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最小化工作流程以及部门和工作站之间的距离

gams-math modeling mathematical-optimization optimization math
  •  0
  • Sky Full Of Stars  · 技术社区  · 1 年前

    我为一个项目编写了代码。但是第96行有太多错误。我的项目的目的是最大限度地减少工厂中物料流和部门与站点之间的距离。显然,目的是通过改变工厂布局来减少物流中的时间损失。但最关键的一点是,各部门和车站之间只是交换位置。即部门1和部门4或者站3和站10可以被交换。但是3号部门和5号站不能互换。请帮帮我! 

    SETS
    i departments /1*6/
    j stations /1*10/
    m departments2 /1*6/
    n stations2 /1*10/ ;

PARAMETERS
    Table
    Workflow(i, j) Workflow matrix
     1   2   3   4   5   6   7   8   9   10
1    1   1   3   3   3   3   0   4   5   3
2    4   6   5   7   6   6   8   9   7   6
3    1   0   5   4   1   0   0   6   6   5
4    5   8   5   6   7   0   0   1   1   6
5    3   0   4   0   0   0   0   5   6   5
6    3   4   3   0   5   0   4   10  9   4;

PARAMETERS
    Table
    Distance(m, n) Distance matrix
       1   2    3   4   5   6   7   8   9   10
1     35   47  61  74  81  97  111 125 137  55
2     68   86  90  98  104 103  79  78  90  67
3    312  323 335 344 358 367 377 393 414 318
4     72   83  95  106 118 128 136 151 173 57
5    116   0   97   0   0   0   0   39  28  193
6     83   87  69  0   52  0   18  17  12  171;

VARIABLES
    y(m, n) Binary variables
    a(j, n) Binary variables
    b(i, m) Binary variables
    z Objective function;

BINARY VARIABLES
    Q(i, j, m, n);

EQUATIONS
    c1(n)
    c2(j)
    c3(i, j, m, n)
    c4(i, j, m, n)
    c5(i, j, m, n)
    c6(i)
    c7(m)
    c8(i, j, m, n)
    t1(n)
    t2(n)
    t3(n)
    t4(n)
    t5(n)
    t6(n)
    t7(n)
    t8(n)
    t9(n)
    t10(n)
    k1(m)
    k2(m)
    k3(m)
    k4(m)
    k5(m)
    k6(m);
    
c1(n).. sum(j, a(j, n)) =e= 1;
c2(j).. sum(n, a(j, n)) =e= 1;
c6(i).. sum(m, b(i, m)) =e= 1;
c7(m).. sum(i, b(i, m)) =e= 1;

c3(i, j, m, n).. Q(i, j, m, n) =l= a(j, n);
c8(i, j, m, n).. Q(i, j, m, n) =l= b(i, m);

c4(i, j, m, n).. Q(i, j, m, n) =l= y(m, n);
c5(i, j, m, n).. Q(i, j, m, n) =g= a(j, n) + y(m, n) + b(i, m) - 1;

t1(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t2(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t3(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t4(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t5(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t6(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t7(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t8(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t9(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;
t10(n).. sum((i, j, m), Q(i, j, m, n)) =e= 1;


k1(m).. sum((n, i,j), Q(i, j, m, n)) =e= 1;
k2(m).. sum((n, i,j), Q(i, j, m, n)) =e= 1;
k3(m).. sum((n, i,j), Q(i, j, m, n)) =e= 1;
k4(m).. sum((n, i,j), Q(i, j, m, n)) =e= 1;
k5(m).. sum((n, i,j), Q(i, j, m, n)) =e= 1;
k6(m).. sum((n, i,j), Q(i, j, m, n)) =e= 1;



min.. z =e= sum((i, j, m, n), workflow(i, j) * Distance(m, n) * Q(i, j, m, n));


Model Layout /all/;
Solve Layout using RMIP minimizing z;

