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 Jean-Pierre Blanger, PSI Editions, France, 1982]. --------------------------------------------- End of file Appoint.txt