Hello!

I hope you and your family are all healty!!

I would be very happy if you could help me to write the following code into the GAMS.

The following constraint is on the routing of vehicles;

β(m,i,t+to)+β(m,j,t)≤1 ∀m,∀i,∀j∈Nm,∀t+ to≤Tmax, to≤Ttravel(i,j)

The abovementioned constraint is to ensure that the transportation of vehicles among different nodes satisfies the necessary travel time.

simple example is used to explain related constraint: if it takes 2 time periods of vehicle 1 to travel between nodes 1 and 2, we enforce constraints as follows:

β(1,2,t+1)+β(1,1,t)≤1 , ∀t + 1 ≤ T

β(1,2,t+2)+β(1,1,t)≤1 , ∀t + 1 ≤ T

Thus, if β(1,1,t) (vehicle 1 is connected to node 1 at time t),then β(1,2,t+1)= β(1,2,t+2)= 0 (it cannot be connected to node 2 in

the following two time periods due to the necessary travel time from node 1 to node 2).

Mathematical expression is in below:

I wrote the code in GAMS, however, I am getting Error 126, set is under control already and Error 125, set identifier or ( expected. Can you please help me to write code as correct one? I will never forget your guidance!! Thank you in advance.

Best regards,

Ayşe.

““GAMS CODE””"

Scalar Tmax /48/;

Sets

t(*) time periods
i(*) nodes (1-5)

j(*) nodes (1-5)

to time periods

m /m1/

;

Parameters

Travel(i,j)

;

Variables

mu

;

Binary Variables mu;

mu.fx(i,m,t)( ord(t)<=22 and node_num (i)=1)= 1 ; mu.fx(i,m,t) (con_point(i)=0)= 0;

Equations

CONS_1

CONS_2

CONS_3

;

CONS_1(i,m,t) $(HAS_FEEDER(i)=1 and ord(t)<= 22)…

mu(i,m,t) =G=1;

CONS_2(m,t)…

sum(i$(con_point(i)=1), mu(i,m,t)) =L=1;

CONS_3 (i,j,g,t) $ (ord(j)<> ord(i) and ord(t)+1<Tmax )…

sum(t$ (ord(t)<= smin(ord(t)+Travel_g(i,j),Tmax)), mu(j,g,t+1)=l= (1-mu(i,g,t))*smin(Travel(i,j), Tmax- ord(t)));

routing_problem.gms (781 Bytes)