I need to find the solution to transportation problem with transit limitations and below there is the code which works correctly.
However I don't know how to input these limitations in the code.
Lower bound:
| 1 | 2 | 1 | 2 | 1 |
| 2 | 1 | 1 | 1 | 3 |
| 0 | 1 | 2 | 1 | 1 |
| 2 | 1 | 3 | 1 | 2 |
Upper bound:
| 9 | 8 | 6 | 10 | 5 |
| 7 | 15 | 4 | 6 | 9 |
| 5 | 6 | 6 | 5 | 10 |
| 8 | 5 | 7 | 4 | 8 |
All your ideas will be appreciated. Thanks in advance.
import pandas as pd
import pulp
truck_capacity = 6
suppliers = pd.RangeIndex(name='supplier', stop=4)
consumers = pd.RangeIndex(name='consumer', stop=5)
supply = pd.Series(
name='supply',
index=suppliers,
data=(17, 8, 10, 9),
)
demand = pd.Series(
name='demand',
index=consumers,
data=(6, 15, 7, 8, 8),
)
price_per_tonne = pd.DataFrame(
index=suppliers, columns=consumers,
data=(
(10, 8, 5, 9, 16),
( 4, 3, 4, 11, 12),
( 5, 10, 29, 7, 6),
( 9, 2, 4, 1, 3),
),
).stack()
price_per_tonne.name = 'price'
flow = pd.DataFrame(
index=suppliers, columns=consumers,
data=pulp.LpVariable.matrix(
name='flow_s%d_c%d', cat=pulp.LpContinuous, lowBound=0,
indices=(suppliers, consumers),
),
).stack()
flow.name = 'flow'
trucks = pd.DataFrame(
index=suppliers, columns=consumers,
data=pulp.LpVariable.matrix(
name='trucks_s%d_c%d', cat=pulp.LpInteger, lowBound=0,
indices=(suppliers, consumers),
)
).stack()
trucks.name = 'trucks'
price = truck_capacity * pulp.lpDot(price_per_tonne, trucks)
prob = pulp.LpProblem(name='transportation', sense=pulp.LpMinimize)
prob.setObjective(price)
# The flow must not exceed the supply
for supplier, group in flow.groupby('supplier'):
prob.addConstraint(
name=f'flow_supply_s{supplier}',
constraint=pulp.lpSum(group) <= supply[supplier],
)
# The flow must exactly meet the demand
for consumer, group in flow.groupby('consumer'):
prob.addConstraint(
name=f'flow_demand_c{consumer}',
constraint=pulp.lpSum(group) == demand[consumer],
)
# The capacity must be able to carry the flow
for (supplier, consumer), truck_flow in flow.items():
prob.addConstraint(
name=f'capacity_s{supplier}_c{consumer}',
constraint=truck_flow <= trucks[(supplier, consumer)] * truck_capacity
)
print(prob)
prob.solve()
assert prob.status == pulp.LpStatusOptimal
print(f'Total price: ${price.value():.2f}')
print()
print('Flow:')
flow = flow.apply(pulp.value).unstack(level='consumer')
print(flow)
print()
print('Trucks:')
trucks = trucks.apply(pulp.value).unstack(level='consumer')
print(trucks)
print()
print('Prices:')
print(trucks * truck_capacity * price_per_tonne.unstack(level='consumer'))
Call bounds once for every lower/upper flow bound:
import pandas as pd
import pulp
truck_capacity = 6
suppliers = pd.RangeIndex(name='supplier', stop=4)
consumers = pd.RangeIndex(name='consumer', stop=5)
supply = pd.Series(
name='supply',
index=suppliers,
data=(17, 8, 10, 9),
)
demand = pd.Series(
name='demand',
index=consumers,
data=(6, 15, 7, 8, 8),