    错误太多了,没用。

    0 回复  |  直到 1 年前
        1
  •  0
  •   Lutz    1 年前

    总的来说,我建议只关注第一个错误,因为在修复之前的错误后,后续的错误通常会消失。您的第一个错误是: 

      96  min.. z =e= sum((i, j, m, n), workflow(i, j) * Distance(m, n) * Q(i, j, m, n));
****    $168
**** 168  Assignment not allowed to this identifier

    问题是 min 是一个无法分配的关键字。如果将其更改为以下内容,则可以很容易地修复: 

    equation obj;
obj.. z =e= sum((i, j, m, n), workflow(i, j) * Distance(m, n) * Q(i, j, m, n));

    该更改实际上解决了所有编译错误。

    该模型仍然不可行,因此您可能需要检查模型公式和数据。

        2
  •  0
  •   Reinderien    1 年前

    我没有GAMS,所以我在PuLP中演示。

    我在这里做了很多假设,包括:

    • 保留每个部门工作站对的原始工作流
    • 这些工作流将移动到新的部门工作站位置
    • 目标中使用了这些新位置之间的距离
    • 实际上,您正在最小化工作流速率距离的积分,因此,如果工作流以每秒为单位,距离以米为单位,则目标以每秒米为单位。如果所有速度都是恒定的,则简化为米单位。

    您的公式构建过度; Q 维度太高。我演示了如何替换两者 Q 和 y 用较小的 i x m (6x6)连续变量的中间数组。它需要是下界的,并且基于部门分配(您称之为 b )。这种简化的核心是距离、工作流程和站点分配的双矩阵乘积(选择后者是因为它是两个分配矩阵中较大的一个)。

    总之, 

    from io import StringIO

import pandas as pd
import pulp

with StringIO('''
i    1   2   3   4   5   6   7   8   9   10
1    1   1   3   3   3   3   0   4   5   3
2    4   6   5   7   6   6   8   9   7   6
3    1   0   5   4   1   0   0   6   6   5
4    5   8   5   6   7   0   0   1   1   6
5    3   0   4   0   0   0   0   5   6   5
6    3   4   3   0   5   0   4   10  9   4
''') as f:
    workflow = pd.read_fwf(f).set_index('i')
workflow.index.name = 'department'  # i
workflow.columns = pd.Index(name='station', data=workflow.columns.astype(int))   # j

with StringIO('''
i      1    2    3    4    5    6    7    8    9   10
1    116    0   97    0    0    0    0   39   28  193
2     68   86   90   98  104  103   79   78   90   67
3    312  323  335  344  358  367  377  393  414  318
4     72   83   95  106  118  128  136  151  173   57
5    116    0   97    0    0    0    0   39   28  193
6     83   87   69    0   52    0   18   17   12  171
''') as f:
    distance = pd.read_fwf(f).set_index('i')
distance.index.name = 'department'  # i
distance.columns = pd.Index(name='station', data=distance.columns.astype(int))   # j


def two_digits(row: pd.Series) -> str:
    return '{:02d}_to_{:02d}'.format(*row)


station_idx = pd.MultiIndex.from_product(
    iterables=(workflow.columns, workflow.columns), names=('source_station', 'dest_station'),
)
station_assign = (  # a
    (
        'station_' +
        station_idx.to_frame().apply(two_digits, axis=1)
    )
    .apply(pulp.LpVariable, cat=pulp.LpBinary)
    .unstack('dest_station')
)

dept_idx = pd.MultiIndex.from_product(
    iterables=(workflow.index, workflow.index), names=('source_dept', 'dest_dept'),
)
dept_names = 'dept_' + dept_idx.to_frame().apply(two_digits, axis=1)
dept_assign = (  # b
    dept_names
    .apply(pulp.LpVariable, cat=pulp.LpBinary)
    .unstack('dest_dept')
)

factors = (
    ('prod_' + dept_names)
    .apply(pulp.LpVariable, cat=pulp.LpContinuous, lowBound=0)
    .unstack('dest_dept')
)

prob = pulp.LpProblem(name='factory', sense=pulp.LpMinimize)
prob.objective = factors.sum().sum()

for assign in (station_assign, dept_assign):
    for axis in (0, 1):
        for name, total in assign.sum(axis=axis).items():
            prob.addConstraint(
                name=f'excl_{assign.axes[1 - axis].name}_{name}',
                constraint=total == 1,
            )

