Compromise Programming - Lp-metric distance to ideal solution

Overview

Compromise Programming - Lp-metric distance to ideal solution

Output

utility, lower is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Validate inputs for compromise-programming.

   $$L_p(x)={\left[\sum _j{w}_j^p\frac{|f_j^{\ast }-f_j(x){|}^p}{|f_j^{\ast }-f_j^{\circ }{|}^p}\right]}^{1/p}$$

   Zeleny 1973, (pending PDF page verification)

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• Applying COMPROMISE-PROGRAMMING without verifying this assumption.

  Requirement: Criteria preferences are independent (no synergistic interactions)

• Applying COMPROMISE-PROGRAMMING without verifying this assumption.

  Requirement: Compensation is acceptable: high score on one criterion can offset low on another

• Applying COMPROMISE-PROGRAMMING without verifying this assumption.

  Requirement: Decision matrix is complete (no missing values)

• Using COMPROMISE-PROGRAMMING when: Criteria strongly correlated → consider DEMATEL/ANP for interdependence.

  An alternative method is recommended in this situation.

• Using COMPROMISE-PROGRAMMING when: Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE).

  An alternative method is recommended in this situation.

Works with

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