set SHIFTS;               # shifts

param Nsched;             # number of schedules;
set SCHEDS = 1..Nsched;   # set of schedules

set SHIFT_LIST {SCHEDS} within SHIFTS;

param rate {SCHEDS} >= 0;
param required {SHIFTS} >= 0;

minimize Total_Cost;
subject to Shift_Needs {i in SHIFTS}: to_come >= required[i];

var Work {j in SCHEDS} >= 0,
   obj Total_Cost rate[j], 
   coeff {i in SHIFT_LIST[j]} Shift_Needs[i] 1;