param m, integer, > 0;
/* number of conversation partners */

param n, integer, > 0;
/* number of students */

set CP := 1..m;
/* set of conversation partners */

set S := 1..n;
/* set of students */

set days := {'Mo','Tu','We','Th','Fr'};  
/* set days :=1..2; */
set hours := 0..7; 
set TS := days cross hours;
/* all possible times_slots */

set CPA within CP cross TS;
/* conversation partners availability */
 
set CPUN := CP cross TS diff CPA;
/* conversation partners unavailability */
 
set SA within S cross TS;
/* students availability */

set SUN := S cross TS diff SA;
/* students unavailability */

param level{i in S}, >0;
/* english level of students */

param nationality{i in S}, symbolic, in {'Brazil', 'China', 'France', 'Japan', 'Korea', 'Arabia', 'Taiwan', 'Thailand', 'Tunisia', 'Turkey'}; 
/* nationality of students */

param limit{j in CP}, >0;
/* max. number of sessions per CP per week */

var x{i in S, j in CP, (d,h) in TS} ;
/* x[i,j,t]=1 means student i and conversation partner are scheduled 
	to have a session on day d at h hours */


s.t. student_load{i in S}: sum{j in CP, (d,h) in TS} x[i,j,d,h]<=1; 
/* each student has exactly one conversation lesson per week */

/*
s.t. student_feasible{i in S, j in CP, (i,d,h) in SUN}: x[i,j,d,h]=0;
MORE COMPACT FORMLUATION: */
s.t. student_feasible{i in S}: sum{j in CP, (i,d,h) in SUN} x[i,j,d,h]=0;
/* each student has no session when not available */

s.t. partner_load{j in CP}: sum{i in S, (d,h) in TS} x[i,j,d,h]<=limit[j];
/* no partner must be overloaded */

/*
s.t. partner_feasible{j in CP, i in S, (j,d,h) in CPUN}: x[i,j,d,h]=0;
MORE COMPACT FORMLUATION: */
s.t. partner_feasible{j in CP}: sum{i in S, (j,d,h) in CPUN} x[i,j,d,h]=0;
/* partner has no session when not available */

s.t. session{j in CP, (d,h) in TS}: sum{i in S} x[i,j,d,h]<=2;
/* at most two [should be exactly??] students per session */


s.t. feasible_pairs13{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==100} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==300} x[s_2,j,d,h];
s.t. feasible_pairs14{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==100} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==400} x[s_2,j,d,h];
s.t. feasible_pairs15{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==100} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==500} x[s_2,j,d,h];
s.t. feasible_pairs16{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==100} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==600} x[s_2,j,d,h];
s.t. feasible_pairs24{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==200} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==400} x[s_2,j,d,h];
s.t. feasible_pairs25{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==200} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==500} x[s_2,j,d,h];
s.t. feasible_pairs26{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==200} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==600} x[s_2,j,d,h];
s.t. feasible_pairs35{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==300} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==500} x[s_2,j,d,h];
s.t. feasible_pairs36{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==300} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==600} x[s_2,j,d,h];
s.t. feasible_pairs46{j in CP, (d,h) in TS}:
        1 >= sum{s_1 in S: level[s_1]==400} x[s_1,j,d,h]
           + sum{s_2 in S: level[s_2]==600} x[s_2,j,d,h];
                                                                              


/*
s.t. feasible_pairs{s_1 in S, s_2 in S, j in CP, (d,h) in TS: s_1 <> s_2}:
	if ((abs(level[s_1]-level[s_2])>1) or
		(nationality[s_1]=nationality[s_2])) then 
		x[s_1,j,d,h]+x[s_2,j,d,h]<=1; */
/* two students in a session must be of about the same level
	and different nationality */

minimize sessions: sum{i in S, j in CP, (d,h) in TS} -x[i,j,d,h];