'''
If e.g. station 2 moves to the original position of station 4, and
department 5 moves to the original position of department 3,
the workflow from station 2 to department 5 is still 6,
but the distance between them is no longer 0: it's now 344.
minimize (st24)(dp53)*6*344

for dept source
  for dept dest
    for station source
      for station dest
        if these two dept-dept station-station variables are selected, then
        add the (distance between dest dept and dest station) *
        (workflow between source dept and source station)
        
== sum  (deptdept)*(statstat)*(dest distance)*(source workflow)
   ijkl     i   j      k   l             j l               i k

== sum deptdept [sum statstat*(dest distance)*(source workflow)]_ij
    ij       ij   kl    k   l            j l               i k

( workflow @ statstat ) @ distance.T
      i k         k l           l j 
'''

statstat_factors = (workflow @ station_assign) @ distance.T
M = 2*distance.max()*workflow.max()

for dest_dept, dept_col in dept_assign.items():
    for source_dept, is_dept_assigned in dept_col.items():
        statstat = statstat_factors.loc[source_dept, dest_dept]
        factor = factors.loc[source_dept, dest_dept]

        # if is_dept_assigned, then factor >= statstat
        # otherwise, factor >= 0 (by bound)
        prob.addConstraint(
            name=f'prodlo_d{source_dept:02d}_to_d{dest_dept:02d}',
            constraint=factor >= statstat - M*(1 - is_dept_assigned),
        )

print('Station assignment variables:')
print(station_assign, end='\n\n')
print('Department assignment variables:')
print(dept_assign, end='\n\n')
print(prob)
prob.solve()
assert prob.status == pulp.LpStatusOptimal

print('Station solution:')
station_assign = station_assign.applymap(pulp.LpVariable.value)
print(station_assign.astype(int), end='\n\n')

print('Department solution:')
dept_assign = dept_assign.applymap(pulp.LpVariable.value)
print(dept_assign.astype(int), end='\n\n')

results = []
for source_station, workflow_col in workflow.items():
    for source_dept, workflow_rate in workflow_col.items():
        dept_row = dept_assign.loc[source_dept, :]
        dest_dept = dept_row[dept_row > 0.5].first_valid_index()
        stat_row = station_assign.loc[source_station, :]
        dest_station = stat_row[stat_row > 0.5].first_valid_index()
        results.append((
            distance.loc[dest_dept, dest_station], workflow_rate,
            source_dept, source_station, dest_dept, dest_station,
        ))
results = pd.DataFrame(
    results,
    columns=('new_dist', 'workflow', 'source_dept', 'source_stat', 'dest_dept', 'dest_stat'),
).sort_values(by=['workflow', 'new_dist'], ascending=False)

print('Assignments by distance-workflow cost:')
print(results.to_string(index=False))

    Station assignment variables:
dest_station                  1   ...                10
source_station                    ...                  
1               station_01_to_01  ...  station_01_to_10
2               station_02_to_01  ...  station_02_to_10
3               station_03_to_01  ...  station_03_to_10
4               station_04_to_01  ...  station_04_to_10
5               station_05_to_01  ...  station_05_to_10
6               station_06_to_01  ...  station_06_to_10
7               station_07_to_01  ...  station_07_to_10
8               station_08_to_01  ...  station_08_to_10
9               station_09_to_01  ...  station_09_to_10
10              station_10_to_01  ...  station_10_to_10

[10 rows x 10 columns]

