# IE495, HW2 -- Problem 3.
# Network capacity planning model
# Author: Jeff Linderoth


# Set of links
set J;

# Set of demands
set I;

# Set of routes (indexed by demand)
set R{I};

# Set of scenarios
param N;
set S := 1 .. N;
param p{S} default 1/card(S);

var x{J} >= 0;
var f{i in I,r in R[i],S} >= 0;
var t{I,S} >= 0;

param b;
param c{J};
param u{J};
param d{I};

# This is the real capacity ---
param d2{i in I,s in S};


param a{i in I, r in R[i], J} default 0; 


minimize Unserved:
	 sum{i in I, s in S} p[s] * t[i,s];

subject to Budget:
	sum{j in J} c[j] * x[j] <= b;	

subject to ArcCap{j in J, s in S}:
	sum{i in I, r in R[i]} a[i,r,j] * f[i,r,s] <= u[j] + x[j];

subject to CountUnserved{i in I, s in S}:
	sum{r in R[i]} f[i,r,s] + t[i,s] = d2[i,s];