After introducing the SC model, we take an example for it.
Define the struture of SCM as below table and figure:
| Number | Notation | |
|---|---|---|
| vendor | 2 | V = { v1 , v2 } |
| facility | 2 | F = { f1 , f2 } |
| warehouse | 2 | W = { w1 , w2 } |
| customer | 3 | C = { c1 , c2 , c3 } |
| material | 3 | P = { p1 , p2 , p3 } |
| goods | 1 | G = { g1 } |
| time units | 5 | T = { t1 , t2 , t3, t4 , t5 } |
The Python Code and explanation is as below parts.
Note: This code will use pulp to solve the probelm. If you don't install it, you can refer to this article which published by PO-LAB from NCKU IMIS.
Import pulp into python, and define each variables.
from pulp import *
model = pulp.LpProblem("minimum", LpMinimize)
Mcost_tvp = ['LVtvp11', 'LVtvp12', 'LVtvp13', 'LVtvp21', 'LVtvp22','LVtvp23']
Pcost_tfg=["Rtfg11","Rtfg21"]
VF_Tcost_tvfp=["Rtvfp111","Rtvfp112","Rtvfp121","Rtvfp122","Rtvfp131","Rtvfp132",'Rtvfp211', "Rtvfp212", 'Rtvfp221',"Rtvfp222",'Rtvfp231',"Rtvfp232"]
FW_Tcost_tfwg=["Rtfwg111","Rtfwg211","Rtfwg121","Rtfwg221"]
WC_Tcost_twcg=["Rtwcg111","Rtwcg211","Rtwcg121","Rtwcg221","Rtwcg131","Rtwcg231"]
FM_Icost_tfp=["LFtfp11","LFtfp12","LFtfp13",'LFtfp21', 'LFtfp22','LFtfp23']
FG_Icost_tfg=["LFtfg11","LFtfg21"]
W_Icost_twg=["LWtwg11","LWtwg21"]
Key in the given data.
t1={
'LVtvp11':10.5,
'LVtvp12':6.5,
'LVtvp13':8.5,
'LVtvp21':20.5,
'LVtvp22':7.5,
'LVtvp23':7.5,
'Rtfg11':0.4,
'Rtfg21':0.45,
'Rtvfp111':10.5,
'Rtvfp121':6.5,
'Rtvfp131':8.5,
'Rtvfp211':20.5,
'Rtvfp221':7.5,
'Rtvfp231':7.5,
'Rtvfp112':10.5,
'Rtvfp122':6.5,
'Rtvfp132':8.5,
'Rtvfp212':20.5,
'Rtvfp222':7.5,
'Rtvfp232':7.5,
"Rtfwg111":0.2,
"Rtfwg121":0.3,
"Rtfwg211":0.5,
"Rtfwg221":0.1,
"LFtfg11":0.1,
"LFtfg21":0.09,
"LWtwg11":0.07,
"LWtwg21":0.05,
"Rtwcg111":0.6,
"Rtwcg211":0.3,
"Rtwcg121":0.4,
"Rtwcg221":0.5,
"Rtwcg131":0.3,
"Rtwcg231":0.4,
'LFtfp11':0.02,
'LFtfp12':0.02,
'LFtfp13':0.02,
'LFtfp21':0.01,
'LFtfp22':0.01,
'LFtfp23':0.01,
}
t2={
'LVtvp11':10.4,
'LVtvp12':6.4,
'LVtvp13':8.4,
'LVtvp21':20.4,
'LVtvp22':7.4,
'LVtvp23':7.4,
'Rtfg11':0.4,
'Rtfg21':0.45,
'Rtvfp111':10.5,
'Rtvfp121':6.5,
'Rtvfp131':8.5,
'Rtvfp211':20.5,
'Rtvfp221':7.5,
'Rtvfp231':7.5,
'Rtvfp112':10.5,
'Rtvfp122':6.5,
'Rtvfp132':8.5,
'Rtvfp212':20.5,
'Rtvfp222':7.5,
'Rtvfp232':7.5,
"Rtfwg111":0.2,
"Rtfwg121":0.3,
