Critical Path

   {  Exmpl9.8-1_CriticalPath.mpl  }

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

   {  Chapter 9.8, Example 1,  PERT/CPM,  Size: 18x15,  Page 399  }

TITLE
    CriticalPath;

INDEX
    act := (A,B,C,D,E,F,G,H,I,J,K,L,M,N,Finish);
    act2 := act;

    Path[act,act2] :=

       (A,B, B,C, C,D, C,E, C,I, D,G, E,F, E,H, F,J,
        G,H, H,M, I,J, J,K, J,L, K,N, L,N, M,Finish, N,Finish)

DATA
    Duration[act] := (2,4,10,6,4,5,7,9,7,8,4,5,2,6,0);


VARIABLES
    StartTime[act] -> "";

MODEL

    MIN FinishTime = StartTime[Finish];

SUBJECT TO

   SeqRelation[act,act2 IN Path]:

       StartTime[act] + Duration[act]

    <=

       StartTime[act:=act2];


END