Department assignment variables:
dest_dept                1              2  ...              5              6
source_dept                                ...                              
1            dept_01_to_01  dept_01_to_02  ...  dept_01_to_05  dept_01_to_06
2            dept_02_to_01  dept_02_to_02  ...  dept_02_to_05  dept_02_to_06
3            dept_03_to_01  dept_03_to_02  ...  dept_03_to_05  dept_03_to_06
4            dept_04_to_01  dept_04_to_02  ...  dept_04_to_05  dept_04_to_06
5            dept_05_to_01  dept_05_to_02  ...  dept_05_to_05  dept_05_to_06
6            dept_06_to_01  dept_06_to_02  ...  dept_06_to_05  dept_06_to_06

[6 rows x 6 columns]

factory:
MINIMIZE
1*prod_dept_01_to_01 + 1*prod_dept_01_to_02 + 1*prod_dept_01_to_03 + 1*prod_dept_01_to_04 ...
SUBJECT TO
excl_dest_station_1: station_01_to_01 + station_02_to_01 + station_03_to_01
 + station_04_to_01 + station_05_to_01 + station_06_to_01 + station_07_to_01
 + station_08_to_01 + station_09_to_01 + station_10_to_01 = 1
...


excl_source_station_1: station_01_to_01 + station_01_to_02 + station_01_to_03
 + station_01_to_04 + station_01_to_05 + station_01_to_06 + station_01_to_07
 + station_01_to_08 + station_01_to_09 + station_01_to_10 = 1
...


prodlo_d01_to_d01: - 51030 dept_01_to_01 + prod_dept_01_to_01
 - 116 station_01_to_01 - 97 station_01_to_03 - 39 station_01_to_08
 - 28 station_01_to_09 - 193 station_01_to_10 - 116 station_02_to_01
 - 97 station_02_to_03 - 39 station_02_to_08 - 28 station_02_to_09
 - 193 station_02_to_10 - 348 station_03_to_01 - 291 station_03_to_03
 - 117 station_03_to_08 - 84 station_03_to_09 - 579 station_03_to_10
 - 348 station_04_to_01 - 291 station_04_to_03 - 117 station_04_to_08
 - 84 station_04_to_09 - 579 station_04_to_10 - 348 station_05_to_01
 - 291 station_05_to_03 - 117 station_05_to_08 - 84 station_05_to_09
 - 579 station_05_to_10 - 348 station_06_to_01 - 291 station_06_to_03
 - 117 station_06_to_08 - 84 station_06_to_09 - 579 station_06_to_10
 - 464 station_08_to_01 - 388 station_08_to_03 - 156 station_08_to_08
 - 112 station_08_to_09 - 772 station_08_to_10 - 580 station_09_to_01
 - 485 station_09_to_03 - 195 station_09_to_08 - 140 station_09_to_09
 - 965 station_09_to_10 - 348 station_10_to_01 - 291 station_10_to_03
 - 117 station_10_to_08 - 84 station_10_to_09 - 579 station_10_to_10 >= -51030
...



