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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  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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  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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