)
price_per_tonne = pd.DataFrame(
index=suppliers, columns=consumers,
data=(
(10, 8, 5, 9, 16),
( 4, 3, 4, 11, 12),
( 5, 10, 29, 7, 6),
( 9, 2, 4, 1, 3),
),
).stack()
price_per_tonne.name = 'price'
flow = pd.DataFrame(
index=suppliers, columns=consumers,
data=pulp.LpVariable.matrix(
name='flow_s%d_c%d', cat=pulp.LpContinuous,
indices=(suppliers, consumers),
),
).stack()
flow.name = 'flow'
flow_lower = pd.DataFrame(
index=suppliers, columns=consumers,
data=(
(1, 2, 1, 2, 1),
(2, 1, 1, 1, 3),
(0, 1, 2, 1, 1),
(2, 1, 3, 1, 2),
),
)
flow_upper = pd.DataFrame(
index=suppliers, columns=consumers,
data=(
(9, 8, 6, 10, 5),
(7, 15, 4, 6, 9),
(5, 6, 6, 5, 10),
(8, 5, 7, 4, 8),
),
)
for (supplier, consumer), flow_value in flow.items():
flow_value.bounds(
low=flow_lower.loc[supplier, consumer],
up=flow_upper.loc[supplier, consumer],
)
trucks = pd.DataFrame(
index=suppliers, columns=consumers,
data=pulp.LpVariable.matrix(
name='trucks_s%d_c%d', cat=pulp.LpInteger, lowBound=0,
indices=(suppliers, consumers),
)
).stack()
trucks.name = 'trucks'
price = truck_capacity * pulp.lpDot(price_per_tonne, trucks)
prob = pulp.LpProblem(name='transportation', sense=pulp.LpMinimize)
prob.setObjective(price)
# The flow must not exceed the supply
for supplier, group in flow.groupby('supplier'):
prob.addConstraint(
name=f'flow_supply_s{supplier}',
constraint=pulp.lpSum(group) <= supply[supplier],
)
# The flow must exactly meet the demand
for consumer, group in flow.groupby('consumer'):
prob.addConstraint(
name=f'flow_demand_c{consumer}',
constraint=pulp.lpSum(group) == demand[consumer],
)
# The capacity must be able to carry the flow
for (supplier, consumer), truck_flow in flow.items():
prob.addConstraint(
name=f'capacity_s{supplier}_c{consumer}',
constraint=truck_flow <= trucks[(supplier, consumer)] * truck_capacity
)
print(prob)
prob.solve()
assert prob.status == pulp.LpStatusOptimal
print(f'Total price: ${price.value():.2f}')
print()
print('Flow:')
flow = flow.apply(pulp.value).unstack(level='consumer')
print(flow)
print()
print('Trucks:')
trucks = trucks.apply(pulp.value).unstack(level='consumer')
print(trucks)
print()
print('Prices:')
print(trucks * truck_capacity * price_per_tonne.unstack(level='consumer'))
Result - Optimal solution found
Objective value: 966.00000000
Enumerated nodes: 0
Total iterations: 0
Time (CPU seconds): 0.00
Time (Wallclock seconds): 0.00
Option for printingOptions changed from normal to all
Total time (CPU seconds): 0.00 (Wallclock seconds): 0.00
Total price: $966.00
Flow:
consumer 0 1 2 3 4
supplier
0 2.0 8.0 1.0 5.0 1.0
1 2.0 1.0 1.0 1.0 3.0
2 0.0 5.0 2.0 1.0 2.0
3 2.0 1.0 3.0 1.0 2.0
Trucks:
consumer 0 1 2 3 4
supplier
0 1.0 2.0 1.0 1.0 1.0
1 1.0 1.0 1.0 1.0 1.0
2 0.0 1.0 1.0 1.0 1.0
3 1.0 1.0 1.0 1.0 1.0
Prices:
consumer 0 1 2 3 4
supplier
0 60.0 96.0 30.0 54.0 96.0
1 24.0 18.0 24.0 66.0 72.0
2 0.0 60.0 174.0 42.0 36.0
3 54.0 12.0 24.0 6.0 18.0