Modeling problem about using variable value for indexing and conditional summation

Dear all,

Please have a look at the example below. This is not programmatically correct, but I want to show the idea and get your thoughts on implementing it in Gurobi.

start_time = {n: t for n, t in the schedule.items()} # dictionary containing action start times at various nodes
tx = m.addVars(nodes, lb=0) # Decision variable takes the duration of activity at each node
cx = m.addVars(time_horizon, vtype=GRB.BINARY) # An activity takes place at time t

Now I want to write a constraint for cx. Nodes is the set of all nodes.

for j in nodes:
   start = time[j]
   for t in range(start, start + tx[j]):
      m.addConstr[cx[t] == 1]

Of course, this does not work because I cannot have a variable for index subsetting like this. But do you have any idea as to how I can make it work? A pseudo-example might be super helpful. Thank you.

Modeling problem about using variable value for indexing and conditional summation

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