Originally posted by: ml130@humboldt.edu

I have cross ask this question https://stackoverflow.com/questions/58691563/objective-function-per-week-help-writing-the-code-cplex

( The OPL model and the Lindo model are in the code box )

I need some help with this problem. My goal is to organize which trucks will be shipped from origin to destination each week (week 1, 2, 3 and 4). In this example, there are a total of 6 trucks, and at least one must be shipped per week. Each shipment has an associated cost, and the goal is to minimize the cost in the first week, then the second, third and fourth. It's a lexicographic goal programming problem. I made the extended model in other software (Lindo) and it worked, but I am having difficulty writing in OPL. Could someone help me please?

Xijt, i= pickup point (1,2,3,4,5) , j= destination (1,2), t = weeks (1,2,3,4)

! My code in Lindo:
MIN p4
subject to
p1 = 10
p2 = 10
p3 = 100

! Cost 

0 X111 + 0 X211 + 90 X311+  0 X411 + 10 X511 + 0 X121 + 100 X221 + 0 X321 + 50 X421 + 10 X521 -p1 + n1 = 0 ! Week 1 
0 X112 + 0 X212 + 90 X312+  0 X412 + 10 X512 + 0 X122 + 100 X222 + 0 X322 + 50 X422 + 10 X522 -p2 + n2 = 0 ! Week 2 
0 X113 + 0 X213 + 90 X313+  0 X413 + 10 X513 + 0 X123 + 100 X223 + 0 X323 + 50 X423 + 10 X523 -p3 + n3 = 0 ! Week 3 
0 X114 + 0 X214 + 90 X314+  0 X414 + 10 X514 + 0 X124 + 100 X224 + 0 X324 + 50 X424 + 10 X524 -p4 + n4 = 0 ! Week 4 


! Number of trucks

X311 + X312 + X313 + X314  = 1 !In 4 weeks, there is 1 truck from pickup point 3 to destination 1
X511 + X512 + X513 + X514  = 1
X221 + X222 + X223 + X224  = 2
X421 + X422 + X423 + X424  = 1
X521 + X522 + X523 + X524  = 1 


! Week restriction
!At least one truck must be used per week
X311 + X511 + X221 + X421 + X521 >=1
X312 + X512 + X222 + X422 + X522 >=1
X313 + X513 + X223 + X423 + X523 >=1
X314 + X514 + X224 + X424 + X524 >=1


END

INT X311 
INT X312 
INT X313 
INT X314 

INT X511
INT X512 
INT X513 
INT X514

INT X221 
INT X222
INT X223 
INT X224 

INT X421 
INT X422 
INT X423 
INT X424

INT X521
INT X522
INT X523
INT X524 
---------------------------------------------------
// CPLEX
using CP;
// decision variables

{string} Pickup = {"A","B","C","D","E"};
{string} Destination = {"D1" , "D2"};
{string} Weeks = {"W1", "W2", "W3", "W4"};

int Trucks [Pickup][Destination]= [[0,0],[0,2],[1,0],[0,1],[1,1]]; 
int Cost [Pickup]=[140,100,90,50,10]; 

//Decision Variables
dvar int  Delivered [Forest][Destination][Weeks]; //not sure if it is right

//Expressions
dexpr int Week1 = sum (u in Pickup, c in Destination, W1 in Weeks) Trucks[u][c] * Freshness [u] * Delivered[u][c][W1];
dexpr int Week2 = sum (u in Pickup, c in Destination, W2 in Weeks) Trucks[u][c] * Freshness [u] * Delivered[u][c][W2];
dexpr int Week3 = sum (u in Pickup, c in Destination, W3 in Weeks) Trucks[u][c] * Freshness [u] * Delivered[u][c][W3];
dexpr int Week4 = sum (u in Pickup, c in Destination, W4 in Weeks) Trucks[u][c] * Freshness [u] * Delivered[u][c][W4];



//Objective Function
minimize staticLex (Week1,Week2,Week3,Week4);

//Constraint
subject to {
forall (u in Pickup)
    forall (c in Destination)
        sum (W1 in Weeks)
            Trucks [u][c] >= 1;

forall (u in Forest)
    forall (c in Destination)
        sum (W2 in Weeks)
            Trucks [u][c] >= 1;

forall (u in Pickup)
    forall (c in Destination)
        sum (W3 in Weeks)
            Trucks [u][c] >= 1;

forall (u in Pickup)
    forall (c in Destination)
        sum (W4 in Weeks)
            Trucks [u][c] >= 1;

}


execute Output {
    writeln ("Delivered Plan")
        for (var t in Trucks)
            for (var u in Pickup)
                for (var c in Destination)
                    for (var w in Weeks)
                        if (Delivered [t][u][c][w]>0) {
                        writeln (Delivered [t][u][c][w] + '' + " number of trucks " + '' + t + '' + "  delivered from pickup poit " + '' + u +" to destination " +''+ c + " in the week "+''+ w);

I answered on stack overflow. Please come back in case the answer there is not sufficient.

Originally posted by: ml130@humboldt.edu

Thank you Daniel.   But I am still getting "no value" for the Decision variable (Delivered) and also "no value" for the Decision Expressions (Week 1, Week 2, Week 3 and Week 4 ) . I wonder why.  

I updated my answer in stackoverflow. We should continue the discussion there.