# UNIT RESTRICTION MODEL
# This problem finds a maximum profit harvest schedule that meets
# adjacency constraints
set A;
/* stands */
set B {k in A};
#adjacency stands
param m;
/* number of periods */
param a{i in A};
/* area stands (ha) */
param npv{i in A, t in 1..m};
param v{i in A, t in 1..m};
/* yield observed from harvesting stand i in period t */
var x{i in A, t in 1..m} binary;
/* whether (1) or not (0) stand i is harvested in period t */
var h{t in 1..m};
/* auxiliary to account for total volume harvested in period t */
maximize sandia: sum{i in A, t in 1..m}  a[i]*x[i,t]*npv[i,t];
/* rent from harvesting stands */
s.t. area{i in A}: sum{t in 1..m} x[i,t] <= 1;
/* observe area constraints */
s.t. adj{i in A, t in 1..m}: x[i,t] + sum{k in B[i]} x[k,t] <= 2;
/* observe adjacency constraints */
s.t. harv{t in 1..m}: h[t] = sum{i in A} a[i]*x[i,t]*v[i,t];
/* calculate total harvest per period */
s.t. ndy{t in 1..m-1}: h[t+1]>=h[t];
/* non-declining yield constraints */

data;
set A := 1 2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	81;

set B[1] :=	22	34	2	81;
set B[3] :=	4	2             ;
set B[4] :=	3	5	6	7	75	2 ;
set B[5] :=	4	75                         ;
set B[6] :=	4	7	2                   ;
set B[7] :=	4	6	2                    ;
set B[8] :=	9	12	2	81            ;
set B[9] :=	8	12                             ;
set B[10] :=	12	13	76                      ;
set B[11] :=	12	76	77	81               ;
set B[12] :=	8	9	10	11	13	76	2	81;
set B[13] :=	10	12	14	15	17	76                 ;
set B[14] :=	13	17	36	39	40	47                  ;
set B[15] :=	13	16	17	18	19	48	68	76   ;
set B[16] :=	15	17	44	48                                    ;
set B[17] :=	13	14	15	16	44	47                     ;
set B[18] :=	15	68	78	79                                      ;
set B[19] :=	15	48	68                                               ;
set B[20] :=	21	34	78	81                                        ;
set B[21] :=	20	35	78                                                 ;
set B[22] :=	1	34	81                                                  ;
set B[23] :=	33	34                                                           ;
set B[24] :=	27	34	35	64	66	70                            ;
set B[25] :=	64	65	66	67                         ;
set B[26] :=	63	64                                          ;
set B[27] :=	24	28	33	34	70	71           ;
set B[28] :=	27	33	71	73                            ;
set B[29] :=	31	32                                             ;
set B[30] :=	32	33	74	80                              ;
set B[31] :=	29	32                                               ;
set B[32] :=	29	30	31                                        ;
set B[33] :=	23	27	28	30	34	73	74         ;
set B[34] :=	1	20	22	23	24	27	33	35	81;
set B[35] :=	21	24	34	66	78                                 ;
set B[36] :=	14	37	39	40	41	42	43                  ;
set B[37] :=	36	38	39	43	46                                   ;
set B[38] :=	37	43	46                                                    ;
set B[39] :=	14	36	37	46	47                                     ;
set B[40] :=	14	36	41                                                      ;
set B[41] :=	36	40	42                                                       ;
set B[42] :=	36	41	43	46                                                ;
set B[43] :=	36	37	38	42	46                                         ;
set B[44] :=	16	17	45	46	47                                          ;
set B[45] :=	44	46                                  ;
set B[46] :=	37	38	39	42	43	44	45	47;
set B[47] :=	14	17	39	44	46                         ;
set B[48] :=	15	16	19	52	67	68                  ;
set B[49] :=	50	52	56	57	59	67                   ;
set B[50] :=	49	51	52	59                                    ;
set B[51] :=	50	52	59                                             ;
set B[52] :=	48	49	50	51	67                              ;
set B[53] :=	61	62	63                                               ;
set B[54] :=	61                                                                ;
set B[55] :=	58	60	61	62                                         ;
set B[56] :=	49	57	65	67                                          ;
set B[57] :=	49	56	58	59	65                                   ;
set B[58] :=	55	57	60	62	63	65                            ;
set B[59] :=	49	50	51	57	60                                     ;
set B[60] :=	55	58	59	61                                              ;
set B[61] :=	53	54	55	60	62        ;
set B[62] :=	53	55	58	61	63         ;
set B[63] :=	26	53	58	62	64	65	69	70;
set B[64] :=	24	25	26	63	65	66	70         ;
set B[65] :=	25	56	57	58	63	64	67          ;
set B[66] :=	24	25	35	64	68	78                   ;
set B[67] :=	25	48	49	52	56	65	68            ;
set B[68] :=	15	18	19	48	66	67	78             ;
set B[69] :=	63	70                                                      ;
set B[70] :=	24	27	63	64	69	71	72               ;
set B[71] :=	27	28	70	72	73                                ;
set B[72] :=	70	71	73                                                 ;
set B[73] :=	28	33	71	72	74                                  ;
set B[74] :=	30	33	73	80                                          ;
set B[75] :=	4	5                                                            ;
set B[76] :=	10	11	12	13	15	77	79                    ;
set B[77] :=	11	76	78	79	81                                     ;
set B[78] :=	18	20	21	35	66	68	77	79	81      ;
set B[79] :=	18	76	77	78                                               ;
set B[80] :=	30	74                                                                ;
set B[2] :=	1	3	4	6	7	8	12	81                 ;
set B[81] :=	1	8	11	12	20	22	34	77	78	2   ;



