求解容量选址问题的Gurobi算法

Question

我正在尝试从名为capa的OR数据库中解决容量定位问题

或文件here

答案应该是：

capa 19240822.449 (capacity 8000)

但我发现：

Best objective 3.145815023928e+08

这肯定是我的代码中的一个问题……有人能帮我吗？也许我在优化公式上做错了什么.或者关于我的运输需求的构建。我真的不知道，因为它在我看来是正确的。

任何帮助都将不胜感激。提前感谢

from itertools import product
from math import sqrt
import gurobipy as gp
from gurobipy import GRB
import time

# Get Clients and Facilities
def getFacilities_Clients(file_list):
    return int(file_list[0]), int(file_list[1])

# Get Facilities Fixed Costs
def getFacilities_STRCapacity_FixedCosts(file_list, num_facilities):
    shift = 2
    capacity = []
    cost = []
    
    #loop to get all i location costs
    for i in range(0,num_facilities*2,2):
        #capacity.append(file_list[i+shift])
        capacity.append(8000)
        cost.append(int(file_list[i+1+shift].replace(".","")))
    
    return capacity, cost

# Get Demand and Allocation Costs for j(customer) to each i(client)
def getClient_Demand_AllocationCosts(file_list, num_facilities, num_customers):
    shift = 2 + (num_facilities*2)
    demand = []
    allocation_cost = []
    
    #loop to get all j Clients 
    j=0
    for r in range(0,num_customers):
    
        #get demand
        demand.append(int(file_list[j+shift]))

        #loop to get all i location costs
        for i in range(0,num_facilities):
            allocation_cost.append(float(file_list[j+1+i+shift]))
            
        #fix j
        j += num_facilities+1
 
    
    return demand, allocation_cost

#Read File from OR datasets
fileName='datasets/ORcapa'
ORlist = []

with open(fileName, "r") as f:
    ORlist = f.read().split()

##### Sets and Indices #####
num_facilities, num_customers = getFacilities_Clients(ORlist)
capacity, fixed_cost = getFacilities_STRCapacity_FixedCosts(ORlist, num_facilities)
cartesian_prod = list(product(range(num_customers), range(num_facilities)))
# shipping costs
demand, alloc_cost = getClient_Demand_AllocationCosts(ORlist, num_facilities, num_customers)
shipping_cost = dict(zip(cartesian_prod, alloc_cost))

shipping_demand={}
for k, v in shipping_cost.items():
    shipping_demand[k] = v * demand[k[0]]

#setup cost
setup_cost = fixed_cost
#demand of customer
dc = demand
#max production
maxp= capacity

start = time.time()
# MIP  model formulation
m = gp.Model('CFLP')

##### Decision Variable #####
x = m.addVars(num_facilities, vtype=GRB.BINARY, name='x')
y = m.addVars(cartesian_prod, ub=1, vtype=GRB.CONTINUOUS, name='y')

##### Constraints #####
m.addConstrs((y[(c,f)] <= x[f] for c,f in cartesian_prod), name='Shipping')
m.addConstrs((gp.quicksum(y[(c,f)] for f in range(num_facilities)) == 1 for c in range(num_customers)), name='Demand')
m.addConstrs((gp.quicksum(dc[c]*y[(c,f)] for c in range(num_customers)) <= maxp[f]*x[f] for f in range(num_facilities)), name='Capacity')

##### Objective Function #####
m.setObjective(x.prod(setup_cost)+y.prod(shipping_demand), GRB.MINIMIZE)

m.Params.Method = 1
# Options are:-1=automatic, 0=primal simplex, 1=dual simplex, 2=barrier, 3=concurrent, 4=deterministic concurrent, 5=deterministic concurrent simplex

m.optimize()
end = time.time()

Answer 1

这解决了我的问题：

m.setObjective(x.prod(setup_cost)+y.prod(shipping_cost)，GRB.MINIMIZE)

我在计算一个不同的运费价值。