6 / 8
B.N. Korobets
140
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 6
The results (combined project III) are summarised below:
Option …….
0
1
2
3
4
5
Costs ………
0
4
6
9
10
15
RL ………….
0
7
8
12
15
20
Step 4.
Take combined projects I and III. The solution is given in the Table 4.
Table 4
The solution
2
(7; 13) (11; 20) (13; 21) (16; 25)
–
–
1
(3; 7)
(7; 14)
(9; 15) (12; 19) (13; 22) (18; 27)
0
0
(4; 7)
(6; 8)
(9; 12) (10; 15) (15; 20)
I / III
0
1
2
3
4
5
In the Table 4, find a box with the lowest first number out of the boxes where the
second number is higher than, or equal to,
2
25.
It is box (16; 25) with costs equal
to 16; accordingly,
s
3
= 16.
To determine
s
2
, find a box with the lowest first number out of the boxes where
the second number is higher than, or equal to,
1
15.
It is box (9; 15) with costs
equal to
s
2
= 9.
Find the solutions, i. e. the eligible projects, using the backward algorithm [10].
Box (16; 25) corresponds to option 2 in the combined project I Table 4, i. e. inclusion
of projects 1 and 2 into the programme, and option 3 of the combined project III
table 4. Option 3 of the combined project III Table 4 corresponds to option 2 of the
combined project II Table 3, i. e. inclusion of projects 3 and 4 into the programme.
Therefore, to achieve score 3, we need to include projects 1, 2, 3 and 4 in the pro-
gramme.
Do the same to determine the eligible projects to get score 2. Box (9; 15) cor-
responds to option 1 of the combined project I table 4, i. e. inclusion of project 1 into
the programme, and option 2 of the combined project III Table 4, i. e. inclusion of
project 5 into the programme.
Stage II.
By solving
m
problems of Stage I, we got a table of minimum costs (
s
ij
)
required to achieve (maintain) comprehensive scores 1, 2 and 3 (Table 5). Since po-
tential approaches to solving Stage II problems are mentioned in [11], we would only
discuss one of the options through the example of a comprehensive scoring system
from Fig. 2.
Table 5
A table of minimum costs
s
ij
j
i
1
2
3
4
1
5
4
7
3
2
16
10
13
9
3
25
20
21
18