# AMPL nurse staffing model
#  IE398, HW4 -- Problem #2
#  Jeff Linderoth

set S;

var xSat >= 0 integer;
var xSun >= 0 integer;
var xMon >= 0 integer;

var ySM{S} >= 0 integer;
var eSat{S} >= 0 integer;
var eSun{S} >= 0 integer;
var eMon{S} >= 0 integer;

param dSat{S};
param dSun{S};
param dMon{S};

param p{S} default 1.0/card(S);

minimize cost:
	 300 * xSat + 300 * xSun + 300 * xMon + 
	 sum{s in S} p[s] * (800 * ySM[s] + 50 * eSat[s] + 50 * eSun[s] + 50 * eMon[s]);

subject to SatDemand{s in S}:
	10 * xSat + eSat[s] >= dSat[s];

subject to SunDemand{s in S}:
	10 * xSun + 10 * ySM[s] + eSun[s] >= dSun[s];

subject to MonDemand{s in S}:
	10 * xMon + 10 * ySM[s] + eMon[s] >= dMon[s];

subject to NoAnticipate{s1 in S, s2 in S: dSat[s1] = dSat[s2]}:
	ySM[s1] = ySM[s2];