/* ***************************************************************** */
data;

param m :=62;

param n := 172;

param level :=
     1	100
     2	200
     3	200
     4	600
     5	400
     6	400
     7	400
     8	400
     9	600
    10	100
    11	100
    12	400
    13	400
    14	100
    15	100
    16	600
    17	500
    18	100
    19	600
    20	600
    21	100
    22	400
    23	500
    24	100
    25	100
    26	400
    27	600
    28	600
    29	600
    30	400
    31	400
    32	400
    33	400
    34	600
    35	600
    36	600
    37	500
    38	500
    39	600
    40	600
    41	600
    42	100
    43	600
    44	400
    45	600
    46	100
    47	200
    48	400
    49	100
    50	100
    51	200
    52	200
    53	100
    54	100
    55	500
    56	400
    57	400
    58	600
    59	600
    60	100
    61	400
    62	100
    63	100
    64	500
    65	400
    66	400
    67	600
    68	400
    69	400
    70	600
    71	600
    72	600
    73	200
    74	200
    75	100
    76	400
    77	600
    78	600
    79	500
    80	500
    81	400
    82	100
    83	400
    84	400
    85	400
    86	100
    87	200
    88	600
    89	400
    90	500
    91	600
    92	500
    93	400
    94	600
    95	200
    96	600
    97	100
    98	400
    99	100
   100	600
   101	100
   102	600
   103	400
   104	500
   105	600
   106	500
   107	500
   108	100
   109	400
   110	600
   111	600
   112	600
   113	600
   114	600
   115	400
   116	400
   117	100
   118	400
   119	600
   120	100
   121	400
   122	100
   123	400
   124	600
   125	600
   126	600
   127	400
   128	400
   129	600
   130	600
   131	600
   132	600
   133	200
   134	100
   135	500
   136	600
   137	200
   138	600
   139	600
   140	400
   141	500
   142	600
   143	500
   144	600
   145	600
   146	600
   147	400
   148	500
   149	600
   150	600
   151	600
   152	600
   153	400
   154	600
   155	600
   156	500
   157	500
   158	400
   159	100
   160	400
   161	600
   162	400
   163	400
   164	600
   165	600
   166	600
   167	600
   168	500
   169	200
   170	200
   171	400
   172	400;

param nationality :=
     1	'Korea'
     2	'Thailand'
     3	'Korea'
     4	'Japan'
     5	'Taiwan'
     6	'Japan'
     7	'Japan'
     8	'Japan'
     9	'Korea'
    10	'Korea'
    11	'Japan'
    12	'Korea'
    13	'Japan'
    14	'Korea'
    15	'Japan'
    16	'Korea'
    17	'Korea'
    18	'Korea'
    19	'Japan'
    20	'Korea'
    21	'Korea'
    22	'Japan'
    23	'Taiwan'
    24	'Taiwan'
    25	'Japan'
    26	'Korea'
    27	'Korea'
    28	'Japan'
    29	'Japan'
    30	'Korea'
    31	'Japan'
    32	'Japan'
    33	'Korea'
    34	'Korea'
    35	'Japan'
    36	'Korea'
    37	'Korea'
    38	'Korea'
    39	'Japan'
    40	'France'
    41	'Korea'
    42	'Thailand'
    43	'Korea'
    44	'Japan'
    45	'Korea'
    46	'Tunisia'
    47	'Korea'
    48	'Korea'
    49	'Korea'
    50	'Brazil'
    51	'Japan'
    52	'Japan'
    53	'Korea'
    54	'Korea'
    55	'Taiwan'
    56	'Korea'
    57	'Japan'
    58	'Korea'
    59	'Korea'
    60	'Japan'
    61	'Korea'
    62	'Thailand'
    63	'Taiwan'
    64	'Korea'
    65	'Thailand'
    66	'Japan'
    67	'Taiwan'
    68	'Korea'
    69	'Taiwan'
    70	'Korea'
    71	'Taiwan'
    72	'Korea'
    73	'Korea'
    74	'Japan'
    75	'Japan'
    76	'Taiwan'
    77	'Korea'
    78	'China'
    79	'Korea'
    80	'Korea'
    81	'Taiwan'
    82	'Taiwan'
    83	'Japan'
    84	'Japan'
    85	'Korea'
    86	'Korea'
    87	'Korea'
    88	'Taiwan'
    89	'Korea'
    90	'Korea'
    91	'Korea'
    92	'Korea'
    93	'Taiwan'
    94	'Korea'
    95	'Japan'
    96	'Korea'
    97	'Taiwan'
    98	'Korea'
    99	'Japan'
   100	'Korea'
   101	'Korea'
   102	'Korea'
   103	'Japan'
   104	'Japan'
   105	'Korea'
   106	'Japan'
   107	'Korea'
   108	'Japan'
   109	'Taiwan'
   110	'Japan'
   111	'Korea'
   112	'Korea'
   113	'Japan'
   114	'Korea'
   115	'Taiwan'
   116	'Japan'
   117	'Korea'
   118	'China'
   119	'Japan'
   120	'Thailand'
   121	'Turkey'
   122	'Korea'
   123	'Taiwan'
   124	'Japan'
   125	'Korea'
   126	'Korea'
   127	'Korea'
   128	'Japan'
   129	'Korea'
   130	'Korea'
   131	'Japan'
   132	'Korea'
   133	'Brazil'
   134	'Taiwan'
   135	'Taiwan'
   136	'China'
   137	'Japan'
   138	'Korea'
   139	'Korea'
   140	'Korea'
   141	'Japan'
   142	'Korea'
   143	'Japan'
   144	'Korea'
   145	'Korea'
   146	'Korea'
   147	'Japan'
   148	'Turkey'
   149	'Korea'
   150	'Japan'
   151	'Taiwan'
   152	'Japan'
   153	'Japan'
   154	'Arabia'
   155	'Korea'
   156	'Thailand'
   157	'Korea'
   158	'Korea'
   159	'Japan'
   160	'Turkey'
   161	'Korea'
   162	'Korea'
   163	'Japan'
   164	'China'
   165	'Korea'
   166	'Taiwan'
   167	'Korea'
   168	'Korea'
   169	'Korea'
   170	'Japan'
   171	'Korea'
   172	'Japan';

