Cargo Airplane: Implementation in Python (Optional)

Note

Gurobi cannot be loaded in this online book, so download this notebook to work on it with Gurobi locally installed. Instruction on how to do that are in the README.md and PA_2_4_A_gurobilicious.ipynb of week 2.4.

MUDE Exam Information

For the exam, you are expected to have a clear understanding behind the Simplex method and how to do it. you will not need to do the calculations by hand in the exam or on Friday’s assignment.

import gurobipy as gp
import numpy as np
import pandas as pd

model = gp.Model()

# cargo limits
cargo_type, cargo_weight, cargo_volume, cargo_profit = gp.multidict({
    'Type1': [18, 180, 590],
    'Type2': [14, 250, 580],
    'Type3': [20, 300, 580],
    'Type4': [12, 80,  600]
})

# compartment limits
compartment_type, compartment_weight, compartment_volume = gp. multidict({
    'Front': [8,  12000],
    'Center':[12, 10000],
    'Rear':  [14, 6000]
})

## decision variables
x = model.addVars(len(cargo_type),len(compartment_type), vtype = gp.GRB.CONTINUOUS, name = 'x')
model.update()

# set objectives
objective = gp.quicksum(cargo_profit[cargo_type[i]] * x[i, j]
                               for j in range(len(compartment_type))
                               for i in range(len(cargo_type)))

model.setObjective(objective, gp.GRB.MAXIMIZE)

## constraints
# 1. cargo type weight limits
model.addConstrs((gp.quicksum(x[i, j] for j in range(len(compartment_type))) <= cargo_weight[cargo_type[i]]
                  for i in range(len(cargo_type))), name ='Max available cargo to carry')

# 2. compartment weight limits
model.addConstrs((gp.quicksum(x[i, j] for i in range(len(cargo_type))) <= compartment_weight[compartment_type[j]]
                  for j in range(len(compartment_type))), name ='Weight limits on the compartments')

# 3. compartment volume limitations
model.addConstrs((gp.quicksum(x[i, j]*cargo_volume[cargo_type[i]] for i in range(len(cargo_type))) <= compartment_volume[compartment_type[j]]
                  for j in range(len(compartment_type))), name ='Volume limits on the compartments')

# Complete model
model.update()
model.display()

Maximize
590.0 x[0,0] + 590.0 x[0,1] + 590.0 x[0,2] + 580.0 x[1,0] + 580.0 x[1,1]
+ 580.0 x[1,2] + 580.0 x[2,0] + 580.0 x[2,1] + 580.0 x[2,2] + 600.0 x[3,0]
+ 600.0 x[3,1] + 600.0 x[3,2]
Subject To
  Max available cargo to carry[0]: x[0,0] + x[0,1] + x[0,2] <= 18
  Max available cargo to carry[1]: x[1,0] + x[1,1] + x[1,2] <= 14
  Max available cargo to carry[2]: x[2,0] + x[2,1] + x[2,2] <= 20
  Max available cargo to carry[3]: x[3,0] + x[3,1] + x[3,2] <= 12
  Weight limits on the compartments[0]: x[0,0] + x[1,0] + x[2,0] + x[3,0] <= 8
  Weight limits on the compartments[1]: x[0,1] + x[1,1] + x[2,1] + x[3,1] <= 12
  Weight limits on the compartments[2]: x[0,2] + x[1,2] + x[2,2] + x[3,2] <= 14
Volume limits on the compartments[0]: 180.0 x[0,0] + 250.0 x[1,0] + 300.0 x[2,0] + 80.0
 x[3,0] <= 12000
Volume limits on the compartments[1]: 180.0 x[0,1] + 250.0 x[1,1] + 300.0 x[2,1] + 80.0
 x[3,1] <= 10000
Volume limits on the compartments[2]: 180.0 x[0,2] + 250.0 x[1,2] + 300.0 x[2,2] + 80.0
 x[3,2] <= 6000

C:\Users\tomvanwoudenbe\AppData\Local\Temp\ipykernel_7320\1502344741.py:3: DeprecationWarning: Model.display() is deprecated
  model.display()

# Solve
model.optimize()

Attribution

This chapter is written by Gonçalo Homem de Almeida Correia, Maria Nogal Macho, Jie Gao and Bahman Ahmadi. Find out more here.