Note that
the objective attempts to make the zl values as large as possible, and these are bounded
from above by the ylm values in Constraint 3, so that we would also like to make the latter
values as large as possible. Thus ylm will be set to 1 in the optimal solution as long as a tag
at position l with orientation m can be covered by at least one reader; otherwise Constraint
190 RFID Handbook: Applications, Technology, Security, and Privacy
2 forces ylm to be 0. Therefore, the problem can be reduced to N??L binary variables and
L3M continuous variables in the range [0,1]. However, the number of constraints cannot
be reduced.
Unfortunately, the integer program is poorly structured and it is impractical to solve the
problem to optimality with a high level of discretization for the portal space as well as the
orientations. The fact that the number of constraints is very large and cannot be reduced,
and that the technological coef?¬?cient matrix problem for the problem is dense makes it a
very hard integer programming problem.
10.3.3 Enumeration Scheme for Multiple Reader Coverage
Given that integer programming presents signi?¬?cant computational problems for large
problems, an enumeration scheme is examined in this section. Suppose we are given a set
of n reader positions. For each reader position and for each of the L points in the tag space,
Friis??™ equation is used for each of M possible orientations to calculate received power.
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