How to store time value to multidict form a constraint in Gurobi

Answered

John Raphy Karippery

January 31, 2022 12:00 Edited

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Hello 

I need to create multidict variable that stores the arrival time of the truck in each node.

I expect values to store in a variable format something like this. TA = {(node,truck): time}

To find TA (arrival time) I have an equation (constraint): departure time truck at previous node + time between the previous node and this node

Part 1 =  \( \sum_{ij}\ x_{ij}^h\ast d_{ij}^h/speed\ \ h\forall H \)
Waiting time = part2
Part 2 = \(\sum_{i}max\left(TA_i^h\right)–jTDjh+dij/speedxijhifoh!=ih∀H\)

\( x_{ij}^h \) decision variable if 1 truck travel at edge i,j otherwise 0

And start node and end node time of departure and arrival time = 0 for all truck

TA = model.addVars(node_list, truck, vtype=gp.GRB.CONTINUOUS, name="TA")
TD = model.addVars(node_list, truck, vtype=gp.GRB.CONTINUOUS, name="TD")

model.addConstrs(TA[origin[h],h] == 0 for h in truck)
model.addConstrs(TD[origin[h],h] == 0 for h in truck)

objective_second_part_1 = gp.LinExpr()
for edge in road_network.edges():
    for h in truck:
        objective_second_part_1 += x[edge][h] * road_network.get_edge_data(*edge)["weight"]/speed

objective_second_part_2 = gp.LinExpr()

for i in node_list:
    for h in truck:
        objective_second_part_2 += max(TA[i,h])- quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])

---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-98-03a0f644063a> in <module>

      3 for i in node_list:

      4     for h in truck:

----> 5         objective_second_part_2 += max(TA[i,h])- quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])



TypeError: 'Var' object is not iterable

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 16, 2025 23:45

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  Jaromił Najman

  • Gurobi Staff

  January 31, 2022 13:19

  Hi John,

  I guess that the term

  max(TA[i,h])

  shall be used to model the maximum of all \(\texttt{TA[i,h]}\) for a fixed \(\texttt{i}\).

  Note that Gurobi's max_ function has an additional underscore and it requires a list of variables and not just a single one. Moreover, it has to be modeled via an auxiliary variable and an equality constraint. So very likely, your \(\texttt{for}\)-loop should read something like

  for i in node_list:
      max_list = []
      for h in truck:
          objective_second_part_2 -= quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])
          max_list.append(TA[i,h])
      aux = model.addVar(lb=-gp.GRB.INFINITY, name="auxVar_%d"%(i))
      model.addConstr(aux == gp.max_(max_list), name="auxConstr_%d"%(i))
      objective_second_part_2 += aux

  Best regards, 
  Jaromił

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• 

  John Raphy Karippery

  January 31, 2022 13:47

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  • 
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  Hello Jaromił,
  TA[i,h] = arrival time of truck at node i. That is calculate 

  model.addConstrs(TA[origin[h],h] == 0 for h in truck)
  model.addConstrs(TD[origin[h],h] == 0 for h in truck)

  
  for j in nodelist:
  for h in truck:
  TA[i,h] = quicksum(TD[j,h]+road_network.get_edge_data(j,i)["weight"]/speed for j in node_list if j != origin[h])

  And to find departure time of truck h at node i  =  max arrival time of all truck at node i 

  for i in nodelist:
      for h in tuck:
          model.addConstr(aux== gp.max_(TA[i,h]), name="auxConstr_%d"%(i))
          TD[i,h] = aux
  
  

  objective_second_part_2 += (TD[i,h]-TA[i,h] for i in nodelist for j in nodelist)

  this is what I need.
  
  please help me 

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• 

  Jaromił Najman

  • Gurobi Staff

  January 31, 2022 14:18 Edited

  Hi John,

  As explained in my previous comment, the constraint

  model.addConstr(aux== gp.max_(TA[i,h]), name="auxConstr_%d"%(i))

  will not work because \(\texttt{TA[i,h]}\) is a single variable. However, to my understanding, you want to compute the maximum value of all truck at node \(\texttt{i}\). Thus the \(\texttt{for}\)-loop should be

  aux = {}
  for i in node_list:
      max_list = []
      for h in truck:
          max_list.append(TA[i,h])
      aux[i] = model.addVar(lb=-gp.GRB.INFINITY, name="auxVar_%d"%(i))
      # add constraint aux_i = max(TA[i,0], TA[i,1],...)
      model.addConstr(aux[i] == gp.max_(max_list), name="auxConstr_%d"%(i))

  The \(\texttt{for}\)-loop you are currently using

  for i in nodelist:
      for h in tuck:
          model.addConstr(aux== gp.max_(TA[i,h]), name="auxConstr_%d"%(i))
          TD[i,h] = aux

  just sets \(TD_{i,h} = TA_{i,h}\) because \(\texttt{TA[i,h]}\) is one element and thus \(\max(TA_{i,h}) = TA_{i,h}\).

  Best regards, 
  Jaromił

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