/*
	Shortest Path Probelem: 0-1 IP version
	V = 1:5
	source = 1
	terminal = 5
	E = (1, 2), (1, 3), (2, 3), (2, 4), (3, 4), (3, 5), (4, 6), (5, 6), and there inversions
	w12 = 1, w13 = 5, w23 = 2, w24 = 2, w34 = 3, w35 = 1, w46 = 3, w56 = 4
*/

var x12, binary;
var x21, binary;
var x13, binary;
var x31, binary;
var x23, binary;
var x32, binary;
var x24, binary;
var x42, binary;
var x34, binary;
var x43, binary;
var x35, binary;
var x53, binary;
var x46, binary;
var x64, binary;
var x56, binary;
var x65, binary;

/*
minimize z: 1*(x12+x21) + 5*(x13+x31) + 2*(x23+x32) + 2*(x24+x42) + 3*(x34+x43) + 1*(x35+x53) + 3*(x46+x64) + 4*(x56+x65);
*/

param w12 := 1;
param w13 := 5;
param w23 := 2;
param w24 := 2;
param w34 := 3;
param w35 := 1;
param w46 := 3;
param w56 := 4;

minimize z: w12*(x12+x21) + w13*(x13+x31) + w23*(x23+x32) + w24*(x24+x42) + w34*(x34+x43) + w35*(x35+x53) + w46*(x46+x64) + w56*(x56+x65);

s.t. source1: x12 + x13 - (x21 + x31) = 1;
s.t. terminal5: x53 + x56 - (x35 + x65) = -1;
s.t. mid2: x21 + x23 + x24 - (x12 + x32 + x42) = 0;
s.t. mid3: x31 + x32 + x34 + x35 - (x13 + x23 + x43 + x53) = 0;
s.t. mid4: x42 + x43 + x46 - (x24 + x34 + x64) = 0;
s.t. mid6: x64 + x65 - (x46 + x56) = 0;

end;