Indicator variable that depends on two other indicator variables

Hi,

I want to create an indicator that is defined by two other indicators. More specifically, I have the indicators “start” and “finish”, indicating the whether a machine started working at a position i or whether it finished the work (commodity at 0).  

I encounter a difficulty to define a new variable restricted[i,t], that indicates when fields are started but not finished. 

restricted = 1 only if start[i,t] + finish [i,t] is bigger 0 and smaller 2, otherwise 0. In my binary case I can define restricted = 1 if start + finish = 1

However, when defining such case I get an infeasible model. 

How can I define a case like this?

Below you can find code that creates a test case and the output of my IIS file. 

Python Code:

from gurobipy import Model, GRB, quicksum

# Define the sets I, Ih, T, H
H = [1]
I = [1]
Ih = [0] + I  # I plus the depot 0
T = [0, 1, 2, 3, 4,5]

# Create a new Gurobi model
model = Model("test_model")

# Define variables
commodity = model.addVars(I, range(1), range(1), T, vtype=GRB.CONTINUOUS, name="b", lb=0)
machine_flow = model.addVars(H, Ih, Ih, T, vtype=GRB.CONTINUOUS, name="machine_flow", lb=0)
finish = model.addVars(I, T, vtype=GRB.BINARY, name="finish")
start = model.addVars(I, T, vtype=GRB.BINARY, name="start")
restricted = model.addVars(I, T, vtype=GRB.BINARY, name="restricted")


# Define Values:

# Set artificial commodity values
model.addConstr(commodity[1, 0, 0, 0] == 100)
model.addConstr(commodity[1, 0, 0, 1] == 100)
model.addConstr(commodity[1, 0, 0, 2] == 50)
model.addConstr(commodity[1, 0, 0, 3] == 0)
model.addConstr(commodity[1, 0, 0, 4] == 0)
model.addConstr(commodity[1, 0, 0, 5] == 0)

# Set artificial machine_flow values
model.addConstr(machine_flow[1, 0, 0, 0] == 1)
model.addConstr(machine_flow[1, 0, 1, 1] == 1)
model.addConstr(machine_flow[1, 1, 1, 2] == 1)
model.addConstr(machine_flow[1, 1, 1, 3] == 1)
model.addConstr(machine_flow[1, 1, 0, 4] == 1)
model.addConstr(machine_flow[1, 0, 0, 5] == 1)

# set 0 for all other machine values
for h in H:
    for i in Ih:
        for j in Ih:
            for t in T:
                if (h, i, j, t) not in [(1, 0, 0, 0), (1, 0, 1, 1), (1, 1, 1, 2), (1, 1, 1, 3),
                                        (1, 1, 0, 4), (1, 0, 0, 5)]:
                    model.addConstr(machine_flow[h, i, j, t] == 0)

# Define start variable as an indicator for when a machine has visited a field
for i in I:
    for t in T:

        model.addGenConstrIndicator(
            start[i, t],
            1,
            quicksum(machine_flow[h, i, i, t_bar] for h in H for t_bar in range(t + 1)) >= 1)

        model.addGenConstrIndicator(
            start[i, t],
            0,
            quicksum(machine_flow[h, i, i, t_bar] for h in H for t_bar in range(t + 1)) <= 1e-7)

# Ensure the 'finish' variable is 1 when beets are 0 using indicator constraints
for i in I:
    for t in T:
        model.addGenConstrIndicator(
            finish[i, t],
            0,
            commodity[i, 0, 0, t] >= 1e-7)

        model.addGenConstrIndicator(
            finish[i, t],
            1,
            commodity[i, 0, 0, t] <= 1e-7)

# restricted is 0 when start and finish is 0 (we cant say 0 in gurobi, hence the 1e-7)

for i in I:
    for t in T:
        model.addGenConstrIndicator(
            restricted[i, t],
            1,
            start[i,t] + finish[i,t] == 1)

# restricted is also 0 when start and finish is bigger 2 or smaller 0.5
for i in I:
    for t in T:
        model.addGenConstrIndicator(
            restricted[i, t],
            0,
            start[i,t] + finish[i,t] >= 2)

for i in I:
    for t in T:
        model.addGenConstrIndicator(
            restricted[i, t],
            0,
            start[i,t] + finish[i,t] <= 0.5)

# Optimize the model
model.optimize()

# Check if the model is infeasible
if model.status == GRB.INFEASIBLE:
    print("Model is infeasible. Computing IIS to find the issue...")
    # Compute the Irreducible Inconsistent Subsystem (IIS)
    model.computeIIS()
    # Write the IIS to a file
    model.write("model_iis.ilp")
    print("IIS written to file 'model_iis.ilp'")
    print("Review the IIS file to identify conflicting constraints.")


# Check and print the results
if model.status == GRB.OPTIMAL:
    for i in I:
        for t in T:
            print(f"start[{i}, {t}] = {start[i, t].x}")
            print(f"finish[{i}, {t}] = {finish[i, t].x}")
            print(f"restricted[{i}, {t}] = {restricted[i, t].x}")
            print(f"commodity[{i}, 0, 0, {t}] = {commodity[i, 0, 0, t].x}")
            print(f"machine_flow[1, {i}, {i}, {t}] = {machine_flow[1, i, i, t].x}")

Output:

\ Model test_model_copy
\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize
  0 finish[1,0] + 0 start[1,0] + 0 restricted[1,0]
Subject To
 R0: b[1,0,0,0] = 100
 R26: machine_flow[1,1,1,0] = 0
 GC0: start[1,0] = 1 -> machine_flow[1,1,1,0] >= 1
 GC13: finish[1,0] = 1 -> b[1,0,0,0] <= 1e-07
 GC24: restricted[1,0] = 1 -> finish[1,0] + start[1,0] = 1
 GC30: restricted[1,0] = 0 -> finish[1,0] + start[1,0] >= 2
Bounds
 b[1,0,0,0] free
 machine_flow[1,1,1,0] free
Binaries
 finish[1,0] start[1,0] restricted[1,0]
End