I wrote an optimization model of a paper with imaginary data in AMPL but there is some problem in running in terms of one of constraints about Years - ampl

Question

All you need explain in question title. The mentioned Optimization model belong to a paper with same content but I tried to write the code and analyze what happen exactly through that. I will add the codes to have access to data and find out what is the problem when you are running that. I added the three segment of AMPL code down. Please help me with this.
MOD:
set O;
set J;
set Q;
set R; #use R instead of K because we have K in line 11 as parameter
set T;
param D {q in Q, t in T};
param K {o in O, q in Q};
param C {q in Q, j in J};
param S {r in R, q in Q};
param H {r in R, q in Q};
param F {q in Q};
param G {q in Q};
param B {q in Q};
param Delta;
param Omega;
param I;
param A;
param M;
var X {o in O, q in Q, j in J, t in T} binary;
var Z {o in O, q in Q, t in T} binary;
var P {q in Q, t in T} binary;
var Y {q in Q, t in T} binary;
var z {q in Q, t in T} binary;
var n {q in Q, t in T} integer >=0;
var m {q in Q, t in T} integer >=0;
var N {q in Q, t in T} integer >=0;
var Teta {q in Q, t in T} integer >=0;
var a {r in R, q in Q, t in T} integer >=0;
var b {r in R, q in Q, t in T} integer >=0;
var u binary;
var v binary;
var w binary;
minimize OF: sum {q in Q, j in J, o in O, t in T} C[q, j] * D[q, t] * X[o, q, j, t]
+ sum {o in O, q in Q, t in T} K[o, q] * Z[o, q, t]
+ sum {q in Q , t in T} N[q, t] * Delta
+ sum {t in T, q in Q} Omega * Teta[q, t]
+ sum {t in T, r in R, q in Q} S[r, q] * a[r, q, t]
+ sum {t in T, r in R, q in Q} H[r, q] * b[r, q, t]
+ sum {t in T, q in Q} F[q] * z[q, t]
+ sum {t in T, q in Q} G[q] * Y[q, t]
+ sum {t in T, q in Q} B[q] * P[q, t]
+ I * v + A * u;
subject to c1{q in Q , t in T}: sum {o in O} Z[o, q, t] = D[q, t];
subject to c2{o in O , q in Q , t in T}: sum {j in J} X[o, q, j, t] >= Z[o, q, t];
subject to c3{q in Q , t in T}: n[q, t]= n[q, t-1] + sum {r in R} a[r, q, t-1] + N[q, t] - sum {r in R} a[q, r, t-1];
subject to c4{q in Q , t in T}: m[q, t]= m[q, t-1] + sum {r in R} b[r, q, t-1] + Teta[q, t] - sum {r in R} b[q, r, t-1];
subject to c5{o in O , q in Q , t in T}: Z[o, q, t]<= n[q, t];
subject to c6{q in Q , t in T}: sum {o in O} X[o, q, 1, t]<= m[q, t];
subject to c7{t in T, r in R}: sum {q in Q} a[q, r, t]<= sum{q in Q} n[q, t-1]+ a[r, r, t];
subject to c8{r in R , t in T}: sum {q in Q} b[q, r, t]<= sum{q in Q} m[q, t-1]+ b[r, r, t];
subject to c91{o in O , q in Q , t in T}: X[o, q, 2, t-1]<= X[o, q, 2, t];
subject to c92{o in O , q in Q , t in T}: X[o, q, 3, t-1]<= X[o, q, 3, t];
subject to c10{q in Q , t in T}: sum {o in O} X[o, q, 2, t]- sum {o in O} X[o, q, 2, t-1]<= z[q, t];
subject to c11{q in Q , t in T}: sum {o in O} X[o, q, 3, t]- sum {o in O} X[o, q, 3, t-1]<= P[q, t];
subject to c12{q in Q , t in T , j in J}: X[3, q, j, t]- X[3, q, j, t-1]<= Y[q, t];
subject to c13: sum {t in T, q in Q} Z[4, q, t]<= M * u;
