Supply Chain Modelling and Design - Decision Making Techniques

Supply Chain Modelling and Design

Decision Making Techniques
Contents
Solution of Problem 1......................................................................................................................2
Sol.1(a).........................................................................................................................................2
Sol.1(b)........................................................................................................................................6
Sol.1(c).........................................................................................................................................7
Solution of problem 2....................................................................................................................10
Solution for Problem 3...................................................................................................................12
Solution for Problem 4...................................................................................................................14
References......................................................................................................................................17
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Decision Making Techniques
Solution of Problem 1
Sol.1(a)
As per given condition in problem, we have to solve the situation using multi objective linear
programming (MOLP), In order to solve the problem using MOLP first we will solve the
individual objective using solver, from this two-unit objective in which one increasing garbage
capacity and another one is minimising transportation cost. The calculated result set as target for
MOLP and we should provide weighted condition with few more constraints, so that we can
achieve minimax condition of desired result.
The capacity of plant is decided according to their efficiency recorded for that plant. If plant is of
100 ton rated capacity and its efficiency is 60% then it should produce only 100*0.6 = 60 ton
only. Similarly, the efficiency and rated capacity for garbage processing is given in first table we
must derive actual capacity as per given production capacity and efficiency data.
Site location
1 2 3 4 5
Capacity (Megaton) 10 7 15 12 6
Efficiency 0.35 0.45 0.25 0.75 0.55
Actual capacity 3.5 3.15 3.75 9 3.3
Problem formulation
Suppose the section is denoted as I and site location is j, then Aij is the amount of garbage which
is recycled at the site location j from the sector i.
The value of section I is in the range of 1 ≤i ≤10
The value of site j is in the range of 1 ≤ j≤ 5,
In such scenario the distribution matrix can be given as
1 2 3 4 5
1 A11 A12 A13 A14 A15
2 A21 A22 A23 A24 A25
3 A31 A32 A33 A34 A35
4 A41 A42 A43 A44 A45
5 A51 A52 A53 A54 A55
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Decision Making Techniques
6 A61 A62 A63 A64 A65
7 A71 A72 A73 A74 A75
8 A81 A82 A83 A84 A85
9 A91 A92 A93 A94 A95
10 A101 A102 A103 A104 A105
The given condition of maximum capacity of different site will be taken as constraint for the
given distribution. The given constraint for location is as follows.
A11+ A12+ A13+ A14+ A15 ≤ 4.6 ............(i)
A21 + A22 + A23 + A24 + A25 ≤ 4.6 ............(ii)
A31 + A32 + A33+ A34 + A35 ≤ 4.7 ............(iii)
A41+ A42+ A43+ A44 + A45 ≤ 4.2 ............(iv)
A51 + A52 + A53+ A54 + A55 ≤ 3.8 ............(v)
A61 + A62 + A63 + A64 + A65 ≤3.9 ............(vi)
A71 + A72 + A73+ A74 + A75 ≤ 3.4 ............(vii)
A81 + A82 + A83 + A84 + A85 ≤ 3.3 ............(viii)
A91 + A92 + A93 + A94+ A95 ≤ 3.9 ............(ix)
A101+ A102+ A103+ A104 + A105 ≤ 4.1 ....... (x)
The other five constraints will for site location, which is as follows as per their efficiency and
capacity
A11+ A21+ A31+ A41+ A51+ A61+ A71 + A81 + A91 + A101 ≤ 3.5 .........(xi)
A12 + A22 + A32+ A42 + A52+ A62+ A72+ A82+ A92 + A102 ≤ 3.15 .........(xii)
A13 + A23 + A33 + A43 + A53 + A63 + A73 + A83 + A93 + A103 ≤ 3.75 .........(xiii)
A14 + A24+ A34 + A44 + A54+ A64 + A74 + A84 + A94 + A104 ≤ 9 .............(xiv)
A15 + A25 + A35 + A45 + A55 + A65 + A75 + A85 + A95 + A105 ≤ 3.3 .............(xv)
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