"Rtfwg211":0.5,
"Rtfwg221":0.1,
"LFtfg11":0.1,
"LFtfg21":0.09,
"LWtwg11":0.07,
"LWtwg21":0.05,
"Rtwcg111":0.6,
"Rtwcg211":0.3,
"Rtwcg121":0.4,
"Rtwcg221":0.5,
"Rtwcg131":0.3,
"Rtwcg231":0.4,
'LFtfp11':0.02,
'LFtfp12':0.02,
'LFtfp13':0.02,
'LFtfp21':0.01,
'LFtfp22':0.01,
'LFtfp23':0.01,
}
t3={
'LVtvp11':10.3,
'LVtvp12':6.3,
'LVtvp13':8.3,
'LVtvp21':20.3,
'LVtvp22':7.3,
'LVtvp23':7.3,
'Rtfg11':0.4,
'Rtfg21':0.45,
'Rtvfp111':0.01,
'Rtvfp121':0.01,
'Rtvfp131':0.01,
'Rtvfp211':0.01,
'Rtvfp221':0.01,
'Rtvfp231':0.01,
'Rtvfp112':0.01,
'Rtvfp122':0.01,
'Rtvfp132':0.01,
'Rtvfp212':0.01,
'Rtvfp222':0.01,
'Rtvfp232':0.01,
"Rtfwg111":0.2,
"Rtfwg121":0.3,
"Rtfwg211":0.5,
"Rtfwg221":0.1,
"LFtfg11":0.1,
"LFtfg21":0.09,
"LWtwg11":0.07,
"LWtwg21":0.05,
"Rtwcg111":0.6,
"Rtwcg211":0.3,
"Rtwcg121":0.4,
"Rtwcg221":0.5,
"Rtwcg131":0.3,
"Rtwcg231":0.4,
'LFtfp11':0.02,
'LFtfp12':0.02,
'LFtfp13':0.02,
'LFtfp21':0.01,
'LFtfp22':0.01,
'LFtfp23':0.01,
}
t4={
'LVtvp11':10.2,
'LVtvp12':6.2,
'LVtvp13':8.2,
'LVtvp21':20.2,
'LVtvp22':7.2,
'LVtvp23':7.2,
'Rtfg11':0.4,
'Rtfg21':0.45,
'Rtvfp111':0.01,
'Rtvfp121':0.01,
'Rtvfp131':0.01,
'Rtvfp211':0.01,
'Rtvfp221':0.01,
'Rtvfp231':0.01,
'Rtvfp112':0.01,
'Rtvfp122':0.01,
'Rtvfp132':0.01,
'Rtvfp212':0.01,
'Rtvfp222':0.01,
'Rtvfp232':0.01,
"Rtfwg111":0.2,
"Rtfwg121":0.3,
"Rtfwg211":0.5,
"Rtfwg221":0.1,
"LFtfg11":0.1,
"LFtfg21":0.09,
"LWtwg11":0.07,
"LWtwg21":0.05,
"Rtwcg111":0.6,
"Rtwcg211":0.3,
"Rtwcg121":0.4,
"Rtwcg221":0.5,
"Rtwcg131":0.3,
"Rtwcg231":0.4,
'LFtfp11':0.02,
'LFtfp12':0.02,
'LFtfp13':0.02,
'LFtfp21':0.01,
'LFtfp22':0.01,
'LFtfp23':0.01,
}
t5={
'LVtvp11':10.1,
'LVtvp12':6.1,
'LVtvp13':8.1,
'LVtvp21':20.1,
'LVtvp22':7.1,
'LVtvp23':7.1,
'Rtfg11':0.4,
'Rtfg21':0.45,
'Rtvfp111':0.01,
'Rtvfp121':0.01,
'Rtvfp131':0.01,
'Rtvfp211':0.01,
'Rtvfp221':0.01,
'Rtvfp231':0.01,
'Rtvfp112':0.01,
'Rtvfp122':0.01,
'Rtvfp132':0.01,
'Rtvfp212':0.01,
'Rtvfp222':0.01,
'Rtvfp232':0.01,
"Rtfwg111":0.2,
"Rtfwg121":0.3,
"Rtfwg211":0.5,
"Rtfwg221":0.1,
"LFtfg11":0.1,
"LFtfg21":0.09,
"LWtwg11":0.07,
"LWtwg21":0.05,
"Rtwcg111":0.6,
"Rtwcg211":0.3,
"Rtwcg121":0.4,
"Rtwcg221":0.5,
"Rtwcg131":0.3,
"Rtwcg231":0.4,
'LFtfp11':0.02,
'LFtfp12':0.02,
'LFtfp13':0.02,
'LFtfp21':0.01,
'LFtfp22':0.01,
'LFtfp23':0.01,
}
Declared decision variables into model.