param limit :=
     1	7
     2	1
     3	2
     4	2
     5	5
     6	2
     7	6
     8	2
     9	1
    10	2
    11	2
    12	6
    13	2
    14	3
    15	2
    16	1
    17	2
    18	1
    19	2
    20	4
    21	1
    22	2
    23	2
    24	1
    25	1
    26	4
    27	2
    28	1
    29	4
    30	1
    31	1
    32	3
    33	2
    34	1
    35	3
    36	4
    37	4
    38	2
    39	6
    40	2
    41	2
    42	4
    43	2
    44	5
    45	2
    46	2
    47	3
    48	2
    49	1
    50	4
    51	4
    52	2
    53	1
    54	2
    55	4
    56	2
    57	2
    58	3
    59	7
    60	6
    61	5
    62	5;

set SA := 
1 'We' 1
1 'We' 2
1 'We' 3
1 'We' 4
2 'We' 0
2 'We' 1
2 'We' 2
2 'We' 3
3 'Th' 1
3 'Th' 2
3 'Th' 3
3 'Th' 4
4 'Tu' 1
4 'Tu' 2
4 'Tu' 3
4 'Tu' 4
5 'Tu' 3
5 'Tu' 4
5 'Tu' 5
5 'Tu' 6
6 'Tu' 0
6 'Tu' 2
6 'Tu' 4
6 'Tu' 6
7 'Tu' 1
7 'Tu' 3
7 'Tu' 5
7 'Tu' 7
8 'We' 4
8 'We' 6
9 'Mo' 1
9 'Mo' 5
10 'We' 1
10 'We' 3
11 'Fr' 5
11 'Fr' 7
12 'We' 4
12 'We' 3
13 'We' 4
13 'We' 5
14 'Tu' 2
14 'Tu' 6
15 'Mo' 4
15 'Mo' 7
16 'Th' 2
16 'Th' 1
17 'Mo' 4
17 'Mo' 2
18 'Th' 5
18 'Th' 6
19 'We' 6
19 'We' 7
20 'Fr' 4
20 'Fr' 9
21 'Tu' 4
21 'Tu' 1
22 'Mo' 2
22 'Mo' 3
23 'Fr' 3
23 'Fr' 4
24 'Th' 3
24 'Th' 5
25 'Tu' 2
25 'Tu' 6
26 'We' 4
26 'We' 7
27 'Tu' 4
27 'Tu' 7
28 'Mo' 1
29 'We' 5
29 'We' 2
30 'Fr' 3
30 'Fr' 4
31 'Tu' 2
31 'Tu' 3
32 'Fr' 3
32 'Fr' 5
33 'Mo' 2
33 'Mo' 6
34 'We' 3
34 'We' 4
35 'Mo' 4
35 'Mo' 6
36 'Fr' 2
36 'Fr' 7
37 'Th' 4
37 'Th' 7
38 'We' 6
38 'We' 7
39 'We' 0
39 'We' 1
40 'Fr' 0
40 'Fr' 2
41 'Fr' 0
41 'Fr' 3
42 'Th' 3
42 'Th' 4
43 'Mo' 1
43 'Mo' 5
44 'Mo' 3
44 'Mo' 6
45 'Th' 5
45 'Th' 7
46 'Th' 0
46 'Th' 2
47 'Mo' 4
47 'Mo' 2
48 'Th' 3
48 'Th' 2
49 'We' 2
49 'We' 3
50 'Mo' 4
50 'Mo' 1
51 'We' 5
51 'We' 6
52 'Mo' 4
52 'Mo' 2
53 'Tu' 6
53 'Tu' 3
54 'Tu' 3
54 'Tu' 4
55 'We' 4
55 'We' 5
56 'Tu' 3
56 'Tu' 6
57 'Mo' 4
57 'Mo' 7
58 'We' 5
58 'We' 1
59 'Th' 2
59 'Th' 0
60 'Th' 3
60 'Th' 1
61 'Th' 2
61 'Th' 3
62 'Th' 0
62 'Th' 4
63 'We' 4
63 'We' 5
64 'Tu' 0
64 'Tu' 6
65 'Mo' 5
65 'Mo' 7
66 'Fr' 3
66 'Fr' 1
67 'Mo' 3
67 'Mo' 2
68 'We' 2
68 'We' 3
69 'We' 4
69 'We' 5
70 'We' 3
70 'We' 1
71 'Tu' 6
71 'Tu' 2
72 'Th' 4
72 'Th' 3
73 'Tu' 3
