Compromise Programming

Compromise Programming is a ranking method that orders alternatives into a single sequence once you hold a decision table filled with numbers. Its output is a distance score for every alternative, together with the rank that score produces; the lowest score marks the alternative closest to the ideal, and hence the best compromise. Milan Zeleny proposed it in 1973, and it is discussed alongside a similar approach developed independently in the same period by Po-Lung Yu. The method does not generate criterion weights; weights are supplied from outside.

The idea behind Compromise Programming is to accept that no alternative can be best on every criterion at once. The best value on each criterion is taken separately and gathered into a single hypothetical "ideal point"; this point does not actually exist in any alternative. Real alternatives fall some distance short of this ideal point. The method presents the alternative that minimises this distance as the best compromise.

This idea carries a philosophical consequence: Compromise Programming is compensatory, because the distance is gathered into a single figure, and a shortfall on one criterion can be offset by closeness on another. What distinguishes the method is that the user can choose how this distance is measured. Whether to give weight to the sum of small shortfalls or to the single largest shortfall is a matter of preference, and this preference directly changes the result.

The method proceeds through a single step built on three concepts.

First concept, the ideal and counter-ideal point. For each criterion, the largest value forms the ideal point for a "higher is better" criterion, and the smallest value for a "lower is better" one. The values at the opposite extreme form the counter-ideal (worst) point. These two points define the criterion's range of variation within that analysis.

Second concept, the scaled shortfall. The difference between every alternative's value on every criterion and the ideal value is taken; this difference is divided by the criterion's range of variation to bring it between 0 and 1, and then multiplied by the criterion's weight. This makes the shortfalls of criteria measured in different units comparable on the same scale.

Third concept, the form of combination. These scaled shortfalls are combined using a "p value." If p = 1 is chosen, all shortfalls are summed with equal importance; if p = 2 is chosen, large shortfalls carry disproportionately more weight (straight-line distance); as p approaches infinity, only the single largest shortfall becomes decisive. DecisionMind uses p = 2 by default, but this value can be changed by the user. Alternatives are ranked by this combined distance from lowest to highest; the lowest distance marks the best compromise.

The formulas behind each step are given on the DecisionMind method page; this card carries no formulas.

The distance score shows how far an alternative falls from the ideal point within this particular alternative set, and nothing more. The score does not sit on a fixed scale such as 0–1 and cannot be compared with a score from a different analysis, because the ideal and counter-ideal points are built afresh, in every analysis, from that analysis's own alternatives. The lowest score marks the best alternative; this is the reverse of TOPSIS's rule that the highest score is best.

The result depends directly on the chosen p value. A small p (close to 1) weighs the shortfalls on all criteria evenly; a large p (approaching infinity) gives weight only to the single criterion on which you fall shortest. The report should therefore state which p value was used and how sensitive the result is to this choice. For this reason:

"Compromise Programming found the best alternative"

should be written as:

"With this p value, these weights and this alternative set, the compromise closest to the ideal is this one; the result is sensitive to the chosen p value"

Compromise Programming works with crisp data: one number per cell. DecisionMind currently holds no extension of this method for another data type.

You need alternatives in rows, criteria in columns, one number per cell and no empty cells; direction information for every criterion and weights that sum to 1. Compromise Programming does not produce weights, it asks for them. A p value must also be chosen; the default is 2 (Euclidean distance), with 1 (equal sum of all shortfalls) and infinity (only the worst shortfall) also common choices. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

Compromise Programming is a suitable choice if your criteria can be measured numerically, your table has no gaps, and you accept distance from an ideal point as a common measure. Being able to test sensitivity across different p values is an advantage for decision-makers who want to discuss openly whether the decision was made on a balanced basis or according to the worst-case criterion.

If you will not compromise on one criterion, the method is not suitable; sub-threshold alternatives should first be screened out and only the remainder ranked. Where criteria are strongly linked to one another, that link needs handling first.

A numerical table, compensation accepted, distance-to-ideal-point logic → Compromise Programming

The choice of distance measure should be discussed openly → Compromise Programming (testing the p value)

No compromise on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

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

Compromise Programming's chief advantage is its simplicity and the flexibility it offers through the p value. The decision-maker can directly test the question "should I decide on a balanced basis across all criteria, or according to the criterion on which I fare worst" simply by changing the p value. The idea of distance to an ideal point is easy to convey, and every step can be followed on the table. It also forms the conceptual basis for many later methods, including VIKOR.

Its limitations are shared with the TOPSIS family. When the alternative set changes, the ideal and counter-ideal points shift with it; an alternative added afterwards can change how the others rank relative to one another (García-Cascales and Lamata, 2012). The assumption of full compensation applies: a serious weakness on one criterion can be papered over by others. The choice of p value directly affects the result and is often left unjustified (André and Romero, 2008); different p values applied to the same data can give different orders. The quality of the weights lies outside the method itself.

The most common mistake is marking criterion direction wrongly, which reverses the ideal and counter-ideal points. A second mistake is leaving the p value at its default without ever questioning it; it should not be forgotten that p = 1 and p = 2 can place different alternatives first. A third mistake is reading the lowest distance score as the "worst result"; in Compromise Programming the lowest score marks the best alternative, the opposite of TOPSIS. A fourth mistake is assigning equal weights without justification. A fifth mistake is adding an alternative once the analysis is finished and being surprised the ranking shifts.

The governing principle is this:

Compromise Programming's distance score is a summary of the directions, weights and chosen p value you supplied; if the p value changes, the compromise can change too.