If zl??1 then the point l is covered with 100a% read accuracy
xn is the binary variable. If xn??1 then there is a reader antenna placed at location n
ylm is the binary variable. If ylm??1 then a tag at the point l with orientation m will be
covered by at least one reader antenna
Note that the last three quantities are the decision variables. Whether plmn takes on a
value of 0 or 1 is determined by ?¬?rst computing the received power PR for the location l
with orientation m using Friis??™ equation, and then checking to see whether or not this
exceeds Pmin (the minimum operational power required to activate the tag). Constraint 1
requires that the number of antennas installed be no more than the number available.
Constraint 2 ensures that a tag position with a speci?¬?c orientation is marked as covered
only if the required power is received from at least one of the reader positions. Constraint 3
guarantees that only a point with at least 100a% read accuracy will be counted.
In the above formulation, the number of constraints is 1??(L*M)??L, while the number of
binary variables is N??(L*M)??L. The density of the coef?¬?cient matrix is determined by the
plmn values, and in general will be much higher than it is for typical 0??“1 integer programming
problems of this size. The number of binary variables in the problem can be reduced
because the structure of the model allows for the ylm to be relaxed and de?¬?ned as
continuous variables with lower and upper bounds of 0 and 1, respectively.
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