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

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.

View project on PIFOP