hu.ampl

set WORKERS = 1..5;
set DAYS = 1..31;
set WORKER_DEMAND = {13,13,12,13,13};
set SUNDAYS = {6,13,20,27};

var working {i in DAYS, j in WORKERS} integer >= 0, <= 1;

minimize Total_Work: sum {i in DAYS, j in WORKERS} working[i,j];

subject to Min_Service {i in DAYS}:
   sum {j in WORKERS} working[i,j] >= 2;

subject to Demand_13 {j in {1,2,4,5}}:
  sum {i in DAYS} working[i,j] >= 13;

subject to Demand_12 {j in {3}}:
  sum {i in DAYS} working[i,j] >= 12;

subject to SundayRest {j in WORKERS}:
  sum {i in SUNDAYS} working[i,j] <= 3;

subject to Max_Consecutive {j in WORKERS, i in 2..31}:
  (sum {a in {1}} working[i-1,j] + working[i,j]) <= 1;

option solver cplex;
solve;
display working;

display {i in DAYS} sum {j in WORKERS} working[i,j];

display {j in WORKERS} sum {i in DAYS} working[i,j];

display {j in WORKERS} sum {i in SUNDAYS} working[i,j];