PROMETHEE METHOD

 

Introduction

The PROMETHEE method (Preference Ranking Organization Method for

Enrichment Evaluations) is the one of most recent MCDA methods. It is an

outranking method for a finite set of alternative actions to be ranked and

selected among criteria, which are often conflicting. PROMETHEE is a

simple ranking method in conception and application compared with the

other methods for multi-criteria analysis.The PROMETHEE family of

outranking methods, including the PROMETHEE I is a for partial ranking

method  and the PROMETHEE II is a complete ranking method

PROMETHEE I 

Instead of taking average we just take sum to get leaving and entering flow.

In Promethee-1 instead of rank preference is calculated 

1. Alternative a is preferred over b (aPb)

     Leaving flow(a)>Leaving flow(b) & Entering flow(a)< & Entering flow(b)    

    or

      Leaving flow(a)>Leaving flow(b) & Entering flow(a)= & Entering flow(b) 

or

      Leaving flow(a)=Leaving flow(b) & Entering flow(a)< & Entering flow(b)

2. Indifference Situation(aIb)

      Leaving flow(a)=Leaving flow(b) & Entering flow(a)= & Entering flow(b)

3. In Comparable Situation(aRb)

      Leaving flow(a)>Leaving flow(b) & Entering flow(a)> & Entering flow(b)

      Leaving flow(a)< Leaving flow(b) & Entering flow(a)< & Entering flow(b)

PROMETHEE II

The basic principle of PROMETHEE II is based on a two comparison of

alternatives corresponding to each known condition Alternatives are tested

according to different criteria, which must be maximized or minimized.

The PROMETHEE II implementation requires two types of  additional

information

Weight

 Weights  Determination  is an important step in most multi-criteria methods.

PROMETHEE II assumes that the decision-maker is able to weigh the conditions appropriately, at least when the number of conditions is not too high.

 Preference function

For each criterion, the preference function translates the difference between the

evaluations obtained by two alternatives into a degree of choice from zero to one.For convenience selection of a specific preference function

Steps for PROMETHEE II

Example

CM- closeness of market (CM),

CR- closeness to raw material (CR),

LT- land transportation (LT), 

AT- air transportation (AT), 

CLR- cost of labor (CLR) (in rupees/worker), 

AL- availability of labor (AL),

E- community education (E) 

BC- business climate (BC)

Among these criteria, only CLR is a non-beneficial attribute and the remaining

are the beneficial attributes.Only labor costs are not profitable and some features

are advantageous.

1.Objective data for facility location problem

Location	CM	CR	LT	AT	CLR	AL	E	BC
P1	0.665	0.745	0.665	0.590	250.000	0.665	0.590	0.745
P2	0.745	0.665	0.665	0.745	265.000	0.590	0.665	0.745
P3	0.500	0.665	0.745	0.590	255.000	0.590	0.745	0.665

2.Normalized decision matrix

Location	CM	CR	LT	AT	CLR	AL	E	BC
P1	0.6735	1	0	0	1	1	0	1
P2	1	0	0	1	0	0	0.4839	1
P3	0	0	1	0	0.6667	0	1	0

3. Preference functions for all alternatives

Location	CM	CR	LT	AT	CLR	AL	E	BC
(P1,P2)	0	1	0	0	1	1	0	0
(P1,P3)	0.6735	1	0	0	0.3333	1	0	1
(P2,P1)	0.3265	0	0	1	0	0	0.4839	0
(P2,P3)	1	0	0	1	0	0	0	1
(P3,P1)	0	0	1	0	0	0	1	0
(P3,P2)	0	0	1	0	0.6667	0	0.5161	0

4.Aggregated preference function

Location	P1	P2	P3
P1	-	0.2902	0.59
P2	0.1739	-	0.4548
P3	0.2551	0.2363	-

5.Entering and leaving flows for different location

Location	Leaving flow	Entering flow
P1	0.4401	0.2144
P2	0.3643	0.1182
P3	0.2457	0.5224

6. Net outranking flow values for different location alternative

Location	Net outranking flow	Rank
P1	0.2257	2
P2	0.2461	1
P3	-0.2767	3

Advantages

• The first advantage is its user-friendly outranking method. 

• The second advantage is the success of PROMETHEE in applications to

• real-life planning problems.

• Another advantage of PROMETHEE lies in the completeness of ranking.

• The PROMETHEE I and PROMETHEE II allow partial and complete ranking

• of alternatives, respectively