LVtvp=['LVtvp11','LVtvp12','LVtvp13','LVtvp21','LVtvp22','LVtvp23']
Rtfg=['Rtfg11','Rtfg21']
Rtvfp=['Rtvfp111','Rtvfp121','Rtvfp131','Rtvfp211','Rtvfp221','Rtvfp231','Rtvfp112','Rtvfp122','Rtvfp132','Rtvfp212','Rtvfp222','Rtvfp232']
Rtfwg=['Rtfwg111','Rtfwg121','Rtfwg211','Rtfwg221']
LFtfg=['LFtfg11','LFtfg21']
LWtwg=['LWtwg11','LWtwg21']
Rtwcg=['Rtwcg111','Rtwcg211','Rtwcg121','Rtwcg221','Rtwcg131','Rtwcg231']
LFtfp=['LFtfp11','LFtfp12','LFtfp13','LFtfp21','LFtfp22','LFtfp23']
LVtvp = pulp.LpVariable.dicts("LVtvp",LVtvp, 0)
Rtfg = pulp.LpVariable.dicts("Rtfg",Rtfg, 0)
Rtvfp = pulp.LpVariable.dicts("Rtvfp",Rtvfp, 0)
Rtfwg =pulp. LpVariable.dicts("Rtfwg",Rtfwg, 0)
LFtfg = pulp.LpVariable.dicts("LFtfg",LFtfg, 0)
LWtwg = pulp.LpVariable.dicts("LWtwg",LWtwg, 0)
Rtwcg = pulp.LpVariable.dicts("Rtwcg",Rtwcg, 0)
LFtfp = pulp.LpVariable.dicts("LFtfp",LFtfp, 0)
Input objective function into model.
model += lpSum([(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*LVtvp[i] for i in Mcost_tvp]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*Rtfg[i] for i in Pcost_tfg]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*Rtvfp[i] for i in VF_Tcost_tvfp]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*Rtfwg[i] for i in FW_Tcost_tfwg]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*LFtfg[i] for i in FG_Icost_tfg]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*LWtwg[i] for i in W_Icost_twg]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*Rtwcg[i] for i in WC_Tcost_twcg]+
[(t1[i]+t2[i]+t3[i]+t4[i]+t5[i])*LFtfp[i] for i in FM_Icost_tfp])
Input constrains into model. There are many constrains, the formulas as below are only partial.
# Bounded Contrains
model += lpSum(t1['LWtwg11']*LWtwg['LWtwg11'])<=400
model += lpSum(t2['LWtwg11']*LWtwg['LWtwg11'])<=400
model += lpSum(t3['LWtwg11']*LWtwg['LWtwg11'])<=400
model += lpSum(t4['LWtwg11']*LWtwg['LWtwg11'])<=400
model += lpSum(t5['LWtwg11']*LWtwg['LWtwg11'])<=400
model += lpSum(t1['LWtwg21']*LWtwg['LWtwg21'])<=500
model += lpSum(t2['LWtwg21']*LWtwg['LWtwg21'])<=500
model += lpSum(t3['LWtwg21']*LWtwg['LWtwg21'])<=500
model += lpSum(t4['LWtwg21']*LWtwg['LWtwg21'])<=500
model += lpSum(t5['LWtwg21']*LWtwg['LWtwg21'])<=500
model += lpSum(t1['LFtfg11']*LFtfg['LFtfg11'])<=70
model += lpSum(t2['LFtfg11']*LFtfg['LFtfg11'])<=70
model += lpSum(t3['LFtfg11']*LFtfg['LFtfg11'])<=70
model += lpSum(t4['LFtfg11']*LFtfg['LFtfg11'])<=70
model += lpSum(t5['LFtfg11']*LFtfg['LFtfg11'])<=70
model += lpSum(t1['LFtfg21']*LFtfg['LFtfg21'])<=35
model += lpSum(t2['LFtfg21']*LFtfg['LFtfg21'])<=35
model += lpSum(t3['LFtfg21']*LFtfg['LFtfg21'])<=35
model += lpSum(t4['LFtfg21']*LFtfg['LFtfg21'])<=35
model += lpSum(t5['LFtfg21']*LFtfg['LFtfg21'])<=35
.
.
.
# Flow Balance Constrain
model += lpSum(Rtvfp['Rtvfp111']+Rtvfp['Rtvfp112'])==LVtvp['LVtvp11']
model += lpSum(Rtvfp['Rtvfp121']+Rtvfp['Rtvfp122'])==LVtvp['LVtvp12']
model += lpSum(Rtvfp['Rtvfp131']+Rtvfp['Rtvfp132'])==LVtvp['LVtvp13']
model += lpSum(Rtvfp['Rtvfp211']+Rtvfp['Rtvfp212'])==LVtvp['LVtvp21']
model += lpSum(Rtvfp['Rtvfp221']+Rtvfp['Rtvfp222'])==LVtvp['LVtvp22']
model += lpSum(Rtvfp['Rtvfp232']+Rtvfp['Rtvfp232'])==LVtvp['LVtvp23']
.
.
.
Solve the problem and print the solution of variables.
model.solve()
for v in model.variables():
print(v.name, "=", v.varValue)
print('obj=',value(model.objective))
Finally, we will get the result.
objective function = 2035.22