VARIABLES
0 <= dept_01_to_01 <= 1 Integer
0 <= dept_01_to_02 <= 1 Integer
0 <= dept_01_to_03 <= 1 Integer
0 <= dept_01_to_04 <= 1 Integer
0 <= dept_01_to_05 <= 1 Integer
0 <= dept_01_to_06 <= 1 Integer
0 <= dept_02_to_01 <= 1 Integer
0 <= dept_02_to_02 <= 1 Integer
0 <= dept_02_to_03 <= 1 Integer
0 <= dept_02_to_04 <= 1 Integer
0 <= dept_02_to_05 <= 1 Integer
0 <= dept_02_to_06 <= 1 Integer
0 <= dept_03_to_01 <= 1 Integer
0 <= dept_03_to_02 <= 1 Integer
0 <= dept_03_to_03 <= 1 Integer
0 <= dept_03_to_04 <= 1 Integer
0 <= dept_03_to_05 <= 1 Integer
0 <= dept_03_to_06 <= 1 Integer
0 <= dept_04_to_01 <= 1 Integer
0 <= dept_04_to_02 <= 1 Integer
0 <= dept_04_to_03 <= 1 Integer
0 <= dept_04_to_04 <= 1 Integer
0 <= dept_04_to_05 <= 1 Integer
0 <= dept_04_to_06 <= 1 Integer
0 <= dept_05_to_01 <= 1 Integer
0 <= dept_05_to_02 <= 1 Integer
0 <= dept_05_to_03 <= 1 Integer
0 <= dept_05_to_04 <= 1 Integer
0 <= dept_05_to_05 <= 1 Integer
0 <= dept_05_to_06 <= 1 Integer
0 <= dept_06_to_01 <= 1 Integer
0 <= dept_06_to_02 <= 1 Integer
0 <= dept_06_to_03 <= 1 Integer
0 <= dept_06_to_04 <= 1 Integer
0 <= dept_06_to_05 <= 1 Integer
0 <= dept_06_to_06 <= 1 Integer
prod_dept_01_to_01 Continuous
prod_dept_01_to_02 Continuous
prod_dept_01_to_03 Continuous
prod_dept_01_to_04 Continuous
prod_dept_01_to_05 Continuous
prod_dept_01_to_06 Continuous
prod_dept_02_to_01 Continuous
prod_dept_02_to_02 Continuous
prod_dept_02_to_03 Continuous
prod_dept_02_to_04 Continuous
prod_dept_02_to_05 Continuous
prod_dept_02_to_06 Continuous
prod_dept_03_to_01 Continuous
prod_dept_03_to_02 Continuous
prod_dept_03_to_03 Continuous
prod_dept_03_to_04 Continuous
prod_dept_03_to_05 Continuous
prod_dept_03_to_06 Continuous
prod_dept_04_to_01 Continuous
prod_dept_04_to_02 Continuous
prod_dept_04_to_03 Continuous
prod_dept_04_to_04 Continuous
prod_dept_04_to_05 Continuous
prod_dept_04_to_06 Continuous
prod_dept_05_to_01 Continuous
prod_dept_05_to_02 Continuous
prod_dept_05_to_03 Continuous
prod_dept_05_to_04 Continuous
prod_dept_05_to_05 Continuous
prod_dept_05_to_06 Continuous
prod_dept_06_to_01 Continuous
prod_dept_06_to_02 Continuous
prod_dept_06_to_03 Continuous
prod_dept_06_to_04 Continuous
prod_dept_06_to_05 Continuous
prod_dept_06_to_06 Continuous
0 <= station_01_to_01 <= 1 Integer
0 <= station_01_to_02 <= 1 Integer
0 <= station_01_to_03 <= 1 Integer
0 <= station_01_to_04 <= 1 Integer
0 <= station_01_to_05 <= 1 Integer
0 <= station_01_to_06 <= 1 Integer
0 <= station_01_to_07 <= 1 Integer
0 <= station_01_to_08 <= 1 Integer
0 <= station_01_to_09 <= 1 Integer
0 <= station_01_to_10 <= 1 Integer
0 <= station_02_to_01 <= 1 Integer
0 <= station_02_to_02 <= 1 Integer
0 <= station_02_to_03 <= 1 Integer
0 <= station_02_to_04 <= 1 Integer
0 <= station_02_to_05 <= 1 Integer
0 <= station_02_to_06 <= 1 Integer
0 <= station_02_to_07 <= 1 Integer
0 <= station_02_to_08 <= 1 Integer