73 'Tu' 5
74 'We' 3
74 'We' 4
75 'Tu' 6
75 'Tu' 7
76 'We' 2
76 'We' 7
77 'We' 4
77 'We' 7
78 'Fr' 0
78 'Fr' 1
79 'We' 0
79 'We' 2
80 'We' 2
80 'We' 3
81 'We' 4
81 'We' 5
82 'Mo' 3
82 'Mo' 4
83 'Th' 3
83 'Th' 5
84 'Mo' 3
84 'Mo' 6
85 'Mo' 3
85 'Mo' 7
86 'Tu' 7
86 'Tu' 0
87 'Mo' 6
87 'Mo' 1
88 'Mo' 2
88 'Mo' 3
89 'Th' 0
89 'Th' 4
90 'Mo' 4
90 'Mo' 5
91 'Mo' 4
91 'Mo' 3
92 'We' 4
92 'We' 2
93 'Mo' 4
93 'Mo' 1
94 'Tu' 5
94 'Tu' 6
95 'Tu' 2
95 'Tu' 7
96 'Tu' 3
96 'Tu' 6
97 'Mo' 4
97 'Mo' 6
98 'Mo' 1
98 'Mo' 6
99 'Mo' 4
99 'Mo' 6
100 'Tu' 1
100 'Tu' 7
101 'We' 0
101 'We' 6
102 'We' 3
102 'We' 7
103 'We' 1
103 'We' 6
104 'We' 3
104 'We' 5
105 'Th' 3
105 'Th' 6
106 'We' 3
106 'We' 7
107 'Tu' 4
107 'Tu' 7
108 'We' 3
108 'We' 5
109 'Fr' 4
109 'Fr' 5
110 'Tu' 3
110 'Tu' 2
111 'Mo' 5
111 'Mo' 2
112 'We' 6
112 'We' 1
113 'Tu' 1
113 'Tu' 0
114 'We' 6
114 'We' 1
115 'Mo' 3
115 'Mo' 2
116 'Mo' 6
116 'Mo' 3
117 'Th' 4
117 'Th' 2
118 'Mo' 2
118 'Mo' 4
119 'Tu' 3
119 'Tu' 5
120 'Tu' 4
120 'Tu' 6
121 'Th' 4
121 'Th' 7
122 'Tu' 2
122 'Tu' 6
123 'Th' 3
123 'Th' 5
124 'Th' 3
124 'Th' 4
125 'Th' 3
125 'Th' 2
126 'Mo' 3
126 'Mo' 1
127 'Tu' 3
127 'Tu' 2
128 'We' 3
128 'We' 4
129 'Tu' 2
129 'Tu' 3
130 'Th' 4
130 'Th' 5
131 'Fr' 2
131 'Fr' 5
132 'We' 2
132 'We' 6
133 'We' 4
133 'We' 7
134 'We' 3
135 'We' 1
135 'We' 2
136 'Tu' 4
136 'Tu' 2
137 'Th' 4
137 'Th' 3
138 'Mo' 4
138 'Mo' 3
139 'Th' 3
139 'Th' 2
140 'We' 4
140 'We' 1
141 'We' 0
141 'We' 2
142 'Mo' 5
142 'Mo' 4
143 'Mo' 4
143 'Mo' 5
144 'Tu' 3
144 'Tu' 6
145 'Mo' 1
145 'Mo' 7
146 'We' 1
146 'We' 7
147 'Th' 5
147 'Th' 6
148 'Mo' 3
148 'Mo' 4
149 'Mo' 2
149 'Mo' 3
150 'Mo' 5
150 'Mo' 1
151 'Mo' 5
151 'Mo' 2
152 'Tu' 3
152 'Tu' 4
153 'Tu' 1
153 'Tu' 5
154 'Fr' 3
154 'Fr' 2
155 'Th' 4
155 'Th' 7
156 'We' 2
156 'We' 6
157 'Mo' 4
157 'Mo' 5
158 'We' 3
158 'We' 6
159 'We' 1
159 'We' 7
160 'Mo' 2
160 'Mo' 6
161 'Fr' 3
161 'Fr' 5
162 'Th' 1
162 'Th' 6
163 'Mo' 4
163 'Mo' 5
164 'We' 2
164 'We' 6
165 'Tu' 4
165 'Tu' 7
166 'We' 5
166 'We' 6
167 'Tu' 4
167 'Tu' 6
168 'Fr' 3
168 'Fr' 4
169 'We' 2
169 'We' 5
170 'Fr' 3
170 'Fr' 6
171 'We' 2
171 'We' 7
172 'Tu' 6
172 'Tu' 7;

