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;

param least_assign >= 0;

var Work {j in SCHEDS} >= 0 integer;
var Use  {j in SCHEDS} >= 0 binary;

minimize Total_Cost:
   sum {j in SCHEDS} rate[j] * Work[j];

subject to Shift_Needs {i in SHIFTS}: 
   sum {j in SCHEDS: i in SHIFT_LIST[j]} Work[j] >= required[i];

subject to Least_Use1 {j in SCHEDS}:
   least_assign * Use[j] <= Work[j];

subject to Least_Use2 {j in SCHEDS}:
   Work[j] <= (max {i in SHIFT_LIST[j]} required[i]) * Use[j];
#  Work[j] <= 0.40 * (max {i in SHIFT_LIST[j]} required[i]) * Use[j];