python
Set parameter Username
Set parameter LicenseID to value 2675318
Academic license - for non-commercial use only - expires 2026-06-05
Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 24.5.0 24F74)
CPU model: Apple M4
Thread count: 10 physical cores, 10 logical processors, using up to 10 threads
Optimize a model with 280 rows, 545 columns and 973 nonzeros
Model fingerprint: 0x7d4ec560
Variable types: 0 continuous, 545 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [5e+00, 4e+03]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 5e+02]
Found heuristic solution: objective 6668451.0000
Presolve removed 240 rows and 289 columns
Presolve time: 0.00s
Presolved: 40 rows, 256 columns, 469 nonzeros
Found heuristic solution: objective 6665347.0000
Variable types: 0 continuous, 256 integer (0 binary)
Root relaxation: objective 5.810983e+06, 104 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 5810983.0000 5810983.00 0.00% - 0s
Explored 1 nodes (104 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 10 (of 10 available processors)
Solution count 3: 5.81098e+06 6.66535e+06 6.66845e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 5.810983000000e+06, best bound 5.810983000000e+06, gap 0.0000%
Set parameter MIPGap to value 0
Traceback (most recent call last):
File "src/gurobipy/_util.pyx", line 33, in gurobipy._util._bytestostring
UnicodeDecodeError: 'utf-8' codec can't decode byte 0x88 in position 26: invalid start byte
Exception ignored in: 'gurobipy._core.logcallbackstub'
Traceback (most recent call last):
File "src/gurobipy/_util.pyx", line 33, in gurobipy._util._bytestostring
UnicodeDecodeError: 'utf-8' codec can't decode byte 0x88 in position 26: invalid start byte
Warning: to let Gurobi read it back, use rlp format
Optimal solution found with objective value: 5810983.0以下进行逐行分析：
1. Gurobi许可证初始化
python
Set parameter Username
Set parameter LicenseID to value 2675318
Academic license - for non-commercial use only - expires 2026-06-05- 使用学术许可证（仅限非商业用途），有效期至2026年。
2. 求解器环境信息
python
Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (mac64[arm] - Darwin 24.5.0 24F74)
CPU model: Apple M4
Thread count: 10 physical cores, 10 logical processors, using up to 10 threads- Gurobi版本为12.0.2，运行在Apple M4芯片的MacOS上，使用10线程。
3. 模型统计信息
python
Optimize a model with 280 rows, 545 columns and 973 nonzeros
Model fingerprint: 0x7d4ec560
Variable types: 0 continuous, 545 integer (0 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00] # 约束矩阵系数均为1
Objective range [5e+00, 4e+03] # 目标函数系数范围
Bounds range [0e+00, 0e+00] # 变量无边界限制
RHS range [2e+00, 5e+02] # 约束右侧值范围- 模型规模：280个约束，545个整数变量（无连续或二进制变量）。
- 目标函数涉及的成本范围较大（5到4000），可能与运输距离或租箱成本相关。
4. 启发式求解与预处理
python
Found heuristic solution: objective 6668451.0000 # 初始启发式解
Presolve removed 240 rows and 289 columns # 预处理简化模型
Presolve time: 0.00s
Presolved: 40 rows, 256 columns, 469 nonzeros
Found heuristic solution: objective 6665347.0000 # 简化后的启发式解- 预处理大幅减少了问题规模（从280行到40行），加速求解。
- 启发式算法提供了两个初始解（目标值约666万），但非最优。
5. 松弛问题求解
python
Root relaxation: objective 5.810983e+06, 104 iterations, 0.00 seconds (0.00 work units)- 线性松弛（忽略整数约束）的解为5,810,983，提供了问题的下界（最优解不会低于此值）。
6. 分支定界过程
python
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 5810983.0000 5810983.00 0.00% - 0s- 在根节点（
Nodes=0）即找到整数最优解，目标值与松弛解一致（5,810,983），Gap为0%。 - 关键结论：模型求解非常高效（0秒内完成），且解为全局最优。
7. 求解结果汇总
python
Solution count 3: 5.81098e+06 6.66535e+06 6.66845e+06
Optimal solution found (tolerance 1.00e-04)
Best objective 5.810983000000e+06, best bound 5.810983000000e+06, gap 0.0000%- 共找到3个解，最优解为5,810,983（与松弛解一致，验证了最优性）。
8. 编码错误警告
python
UnicodeDecodeError: 'utf-8' codec can't decode byte 0x88 in position 26
Warning: to let Gurobi read it back, use rlp format- 日志输出时出现编码问题（可能是中文字符处理异常），但未影响求解结果。
- 建议检查输出文件的编码格式或使用
rlp格式保存模型。