| # !pip install pulp | |
| from pulp import * | |
| # 1. Specify optimization problem type | |
| prob = LpProblem("SomeLPProblem", LpMinimize) | |
| # 2. Define the decision variables for each of 12 shelters | |
| x1 = LpVariable("A: 2671Islington", 0, None, LpInteger) | |
| x2 = LpVariable("B1:26Vaughan", 0, None, LpInteger) | |
| x3 = LpVariable("B2:14Vaughan", 0, None, LpInteger) | |
| x4 = LpVariable("C:850Bloor", 0, None, LpInteger) | |
| x5 = LpVariable("D1:38Bathurst", 0, None, LpInteger) | |
| x6 = LpVariable("D2:38Bathurst", 0, None, LpInteger) | |
| x7 = LpVariable("E1:135Sherbourne", 0, None, LpInteger) | |
| x8 = LpVariable("E2:339George", 0, None, LpInteger) | |
| x9 = LpVariable("E3:339George", 0, None, LpInteger) | |
| x10 = LpVariable("E4:339George", 0, None, LpInteger) | |
| x11 = LpVariable("E5:339George", 0, None, LpInteger) | |
| x12 = LpVariable("E6:339George", 0, None, LpInteger) | |
| # 3. Define the first objective function -- minimize monetary cost | |
| # prob += 15*x1 + 30*x2 + 10*x3 + 5*x4 + 5*x5 + 5*x6 + 2*(x7 + x8 + x9 + x10 + x11 + x12) | |
| # 4. Define the second objective function -- minimize time cost | |
| prob += x1 + 1.2*(x2 + x3) + x4 + 1.8*(x5) + 1.7*(x6) + 1.2*(x7 + x8 + x9) + 1.4*(x10 + x11 + x12) | |
| # 5. Add monetary cost constraint (result of first optimization layer) | |
| prob += 15*x1 + 30*x2 + 10*x3 + 5*x4 + 5*x5 + 5*x6 + 2*(x7 + x8 + x9 + x10 + x11 + x12) <= 123 | |
| # 6. Add Capacity/Supply constraints at cluster level: How much is available at the NBHD level | |
| prob += x1 <= 1 | |
| prob += x2 + x3 <= 10 | |
| prob += x4 <= 1 | |
| prob += x5 + x6 <= 3 | |
| prob += x7 + x8 + x9 + x10 + x11 + x12 <= 30 | |
| # 7. Add Demand constraints at cluster level: How many beds are needed at the NBHD level | |
| prob += x1 >= 1 | |
| prob += x2 + x3 >= 5 | |
| prob += x4 >= 1 | |
| prob += x5 + x6 >= 3 | |
| prob += x7 + x8 + x9 + x10 + x11 + x12 >= 19 | |
| # 8. Add Capacity/Supply for each shelter: Shelter-level capacity | |
| prob += x1 <= 1 | |
| prob += x2 <= 5 | |
| prob += x3 <= 5 | |
| prob += x4 <= 1 | |
| prob += x5 <= 2 | |
| prob += x6 <= 1 | |
| prob += x7 <= 6 | |
| prob += x8 <= 5 | |
| prob += x9 <= 4 | |
| prob += x10 <= 2 | |
| prob += x11 <= 1 | |
| prob += x12 <= 12 | |
| # 9. Solve optimization problem | |
| prob.solve() | |
| # 10. Print the variables optimized value and optimized objective function value | |
| for v in prob.variables(): | |
| print(v.name, ": ", int(v.varValue), "additional bed(s).") | |
| print("\nOptimal Value of Objective Function: ", value(prob.objective)) |