LoPM (Limits on Property Method)

LoPM is a ranking method for fields such as engineering and materials selection, where each property carries its own type of requirement: it must reach at least a certain value, stay below a certain value, or sit close to an exact target. Its output is a score for every alternative and the rank that score produces. Farag proposed it for material and process selection in engineering design; together with the weighted property index and the cost-per-unit-property method, it is one of three classical materials-selection approaches defined by the same author.

Most weighted-summation methods assume a one-directional preference for every criterion: "more is better" or "less is better." LoPM does not accept that this is always enough. In engineering, a property can matter because it must stay above or below a specific limit; going far beyond that limit may add no further benefit, and can even bring needless cost. Another property may need to sit close to a given target, neither too little nor too much. LoPM recognises these three cases, floor, ceiling and target, separately, and gives each its own logic for a fitness score.

This is a break from the assumption that "better always means more." The philosophical consequence is that each property is judged against its own natural requirement type, and only at the end are these judgements combined through weights. Farag's own materials-selection framework calls for a preliminary screening with hard, go/no-go requirements before LoPM is applied, with LoPM then used only to discriminate among the remaining, soft, relative requirements.

The method proceeds in a single step, though that step contains a separate logic for each property type.

The step: computing property fitness scores and summing them by weight. Every property is first processed according to its type. For a floor property (the value must exceed a given threshold), the ratio of the limit to the value is computed; a value exactly at the limit gives a ratio of 1. For a ceiling property (the value must stay below a given threshold), the ratio of the value to the limit is computed, again giving 1 when the value sits exactly at the limit. For a target property, the absolute deviation of the value from the target is computed; the smaller the deviation, the better that property is met. Each property's fitness score is multiplied by its own weight and summed across all properties; the higher the total, the better the alternative is judged to be.

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

The score shows an alternative's weighted sum of limit-fitness across all its properties; it is not a percentage or a direct quality measure. For floor and ceiling properties, a value of 1 means "sitting exactly on the limit"; moving away from the limit changes the fitness ratio accordingly. There is an important subtlety here: because the floor ratio is computed by dividing the limit by the value, the ratio does not shrink as the value falls as far as possible BELOW the limit, it grows instead. This means the ratio carries no built-in penalty for falling below a limit; it reflects only closeness to the limit, in either direction.

For this reason, LoPM's raw score does not, on its own, screen out cases where a property falls seriously short of the required minimum; such an alternative can still score highly overall if it is strong on the other properties. Farag's own framework meets this risk by prescribing a preliminary screening with hard, go/no-go requirements before LoPM is applied. Skip that screening and LoPM's score can be misleading.

For this reason, instead of writing:

"LoPM found the best material"

the report should read:

"Among the materials that survived screening against the mandatory minimum and maximum requirements, this is the one that scores highest on fitness with these weights"

LoPM works with crisp numerical data and requires every value to be strictly positive, because the calculation forms a ratio between the limit and the value. DecisionMind carries no extension of this method; it is offered only in its base form, working with crisp numbers alone.

You need a decision table, a limit value for every property, each property's type (floor, ceiling or target), and property weights. LoPM does not produce weights, it takes them from outside. Limit values also come from outside; they should be drawn from a technical specification, a standard or a design requirement, never chosen arbitrarily. For target properties, a smaller deviation is better; this is the opposite reading from the other two types and must not be confused with them.

LoPM is a suitable choice if your properties are not defined as simple "more is better, less is better" preferences, but as limits: "at least this much," "at most this much," or "close to exactly this value." It is used in engineering materials and process selection, particularly where technical specifications are naturally written as limits.

If falling below a limit on a critical property is absolutely unacceptable, LoPM's raw score is not sufficient on its own; a hard preliminary screen on that property must come first, with LoPM used only among the alternatives that survive it. If your properties are simply "more is better, less is better" and no limit concept applies, direct methods such as TOPSIS or WLC are more suitable.

Properties naturally defined as limits (floor/ceiling/target) → LoPM, together with a hard screen first

Properties are only "more/less is better" → TOPSIS, WLC

Falling below a limit is absolutely unacceptable → screen first, LoPM only for what remains

Weights are needed, no numerical limit exists → AHP, BWM, SWARA, Entropy, CRITIC

LoPM's principal strength is that it handles three different requirement types, floor, ceiling and target, within a single framework, each on its own natural logic; this is something methods that only distinguish "more is better" from "less is better" cannot meet. The calculation is simple, and every property's fitness can be traced separately. It fits naturally with engineering practice, where technical specifications are frequently written as limits.

Its limitations stem largely from the behaviour of the raw ratio. For a floor property, the fitness ratio grows rather than shrinks as the value falls as far as possible below the limit; a check the DecisionMind team ran by rebuilding this formula from scratch showed that lowering a property to half its required minimum can push that property's score to nearly TWICE that of a value sitting exactly on the limit. This shows that the ratio is not a "penalty" but merely a "closeness to the limit" measure, and can conceal a serious shortfall when left unchecked. Farag's own framework addresses this by screening with hard requirements before LoPM is applied; this screening is a separate step that must be added from outside, it is not part of LoPM's own calculation. A second limitation is that limit values are set externally and subjectively; shifting a limit slightly can change the scores substantially. Third, because every value must be positive, properties with zero or negative measurements cannot be processed directly. Fourth, because the method is a weighted sum, it is compensatory: a weakness on one property can be masked by another, an undesirable behaviour for hard requirements.

The most common mistake is using LoPM on its own without a prior hard, go/no-go screen; an alternative that seriously breaches a critical threshold can then score highly. A second mistake is assuming that, for a floor property, the ratio behaves as "the lower, the worse"; the ratio actually measures closeness to the limit, not direction. A third is assuming that, for target properties, a large deviation is favourable; on the contrary, a small deviation is favourable. A fourth is setting limit values with unjustified, round numbers without testing how much this choice affects the result. A fifth is running LoPM directly on a zero or negative measurement; the ratio then comes out undefined or meaningless.

The governing principle is this:

The LoPM score is the weighted sum of how close each property sits to its own limit; this ratio does not, by itself, penalise a serious shortfall below a limit, which is why a separate preliminary screen is essential for critical properties.