one; how the targets were set and how sensitive the ranking is to the weights should be shown in the report"

Classical Goal Programming works with crisp data: one number per cell. As of this writing, DecisionMind holds no extension alongside the base method; where targets or data are uncertain, the literature has defined fuzzy and interval forms of Goal Programming (Martel and Aouni, 1998).

You need: alternatives in rows, criteria in columns, one number per cell; a direction for every criterion; criterion weights that sum to 1; and, optionally, your own target value for each criterion. If no target is given, the best observed value in the table is taken as the target. A minimum of two alternatives and two criteria is required.

Goal Programming is a sound choice if, for every criterion, you can say "reaching this level is enough" rather than "the better, the better," and you want alternatives compared by how close they come to these targets. Its typical territory is decisions where several goals are pursued at once, such as resource allocation, production planning and budgeting.

It should not be used where the decision-maker genuinely holds that "the better, the better," and that exceeding the target should also be rewarded; Goal Programming does not reward performance beyond the target. If how the targets should be set is unclear or contested, this must first be settled; arbitrary targets produce an arbitrary ranking.

Each criterion has a sufficiency level, and deviation from it matters → Goal Programming

"The better, the better," and overshooting the target should also be rewarded → compensatory ranking methods such as TOPSIS, SAW

Targets are not clear → do not apply Goal Programming before clarifying the targets

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

Goal Programming's greatest strength is that it directly models the realistic way of thinking in which a decision-maker seeks what is sufficient rather than what is perfect. It pursues several goals at once and shows, step by step, how much deviation occurs on which criterion, making visible which criterion is the binding constraint on the decision. The calculation can be followed by hand, and it offers a natural framework for multi-goal planning problems such as resource allocation.

Its limitations stem from the same framework. First, how the targets are set directly affects the outcome; taking the best observed value in the table as the target means the targets shift whenever the candidate set changes. Second, because performance beyond the target is not rewarded, two alternatives can receive the same deviation score whether one overshoots the target by a wide margin and the other only slightly; this information loss is discussed in detail by Martel and Aouni (1998). Third, the quality of the weights lies outside the method itself. Fourth, dependence between criteria is not assumed; where criteria influence one another, weight can be implicitly counted twice.

The most common mistake is setting targets arbitrarily without reference to the data; a target set too high leaves no alternative able to approach it, while one set too low makes every alternative look equal. A second mistake is reading the deviation score as a percentage or a distance measure; the score only shows how far an alternative strays from the target. A third is treating an alternative that overshoots a target as better still; the method does not reward overshooting, only penalises falling short of it. A fourth is deriving the targets from the candidate set and then adding a new candidate while assuming the targets stay the same.

The governing principle is this:

A Goal Programming result reflects the targets and weights you have set; if the targets are contested, the ranking is contested too, and the report must show how the targets were set.