Crew Assignments

   {  Exmpl11.4-3_CrewAssign.mpl  }

   {  Hillier and Lieberman, Introduction to Operations Research, 9th ed.  }

   {  Chapter 11.4,  Example 3, Set Covering, Size 12x12, Page 485  }


TITLE
   CrewAssignments;

INDEX
   j := 1..12;
   flights := 1..11;

DATA
   Cost[j] :=  (2, 3, 4, 6, 7, 5, 7, 8, 9, 9, 8, 9);
   Feas[flights,j] :=
            (1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
             0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
             0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
             0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1,
             1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0,
             0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0,
             0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1,
             0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0,
             0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
             0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1,
             0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1);

BINARY VARIABLE
   x[j];

MODEL
   MIN TotCost = SUM(j: Cost*x);

SUBJECT TO
   Sched[flights] : SUM(j: Feas*x) >=1;
   Numb : SUM(j: x) =3;

END