Crashing

   {  Exmpl9.8-2_Crashing.mpl  }

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

   {  Chapter 9.8,  Example 2, Crashing,  Size: 18x29,  Page 403  }

TITLE
    CriticalPath;

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

DATA
    NormalTime[act] := (2,4,10,6,4,5,7,9,7,8,4,5,2,6);
    CrashTime[act]  := (1,2,7,4,3,3,4,6,5,6,3,3,1,3);

    NormalCost[act] := 1000 (180, 320, 620, 260, 410, 180, 900,
                             200, 210, 430, 160, 250, 100, 330);
    CrashCost[act]  := 1000 (280, 420, 860, 340, 570, 260, 1020,
                             380, 270, 490, 200, 350, 200, 510);

    MaxReduce[act] := NormalTime - CrashTime;

    CostWeekSaved[act] := CrashCost/MaxReduce - NormalCost/MaxReduce;

VARIABLES
    StartTime[act] -> "";
    Finished
    ReducedTime[act] -> "r"

MODEL

    MIN TotalCost = SUM(act: NormalCost) + SUM(act: CostWeekSaved * ReducedTime);

SUBJECT TO

   SeqRelation[act,act2 IN Path]:

       StartTime[act] + NormalTime[act] - ReducedTime[act]

    <=

       StartTime[act:=act2];

   StartTime[M] + NormalTime[M] - ReducedTime[M] <= Finished;
   StartTime[N] + NormalTime[N] - ReducedTime[N] <= Finished;

BOUNDS
   ReducedTime <= MaxReduce;

   Finished <= 40;

END