subject to c14: sum {t in T, q in Q} Z[5, q, t]<= M * v;
subject to c15{o in O , q in Q , t in T}: X[o, q, 1, t]<= M * (w-1);
subject to c16{q in Q , t in T}: Z[3, q, t]<= M * w;
subject to c17{q in Q , t in T}: Z[2, q, t]<= X[2, q, 1, t];
DATA:
set O := Treat1 Treat2 Treat3 Treat4 Treat5;
set J := Dewater1 Dewater2 Dewater3;
set Q := ArcticBay Arviat CambridgeBay CapeDorse ClydeRiver GjoaHaven;
set R := ArcticBay Arviat CambridgeBay CapeDorse ClydeRiver GjoaHaven; #use R instead of K because we have K in line 15 as parameter
set T := Year1 Year2 Year3 Year4 Year5;
param D :
Year1 Year2 Year3 Year4 Year5 :=
ArcticBay 0 1 0 1 0
Arviat 1 0 0 1 1
CambridgeBay 1 0 0 1 1
CapeDorse 1 0 1 1 1
ClydeRiver 1 1 0 1 0
GjoaHaven 0 0 1 0 1 ;
param K :
ArcticBay Arviat CambridgeBay CapeDorse ClydeRiver GjoaHaven :=
Treat1 4051 4221 6477 5205 6443 4088
Treat2 6758 4012 4994 5437 6215 6267
Treat3 5162 4051 6755 6742 6589 4139
Treat4 6556 5094 5963 6043 5745 5428
Treat5 5289 6050 5144 4456 6474 4432 ;
param C :
Dewater1 Dewater2 Dewater3 :=
ArcticBay 56299 32825 11894
Arviat 5977 15550 5958
CambridgeBay 20654 28654 19782
CapeDorse 3073 35237 33822
ClydeRiver 19218 48466 34032
GjoaHaven 23650 23304 42540 ;
param S :
ArcticBay Arviat CambridgeBay CapeDorse ClydeRiver GjoaHaven :=
ArcticBay 0 1359 1480 1458 1728 849
Arviat 2863 0 1229 1873 2353 2731
CambridgeBay 1821 1972 0 1772 1680 2726
CapeDorse 2754 2219 1817 0 1266 2814
ClydeRiver 1216 2632 2527 2782 0 949
GjoaHaven 1229 1238 2605 1060 2673 0;
param H :
ArcticBay Arviat CambridgeBay CapeDorse ClydeRiver GjoaHaven :=
ArcticBay 0 2269 1497 1218 2290 2344
Arviat 1424 0 1123 2494 2107 1114
CambridgeBay 2452 2365 0 1924 1292 1722
CapeDorse 1799 2003 2071 0 1216 1150
ClydeRiver 1322 1097 1827 1259 0 1191
GjoaHaven 1163 1444 2085 2398 1308 0;
param F :=
ArcticBay 1981
Arviat 1845
CambridgeBay 1529
CapeDorse 1721
ClydeRiver 1778
GjoaHaven 1802;
param G :=
ArcticBay 8639
Arviat 8829
CambridgeBay 11737
CapeDorse 8167
ClydeRiver 8573
GjoaHaven 10890;
param B :=
ArcticBay 6427
Arviat 9508
CambridgeBay 6661
CapeDorse 8016
ClydeRiver 6196
GjoaHaven 8359;
param Delta := 15000;
param Omega := 12000;
param I := 20000;
param A := 17000;
param M := 100000000;
RUN:
reset;
option solver CPLEX;
model SM.mod;
data SM.dat;
solve;
display X, Z, P, Y, z, n, m, N, Teta, a, b, u, v, w>b.out;

Answer 1

You got an error on constraint collection c3 because you are trying to do aritmetic calculations with values of set T, when in fact set T contains only strings (Year1, Year2, etc).
For instance, you wrote n[q, t-1], where t is in T. But what is 'Year1'-1 is not a valid AMPL expression. Other constraint collections have the same problem.
You could simply change the data of set T to be 1 2 3 4 5. But then you would run into other problems, because 1-1 is 0, and n[q,0] does not exist. You have to work on your formulation.
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