Optimisation Problem: Logistics and Supply Chain Management

Optimisation Problem.
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Logistics and Supply chain management

Optimisation Problem.
Contents
Solution 1.........................................................................................................................................3
Solution1(a).................................................................................................................................3
Solution1(b).................................................................................................................................6
Solution1(c).................................................................................................................................7
Solution 2.........................................................................................................................................8
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Optimisation Problem.
Solution 1
Solution1(a)
The formulation of multi objective linear programming start with solving the linear programming
from each variable and combine to make a common objective with and solve this including he
two optimised result obtained from individual objective solving,
The given problem will also work like this, for which first I must understand and identify he
given data in the question,
Recycling Site
1 2 3 4 5
Capacity (Megaton) 10 8 15 11 10
Efficiency 0.35 0.42 0.39 0.75 0.6
Actual capacity 3.5 3.36 5.85 8.25 6
The recycling site from five individual location is given with capacity, which is given above, but
as per the efficiency the actual capacity of all five site is calculated as given above. For
calculation purpose we will consider the actual capacity not the rated capacity, because its
efficiency is given. Now the problem can be formulated as below. The site of the location with
section wise is given as follows.
1 2 3 4 5
1 S11 S12 S13 S14 S15
2 S21 S22 S23 S24 S25
3 S31 S32 S33 S34 S35
4 S41 S42 S43 S44 S45
5 S51 S52 S53 S54 S55
6 S61 S62 S63 S64 S65
7 S71 S72 S73 S74 S75
8 S81 S82 S83 S84 S85
9 S91 S92 S93 S94 S95
10 S101 S102 S103 S104 S105
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Optimisation Problem.
Now for solution we must adjust all the data in above given section and site.
The available constraints for given condition can be formulated as follows
S11+ S12+ S13 +S14 + S15 ≤ 5.0 ............(i)
S21 +S22+ S23+ S24+ S25 ≤ 6.0 ............(ii)
S31 +S32+ S33+ S34 + S35 ≤ 8.0 ............(iii)
S41 + S42 + S43 + S44 + S45 ≤ 9.0 ............(iv)
S51 +S52+ S53+ S54 + S55 ≤3.0 ............(v)
S61 +S62+ S63+ S64+ S65 ≤ 4.0 ............(vi)
S71 +S72+ S73+ S74 + S75 ≤7.0 ............(vii)
S81 +S82+ S83+ S84 +S85 ≤ 3.0 ............(viii)
S91 +S92 +S93 +S94 + S95 ≤ 4.2 ............(ix)
S101+ S102+ S103+ S104+ S105 ≤2.0 ....... (x)
S11+ S21+S31+S41+S51+S61+S71+S81+S91+S101 ≤ 3.50...... (11)
S12+ S22+S32+S42+S52+S62+S72+S82+S92+S102 ≤ 3.36...... (12)
S13+ S23+S33+S43+S53+S63+S73+S83+S92+S103 ≤ 5.85 ...... (13)
S14+ S24+S34+S44+S54+S64+S74+S84+S94+S104 ≤ 8.25 . .... (14)
S15+ S25+S35+S45+S55+S65+S75+S85+S95+S105 ≤ 6.0 ....... (15)
After complete ting the decision variable we must define the objective function for the given
problem, which will be as follows
F1 ( Max )= ( S11 + S12 +S13 + S14 + S15 ) + ( S21 + S22 + S23 + S24 + S25 ) + ( S31 + S32 + S33 + S34 + S35 ) + ( S41 + S42
This is the formulation of the linear programming for first problem. We have to arrange all the
data in excel solver which is given as a screen short.
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