Logistics network design problem

what is this

[Logistics Network Design Issues](http://www.orsj.or.jp/~wiki/wiki/index.php/%E3%80%8A%E3%83%AD%E3%82%B8%E3% 82% B9% E3% 83% 86% E3% 82% A3% E3% 82% AF% E3% 82% B9% E3% 83% 8D% E3% 83% 83% E3% 83% 88% E3% 83% AF% E3% 83% BC% E3% 82% AF% E8% A8% AD% E8% A8% 88% E5% 95% 8F% E9% A1% 8C% E3% 80% 8B)

Find out where, what, how much, and how to transport so that the sum of transportation and production costs is minimized while satisfying demand.

Try with Python

Specifications

python


Product= list('AB')
Demand area= list('PQ')
factory= list('XY')
lane= (2, 2)

Shipping cost table

python


import numpy as np, pandas as pd
tbdi = pd.DataFrame(((j, k)for j in demand area for k in factory), columns=['Demand area', 'factory'])
tbdi['Shipping costs'] = [1,2,3,1]
tbdi
Demand area Factory Shipping costs
0 P X 1
1 P Y 2
2 Q X 3
3 Q Y 1

Demand table

python


tbde = pd.DataFrame(((j, i)for j in demand area for i in products), columns=['Demand area', 'Product'])
tbde['demand'] = [10, 10, 20, 20]
tbde
Demand area Product Demand
0 P A 10
1 P B 10
2 Q A 20
3 Q B 20

Production table

python


tbfa = pd.DataFrame(((k, l, i, 0, np.inf) for k, nl in zip(factory,lane)
    for l in range(nl)for i in product), columns=['factory', 'lane', 'Product', 'lower limit', 'upper limit'])
tbfa['Production cost'] = [1, np.nan, np.nan, 1, 3,  np.nan, 5, 3]
tbfa.dropna(inplace=True)
tbfa.ix[4, 'upper limit'] = 10
tbfa
Factory Lane Product Lower limit Upper limit Production cost
0 X 0 A 0 inf 1.0
3 X 1 B 0 inf 1.0
4 Y 0 A 0 10.000000 3.0
6 Y 1 A 0 inf 5.0
7 Y 1 B 0 inf 3.0

solve

python


from ortoolpy import logistics_network
_, tbdi2, _ = logistics_network(tbde, tbdi, tbfa)

Result: Production volume (ValY)

python


tbfa
Factory Lane Product Lower limit Upper limit Production cost VarY ValY
0 X 0 A 0 inf 1.0 v9 20.0
3 X 1 B 0 inf 1.0 v10 10.0
4 Y 0 A 0 10.000000 3.0 v11 10.0
6 Y 1 A 0 inf 5.0 v12 0.0
7 Y 1 B 0 inf 3.0 v13 20.0

Result: Transport volume (ValX)

python


tbdi2
Demand area Factory Shipping costs Product VarX ValX
0 P X 1 A v1 10.0
1 P X 1 B v2 10.0
2 Q X 3 A v3 10.0
3 Q X 3 B v4 0.0
4 P Y 2 A v5 0.0
5 P Y 2 B v6 0.0
6 Q Y 1 A v7 10.0
7 Q Y 1 B v8 20.0

that's all

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