[Help-glpk] Expressing constraints

[Sam]

Hi there

I am a newbie to glpk and linear programming in general.  I come from a 
computer science background, so I have some mathematical understanding, 
but its not what I would call great.  I have read the glpk article at 
IBM 
(http://www-128.ibm.com/developerworks/linux/library/l-glpk1/index.html), 
which I found very useful, and have now starting formulating my own 
problems.

The first was very simple and worked almost straight away (it was a 
variation of Giapetto's problem).  The second I have been having trouble 
with, and that is why I'm writing to the list (apologies if this problem 
has already been dealt with).  I'm not sure if the trouble I am 
experiencing is due to my limited understanding of linear programming, 
but I'm sure you will point me in the right direction.

The problem is as follows:  A wireless network design has been approved 
that contains 18 sites.  Each of these sites has been evaluated and a 
transmit power has been estimated.  There are two types of wireless 
nodes, A and B.  A costs $450 and can transmit at levels 1-15.  B costs 
$250, but can only transmit at levels 8-18.  Minimize the cost of the 
nodes while taking the transmit power in to account.

I model this as the following:

/* Sets */
set NODES;

/* Parameters */
param power {i in NODES};

/* Decision variables */
var a_node {i in NODES},binary;
var b_node {i in NODES},binary;

/* Objective function */
minimize z : sum{i in NODES} a_node[i] * 450 + sum{j in NODES} b_node[j] 
* 250;

/* Constraints */
s.t. that{i in NODES} : a_node[i] + b_node[i] = 1;

/* This is where I am having trouble */
s.t. a_value{i in NODES} : if (power[i] >= 1 and power[i] < 8) then 
a_node[i] = 1;
s.t. b_value{i in NODES}:  if (power[i] > 15 and power[i] <= 18) then 
b_node[i] = 1;

data;
set NODES := 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18;

param power :=
1    8
2    5
3    9
4    4
5    12
6    11
7    7
8    13
9    18
10    14
11    7
12    9
13    15
14    12
15    7
16    4
17    13
18    11;

end;

I am having trouble expressing the transmit power constraint.  If what I 
understand from the documentation is correct, then a constraint must be 
a linear expression and hence cannot contain boolean operators or 
conditional statements.  Have I done the right thing using two binary 
variables, and if so, how can I express the transmit power constraint as 
a linear expression? 

The main thing I don't understand is how to relate a parameter such as 
power to a variable in a constraint, such that the constraint only 
applies to that variable, and not to the whole problem.  Is this 
possible, or am I violating the laws of linear programming!!

Thanks in advance :)
Sam