EXPLANATION FILE OF PROGRAM APPOINT
===================================
APPOINTMENT METHOD

1. Kinds of problems

The appointment method allows calculating the best appointment configura
tion among a certain amount of possible assignments. The seeked solution gene
rally minimizes a cost or maximizes earnings. So the method will indicate the
appointmentt having the maximum efficiency for a given problem.
2. The Model

To determine the best appointment, the method uses a matrix of appointment
costs or quantities. Then by using successive iterations based on Hungarian
algorithm, the best appointment configuration is found.
The model is conceived to minimize a total cost; or sometimes to maximize a
satisfaction. In the latter case, the cost matrix must be transformed into a
"regret" matrix. For that purpose, we have to either to make a complement by
a value greater than all of the matrix elements, or to take the maximum ele
ment of the matrix and to replace each elemnt by the substration, max. value
minus element value.
Sometimes, the number of locations to be appointed and the number of candi
dates are different. Two cases may happen:
 number of locations < number of candidates
We must create fictitious locations with a zero value as in table below:
Locations
A B C
 1 80 20 0 Here C values are null.
candidates 
 2 75 5 0

 3 10 0 0
 number of locations > number of candidates
In this case, we must create fictitious candidates as in table below:
Locations
A B C
 1 80 20 50 Here line 3 values are null.
candidates 
 2 75 10 70

 3 0 0 0
3. Examples

3.1 Wording
An employer has received four trainees to whom he asked to give a grade,
from 1 to 100, for their preference concerning four jobs to be appointed.
The grades are shown in the table below:
Jobs
J1 J2 J3 J4
 T1 90 80 20 40

 T2 90 70 30 80
trainees 
 T3 40 70 20 80

 T4 50 40 20 60
The employer's goal is to make the four job appointments so as the global
satisfaction of the trainees is the greatest possible. He will use the
appointment model.
3.2 Resolution
First we must change the satisfaction matrix into a regret matrix, for
instance if the satisfaction is 90, the regret is 100  90 = 10:
Jobs
J1 J2 J3 J4
 T1 10 20 80 60

 T2 10 30 70 20
trainees 
 T3 60 30 80 20

 T4 50 60 80 40
Now we can use program Appoint as follows:
Number of jobs: 4
Trainee #1 J1 = 10 J2 = 20 J3 = 80 J4 = 60
Trainee #2 J1 = 10 J2 = 30 J3 = 70 J4 = 20
Trainee #3 J1 = 60 J2 = 30 J3 = 80 J4 = 20
Trainee #4 J1 = 50 J2 = 60 J3 = 80 J4 = 40
Results:
Trainee #1 ==> Job #2 (S=80)
Trainee #2 ==> Job #1 (S=90)
Trainee #3 ==> Job #4 (S=80)
Trainee #4 ==> Job #3 (S=20)
Total satisfaction: 270
From [Modèles pratiques de décision Tome 2, By JeanPierre Blanger,
PSI Editions, France, 1982].

End of file Appoint.txt