0 <= station_02_to_09 <= 1 Integer
0 <= station_02_to_10 <= 1 Integer
0 <= station_03_to_01 <= 1 Integer
0 <= station_03_to_02 <= 1 Integer
0 <= station_03_to_03 <= 1 Integer
0 <= station_03_to_04 <= 1 Integer
0 <= station_03_to_05 <= 1 Integer
0 <= station_03_to_06 <= 1 Integer
0 <= station_03_to_07 <= 1 Integer
0 <= station_03_to_08 <= 1 Integer
0 <= station_03_to_09 <= 1 Integer
0 <= station_03_to_10 <= 1 Integer
0 <= station_04_to_01 <= 1 Integer
0 <= station_04_to_02 <= 1 Integer
0 <= station_04_to_03 <= 1 Integer
0 <= station_04_to_04 <= 1 Integer
0 <= station_04_to_05 <= 1 Integer
0 <= station_04_to_06 <= 1 Integer
0 <= station_04_to_07 <= 1 Integer
0 <= station_04_to_08 <= 1 Integer
0 <= station_04_to_09 <= 1 Integer
0 <= station_04_to_10 <= 1 Integer
0 <= station_05_to_01 <= 1 Integer
0 <= station_05_to_02 <= 1 Integer
0 <= station_05_to_03 <= 1 Integer
0 <= station_05_to_04 <= 1 Integer
0 <= station_05_to_05 <= 1 Integer
0 <= station_05_to_06 <= 1 Integer
0 <= station_05_to_07 <= 1 Integer
0 <= station_05_to_08 <= 1 Integer
0 <= station_05_to_09 <= 1 Integer
0 <= station_05_to_10 <= 1 Integer
0 <= station_06_to_01 <= 1 Integer
0 <= station_06_to_02 <= 1 Integer
0 <= station_06_to_03 <= 1 Integer
0 <= station_06_to_04 <= 1 Integer
0 <= station_06_to_05 <= 1 Integer
0 <= station_06_to_06 <= 1 Integer
0 <= station_06_to_07 <= 1 Integer
0 <= station_06_to_08 <= 1 Integer
0 <= station_06_to_09 <= 1 Integer
0 <= station_06_to_10 <= 1 Integer
0 <= station_07_to_01 <= 1 Integer
0 <= station_07_to_02 <= 1 Integer
0 <= station_07_to_03 <= 1 Integer
0 <= station_07_to_04 <= 1 Integer
0 <= station_07_to_05 <= 1 Integer
0 <= station_07_to_06 <= 1 Integer
0 <= station_07_to_07 <= 1 Integer
0 <= station_07_to_08 <= 1 Integer
0 <= station_07_to_09 <= 1 Integer
0 <= station_07_to_10 <= 1 Integer
0 <= station_08_to_01 <= 1 Integer
0 <= station_08_to_02 <= 1 Integer
0 <= station_08_to_03 <= 1 Integer
0 <= station_08_to_04 <= 1 Integer
0 <= station_08_to_05 <= 1 Integer
0 <= station_08_to_06 <= 1 Integer
0 <= station_08_to_07 <= 1 Integer
0 <= station_08_to_08 <= 1 Integer
0 <= station_08_to_09 <= 1 Integer
0 <= station_08_to_10 <= 1 Integer
0 <= station_09_to_01 <= 1 Integer
0 <= station_09_to_02 <= 1 Integer
0 <= station_09_to_03 <= 1 Integer
0 <= station_09_to_04 <= 1 Integer
0 <= station_09_to_05 <= 1 Integer
0 <= station_09_to_06 <= 1 Integer
0 <= station_09_to_07 <= 1 Integer
0 <= station_09_to_08 <= 1 Integer
0 <= station_09_to_09 <= 1 Integer
0 <= station_09_to_10 <= 1 Integer
0 <= station_10_to_01 <= 1 Integer
0 <= station_10_to_02 <= 1 Integer
0 <= station_10_to_03 <= 1 Integer
0 <= station_10_to_04 <= 1 Integer
0 <= station_10_to_05 <= 1 Integer
0 <= station_10_to_06 <= 1 Integer
0 <= station_10_to_07 <= 1 Integer
0 <= station_10_to_08 <= 1 Integer
0 <= station_10_to_09 <= 1 Integer
0 <= station_10_to_10 <= 1 Integer

