jtÊÊÊm 
- 284 - 
+ c...x. + c. 0 x. + c.. x.. 
il il i2 i2 ii.li. 
J i J i 
-c - c 0 x _ 
ni ni n2 n2 
c . x . 
nj nj 
n •'n 
E c. . x. 
il. il . 
J î J î 
C X 
with the restrictions 
j2 
i 1 j * i'j ' 
= n 
jMj M -jyij t! 
= n 
nj. 
ail 
0, 
Each x.. represents a type from a certain category of the system and takes 
the value 1 in the case it is chosen in the optimum system and zero in the 
contrary. The coefficients c.. represents the "Unit” costs, more precisely, 
the costs associated to the different types j. category i in units comparable 
within the same category. The first group ofRestrictions is referring to 
the condition that from each category of the system should be selected only 
a representative. The second group of restrictions contains the different 
consistent combinations implied by the interactions between certain types 
from the different categories. Finally, the conditions that all x.. be equal 
to 0 or to 1 is the fundamental premise of the binary programming. 1 *' 
To bring the problem to the classical form of binary programming 
it should - be minimized f = C X 
with the restrictions B + A X 0 
X = 0, 1 
In order to solve by means of Balas' algorithm it will be 
necessary only the following transformations of the restrictions: 
1 - EX > 0 1 - EX > 0 
EX =1 =>1-EX=0=> => 
1 - EX < 0 - 1 + EX > 0 
With these observations the problem may be solved as a typical 
problem of binary linear programming at a computer /13/.