Python+Gurobi求解案例

模型描述

下面是一个工厂的生产计划模型。模型的集合、参数、决策变量与数学模型描述如下：

编程求解

模型参数通过一个简单的测试数据给出，模型是在python里面从零开始建立，最后输出结果。代码如下：

import gurobipy as gp
from gurobipy import GRB

#production rate of machine k at facility m
pro_rate = [5,5,5,4,4,4,3,3,3,3]

#total capicity of machine k at facility m
capicity = [30,30,30,30,30,30,30,30,30,30] 

#usage cost per unit of machine k
usage_cost = [3,3,3,2,2,2,1,1,1,1]

#number of worker required for machine k
woker_req = [3,3,3,3,3,3,3,3,3,3]

#energy consume cost of factory m
energy_cost = 20

#number of fixed worker at factory m
fixed_worker = 21

#labor cost per unit time of fixed worker
fixed_cost = 0.3

#labor cost per unit time of flexible worker
flexible_cost = 0.5

#output value per unit product
unit_value = 3

#earning per output value when the required value is satisfied
earning_value = 1

#penalty cost per output value when the required value is not satisfied
penalty_cost_value = 3

#the objective output value
req_value = 1900

#the reqiured production quantity
req_quantity = 800

#a big real value number
big_m = 100000

#Range of machines
machines = range(len(capicity))

#build an empty model named factory_decision model
m = gp.Model("factory_decision_model")

#decision variable of machine production time：X[k]
pro_time = m.addVars(machines,lb=0, vtype=GRB.CONTINUOUS, name="pro_time")

#decision variable of fixed worker:Y[k]
fix_worker = m.addVars(machines,lb=0, vtype=GRB.INTEGER, name="fix_worker")

#decision variable of flexible worker:Z[k]
flex_worker = m.addVars(machines,lb=0, vtype=GRB.INTEGER, name="flex_worker")

#decision variable of machine setup: beta[k]
beta = m.addVars(machines,lb=0, ub=1, vtype=GRB.BINARY, name="beta")

#decison variable of maximum production time:T
max_time = m.addVar(lb=0, ub=30, vtype=GRB.CONTINUOUS, name="max_time")

#decision variable of quantity of output value which beyond the requirement
sup_value = m.addVar(lb=0, ub=float("inf"), vtype=GRB.CONTINUOUS, name="sup_value")

#decision variable of quantity of output value which not satisfy the requirement
blow_value = m.addVar(lb=0, ub=float("inf"), vtype=GRB.CONTINUOUS, name="blow_value")

#set objective function: usage cost of machine + labor cost + enerry cost + output value
m.setObjective(gp.quicksum(usage_cost[k]*pro_time[k] for k in machines) 
                + gp.quicksum((fixed_cost*fix_worker[k] + flexible_cost*flex_worker[k])*pro_time[k] for k in machines)
                + energy_cost*max_time + penalty_cost_value*blow_value, GRB.MINIMIZE)

#Add constraint: production quantity
m.addConstr(gp.quicksum(pro_rate[k]*pro_time[k] for k in machines) == req_quantity, "production")

#Add constraint: output value
m.addConstr(req_quantity*unit_value == req_value + sup_value - blow_value, "output_value")

#Add constrains: capacity
m.addConstrs((pro_time[k] <= capicity[k] for k in machines),"capacity")

#Add constrains: labor requirement
m.addConstrs((fix_worker[k] + flex_worker[k] == woker_req[k]*beta[k] for k in machines),"labor")

#Add constrains: machine setup
m.addConstrs((beta[k]*big_m >= pro_time[k] for k in machines),"setup")

#Add constrains: machine setup_1
m.addConstrs((beta[k] <= pro_time[k]*big_m for k in machines),"setup_1")

#Add constraint: max_time
m.addConstrs((max_time >= pro_time[k] for k in machines), "max_time")

#Add constraint: fixed_worker
m.addConstr(gp.quicksum(fix_worker[k] for k in machines) <= fixed_worker, "fixed_worker")

#save model
m.write('factory_decision_modelPY_2.lp')

m.setParam('NonConvex', 2)
#Optimize
m.optimize()

#Print solution
print('nTotal costs:%g'%m.objVal)
print('SOLUTION:')
total_production = 0
for k in machines:
    if beta[k].x > 0.99:
        print('machine %s is setup'% k)
        print('Machine %s production time is %g'% (k, pro_time[k].x))
        total_production += pro_time[k].x*pro_rate[k]
print('The total production amount is %g'%total_production)
print('---------------------------------------')
total_fix_worker = 0
total_flex_worker = 0
for k in machines:
    if beta[k].x > 0.99:
        print('machine %s is setup'% k)
        print('Machine %s need %g fixed worker'%(k,fix_worker[k].x))
        print('Machine %s need %g flexiable worker'%(k,flex_worker[k].x))
        total_fix_worker += fix_worker[k].x
        total_flex_worker += flex_worker[k].x
print('The total fixed worker is %g'%total_fix_worker)
print('The total flexible worker is %g'%total_flex_worker)
print('---------------------------------------')
print('The maximum produciton time is %g'%max_time.x)

参考资料

1.Gurobi官网给的example.

链接：https://pan.baidu.com/s/13YBcRDircm8FW5g_y62otg
提取码：3v76

2.Gurobi官网的reference manual.

链接：https://pan.baidu.com/s/1Tz2hJ4ETYPptUcCvnKyfqw
提取码：q05j

总结

其实使用python+gurobi的建模不复杂，如果有问题可以先看下gurobi官网给的example，给出了各种模型的建模和求解示例。如果对于gurobi方法或参数不了解的，则可以进一步查看参考手册。

Python+Gurobi求解案例

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