Welcome to the CBC MILP Solver 
Version: 2.10.3 
Build Date: Dec 15 2019 

At line 2 NAME          MODEL
At line 3 ROWS
At line 73 COLUMNS
At line 2982 RHS
At line 3051 BOUNDS
At line 3188 ENDATA
Problem MODEL has 68 rows, 172 columns and 2600 elements
Coin0008I MODEL read with 0 errors
Option for timeMode changed from cpu to elapsed
...


Result - Optimal solution found

Objective value:                17271.00000000
Enumerated nodes:               1109
Total iterations:               45726
Time (CPU seconds):             3.43
Time (Wallclock seconds):       3.43

Option for printingOptions changed from normal to all
Total time (CPU seconds):       3.43   (Wallclock seconds):       3.43

Station solution:
dest_station    1   2   3   4   5   6   7   8   9   10
source_station                                        
1                0   0   1   0   0   0   0   0   0   0
2                0   0   0   0   0   0   0   0   1   0
3                1   0   0   0   0   0   0   0   0   0
4                0   0   0   0   0   0   0   1   0   0
5                0   0   0   0   0   1   0   0   0   0
6                0   0   0   0   0   0   0   0   0   1
7                0   0   0   0   1   0   0   0   0   0
8                0   0   0   0   0   0   1   0   0   0
9                0   1   0   0   0   0   0   0   0   0
10               0   0   0   1   0   0   0   0   0   0

Department solution:
dest_dept    1  2  3  4  5  6
source_dept                  
1            0  0  0  1  0  0
2            0  0  0  0  1  0
3            0  1  0  0  0  0
4            0  0  0  0  0  1
5            0  0  1  0  0  0
6            1  0  0  0  0  0

Assignments by distance-workflow cost:
 new_dist  workflow  source_dept  source_stat  dest_dept  dest_stat
        0        10            6            8          1          7
        0         9            2            8          5          7
        0         9            6            9          1          2
       12         8            4            2          6          9
        0         8            2            7          5          5
       39         7            2            4          5          8
        0         7            4            5          6          6
        0         7            2            9          5          2
      323         6            5            9          3          2
      193         6            2            6          5         10
       86         6            3            9          2          2
       79         6            3            8          2          7
       28         6            2            2          5          9
       17         6            4            4          6          8
        0         6            2            5          5          6
        0         6            2           10          5          4
        0         6            4           10          6          4
      377         5            5            8          3          7
      344         5            5           10          3          4
      116         5            2            3          5          1
       98         5            3           10          2          4
       83         5            4            3          6          1
       83         5            1            9          4          2
       69         5            4            1          6          3
       68         5            3            3          2          1
        0         5            6            5          1          6
      312         4            5            3          3          1
      136         4            1            8          4          7
       97         4            2            1          5          3
       78         4            3            4          2          8
       28         4            6            2          1          9
        0         4            6            7          1          5
        0         4            6           10          1          4
      335         3            5            1          3          3
      151         3            1            4          4          8
      128         3            1            5          4          6
      116         3            6            3          1          1
      106         3            1           10          4          4
       97         3            6            1          1          3
       72         3            1            3          4          1
       57         3            1            6          4         10
      173         1            1            2          4          9
      103         1            3            5          2          6
       95         1            1            1          4          3
       90         1            3            1          2          3
       87         1            4            9          6          2
       18         1            4            8          6          7
      414         0            5            2          3          9
      393         0            5            4          3          8
      367         0            5            5          3          6
      358         0            5            7          3          5
      318         0            5            6          3         10
      193         0            6            6          1         10
      171         0            4            6          6         10
      118         0            1            7          4          5
      104         0            3            7          2          5
       90         0            3            2          2          9
       67         0            3            6          2         10
       52         0            4            7          6          5
       39         0            6            4          1          8
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