param m := 3;

param a := 1	29.9
2	34.2
3	4.8
4	12.8
5	0.5
6	2.7
7	9.4
8	12.6
9	5.1
10	19.8
11	3.7
12	25.2
13	23.3
14	22.8
15	38.9
16	29.4
17	34.6
18	14.4
19	2.9
20	11.8
21	11.8
22	4.2
23	16.4
24	23.0
25	10.7
26	1.7
27	16.9
28	6.9
29	8.1
30	44.5
31	32.9
32	14.0
33	34.4
34	25.8
35	11.5
36	21.2
37	6.5
38	0.9
39	2.6
40	4.4
41	13.1
42	2.9
43	3.8
44	4.6
45	8.6
46	15.1
47	4.4
48	7.7
49	10.6
50	9.6
51	10.3
52	9.7
53	4.2
54	3.7
55	4.3
56	2.0
57	8.2
58	11.8
59	12.2
60	7.3
61	13.9
62	7.0
63	21.0
64	7.7
65	14.7
66	4.3
67	9.7
68	9.3
69	2.2
70	25.8
71	10.4
72	5.5
73	9.7
74	24.0
75	0.4
76	17.3
77	18.7
78	11.0
79	14.2
80	0.4
81	34.6;

param v : 1 2 3 :=
1	83.0	121.0	149.0
2	293.0	324.0	358.0
3	0.0	20.0	60.0
4	139.0	181.0	231.0
5	208.0	236.0	263.0
6	163.0	203.0	241.0
7	291.0	330.0	362.0
8	83.0	135.0	178.0
9	82.0	132.0	174.0
10	121.0	164.0	215.0
11	71.0	122.0	163.0
12	313.0	341.0	375.0
13	54.0	103.0	151.0
14	42.0	91.0	145.0
15	28.0	84.0	132.0
16	24.0	82.0	129.0
17	29.0	86.0	134.0
18	62.0	112.0	160.0
19	201.0	249.0	281.0
20	142.0	184.0	235.0
21	190.0	232.0	261.0
22	130.0	174.0	224.0
23	137.0	180.0	229.0
24	176.0	222.0	264.0
25	284.0	312.0	346.0
26	268.0	307.0	339.0
27	183.0	232.0	262.0
28	187.0	234.0	263.0
29	194.0	240.0	267.0
30	205.0	251.0	280.0
31	260.0	292.0	324.0
32	271.0	298.0	324.0
33	246.0	273.0	299.0
34	261.0	287.0	310.0
35	234.0	272.0	301.0
36	132.0	175.0	202.0
37	218.0	253.0	285.0
38	195.0	223.0	251.0
39	28.0	84.0	131.0
40	132.0	175.0	226.0
41	105.0	148.0	182.0
42	174.0	203.0	232.0
43	128.0	172.0	210.0
44	208.0	249.0	285.0
45	26.0	81.0	130.0
46	32.0	88.0	136.0
47	127.0	172.0	199.0
48	156.0	184.0	211.0
49	143.0	183.0	231.0
50	141.0	181.0	230.0
51	172.0	202.0	229.0
52	308.0	335.0	352.0
53	72.0	123.0	165.0
54	135.0	176.0	226.0
55	80.0	130.0	171.0
56	229.0	268.0	301.0
57	173.0	203.0	234.0
58	182.0	215.0	246.0
59	167.0	196.0	229.0
60	164.0	195.0	227.0
61	159.0	189.0	223.0
62	248.0	283.0	312.0
63	314.0	342.0	363.0
64	294.0	321.0	344.0
65	264.0	290.0	312.0
66	308.0	335.0	351.0
67	328.0	356.0	380.0
68	304.0	331.0	350.0
69	289.0	324.0	351.0
70	190.0	239.0	266.0
71	184.0	233.0	263.0
72	178.0	217.0	254.0
73	256.0	284.0	311.0
74	223.0	273.0	303.0
75	0.0	15.0	71.0
76	278.0	318.0	352.0
77	104.0	151.0	193.0
78	274.0	311.0	338.0
79	275.0	316.0	350.0
80	205.0	231.0	256.0
81	292.0	321.0	354.0;

