Encoding Finite Domain Functions Function has one out of n possible values: a1X1+ 「d,ord LP Encoding: y∈{0,1}i=1,2, axl x,=(2,d) Encoding Constraints Fixed-charge problem: f(x k:+ 0 if x=0 Minimizing costs Minimizing Zf, (x,)+---+ f,(x,) Yes or no decisions: should each of the activities be undertaken? Introduce auxiliary variables I ifx>o O ifx=0 z=∑cx+ky Which can be written as a linear constraint using big m• Function has one out of n possible values: a1x1+ . . . an xn = [d1 or d2 … or dp] • LP Encoding: yi  {0,1} i=1,2,…p ( 6 yi ) =1 a1x1+ . . . an xn= (6L di yi ) Encoding Finite Domain Functions • Fixed – charge problem: fi (xj ) = | kj + cj xj if xj >0 | 0 if xj =0 Minimizing costs: Minimizing z=f1(x1) +---+ fn(xn) Yes or no decisions: should each of the activities be undertaken? Encoding Constraints Introduce auxiliary variables: y1, …, yn = 0,1 y = 1 if x > 0 0 if x = 0 Which can be written as a linear constraint using big M: x <yM ¦  n i i i i i Z c x k y 1