# Question:Convert max to ILP constraint

## Question:Convert max to ILP constraint

Maple

Given

Tour2:=[[[1, 2, 3, 4]], [[1, 2], [1, 3, 4]], [[1, 3], [1, 2, 4]], [[1, 4], [1, 2, 3]], [[1, 2], [1, 3], [1, 4]]]:

Kitonums code

seq(max(seq(add(d[s[i]]*x[s[i],s[i+1]], i=1..nops(s)-1) , s=t))<=K, t=Tour2); produces

18*x[1, 2]+26*x[2, 3]+11*x[3, 4] <= K, max(18*x[1, 2], 26*x[1, 3]+11*x[3, 4]) <= K, max(26*x[1, 3], 18*x[1, 2]+11*x[2, 4]) <= K, max(11*x[1, 4], 18*x[1, 2]+26*x[2, 3]) <= K, max(18*x[1, 2], 26*x[1, 3], 11*x[1, 4]) <= K

correctly. The problem is I want to pass this through LPSolve and it doesn't like it. So what I need is to convert it to a constraint it will accept. I found a method on stackexchange,

http://stackoverflow.com/questions/10792139/using-min-max-within-an-integer-linear-program

i'm not sure it even works.i would be great if a procedure could could convert the max's in the above expression, or change the code in bold.

max(6*x[1, 4],4*x[1, 2]+3*x[2, 3]), where x[i,j] are binary vars.
x4 >= 6*x[1, 4];
x4 >= 4*x[1, 2]+3*x[2, 3];
Objective:= x4;

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