param npv : 1 2 3 :=
1	3.86	4.01	3.52
2	13.61	10.73	8.45
3	0.00	0.66	1.42
4	6.46	5.99	5.45
5	9.66	7.81	6.21
6	7.57	6.72	5.69
7	13.51	10.93	8.55
8	3.86	4.47	4.20
9	3.81	4.37	4.11
10	5.62	5.43	5.08
11	3.30	4.04	3.85
12	14.54	11.29	8.85
13	2.51	3.41	3.57
14	1.95	3.01	3.42
15	1.30	2.78	3.12
16	1.12	2.72	3.05
17	1.35	2.85	3.16
18	2.88	3.71	3.78
19	9.34	8.25	6.63
20	6.60	6.09	5.55
21	8.82	7.68	6.16
22	6.04	5.76	5.29
23	6.36	5.96	5.41
24	8.17	7.35	6.23
25	13.19	10.33	8.17
26	12.45	10.17	8.00
27	8.50	7.68	6.19
28	8.69	7.75	6.21
29	9.01	7.95	6.30
30	9.52	8.31	6.61
31	12.08	9.67	7.65
32	12.59	9.87	7.65
33	11.43	9.04	7.06
34	12.12	9.50	7.32
35	10.87	9.01	7.11
36	6.13	5.80	4.77
37	10.12	8.38	6.73
38	9.06	7.38	5.93
39	1.30	2.78	3.09
40	6.13	5.80	5.34
41	4.88	4.90	4.30
42	8.08	6.72	5.48
43	5.94	5.70	4.96
44	9.66	8.25	6.73
45	1.21	2.68	3.07
46	1.49	2.91	3.21
47	5.90	5.70	4.70
48	7.25	6.09	4.98
49	6.64	6.06	5.45
50	6.55	5.99	5.43
51	7.99	6.69	5.41
52	14.30	11.09	8.31
53	3.34	4.07	3.90
54	6.27	5.83	5.34
55	3.72	4.31	4.04
56	10.64	8.87	7.11
57	8.03	6.72	5.52
58	8.45	7.12	5.81
59	7.76	6.49	5.41
60	7.62	6.46	5.36
61	7.38	6.26	5.27
62	11.52	9.37	7.37
63	14.58	11.32	8.57
64	13.65	10.63	8.12
65	12.26	9.60	7.37
66	14.30	11.09	8.29
67	15.23	11.79	8.97
68	14.12	10.96	8.26
69	13.42	10.73	8.29
70	8.82	7.91	6.28
71	8.55	7.72	6.21
72	8.27	7.19	6.00
73	11.89	9.40	7.34
74	10.36	9.04	7.15
75	0.00	0.50	1.68
76	12.91	10.53	8.31
77	4.83	5.00	4.56
78	12.73	10.30	7.98
79	12.77	10.46	8.26
80	9.52	7.65	6.04
81	13.56	10.63	8.36;



end;