set CPA :=
1 'Fr' 3
1 'Mo' 3
1 'Mo' 4
1 'Th' 3
10 'We' 0
11 'Mo' 4
12 'Mo' 6
12 'Tu' 7
12 'We' 6
13 'We' 3
14 'Th' 2
14 'Th' 3
15 'Th' 4
15 'Th' 5
16 'Fr' 0
17 'Tu' 6
18 'We' 4
19 'Fr' 0
2 'We' 4
20 'Tu' 2
20 'Tu' 3
21 'Th' 1
22 'Th' 5
23 'We' 4
24 'Th' 2
25 'Mo' 5
26 'We' 4
26 'We' 5
27 'We' 3
28 'Tu' 3
29 'Mo' 4
29 'Mo' 5
3 'Tu' 4
30 'Th' 4
31 'We' 4
32 'Mo' 3
32 'We' 2
32 'We' 3
33 'We' 3
34 'Tu' 2
35 'Mo' 3
35 'Mo' 4
36 'Mo' 3
36 'Mo' 4
37 'Tu' 6
37 'We' 6
38 'We' 1
39 'Fr' 2
39 'Mo' 4
39 'We' 4
4 'Fr' 3
40 'Tu' 1
41 'We' 5
42 'Fr' 3
42 'Th' 3
43 'Mo' 5
44 'Mo' 2
44 'Mo' 3
44 'We' 4
45 'We' 3
46 'Mo' 4
47 'Th' 4
47 'Tu' 3
48 'Th' 2
49 'We' 2
5 'Fr' 2
5 'Mo' 2
5 'We' 2
50 'Fr' 4
50 'Th' 4
51 'Tu' 3
51 'Tu' 4
52 'Fr' 3
53 'Th' 0
54 'We' 0
55 'Mo' 4
55 'Mo' 5
55 'We' 4
56 'We' 2
57 'Tu' 0
58 'Mo' 1
58 'Mo' 2
59 'Tu' 2
59 'We' 0
59 'We' 1
59 'We' 2
6 'Th' 0
60 'Th' 3
60 'Tu' 4
60 'Tu' 5
61 'Mo' 1
61 'Th' 4
61 'Tu' 3
62 'Tu' 3
62 'Tu' 4
7 'Mo' 3
7 'Mo' 4
7 'We' 2
7 'We' 3
8 'Th' 3
9 'Tu' 2;

end;