upper bound for variable 1 = value of variable 2

One way to approach this is to introduce an auxillary variable z(t,k) and solve for following 

Max z(t,k)

s.t 

z(t,k)  <=  x(t,k)

z(t,k) <= y(t,k)

Other way, you can try out is:

Write following constraints (introduce dummy binary variable delta(t,k) and build following relations)

x(t,k) <= y(t,k) + (big-M)*delta(t,k)

x(t,k) >= y(t,k) -(big-M) *(1-delta(t,k))

Write Indicator constraints in AIMMS as 

if delta(t,k)=0 then z(t,k) = x(t,k)

if delta(t,k)=1 then z(t,k) = y(t,k)

Best Wishes,
Kumar.