EXPLANATION FILE OF PROGRAM APPOINT
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  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 Jean-Pierre Blanger,
        PSI Editions, France, 1982].
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End of file Appoint.txt