第8章第4个算例(pert模型2).lg4

一本关于人工智能的起步教材

MODEL:
  ! A PERT/CPM model with crashing;
  !
  ! The precedence diagram is:
  !       /FCAST\---SCHED----COSTOUT\
  !      /       \                   \
  ! FIRST         \                   \
  !      \         \                   \
  !       \SURVEY-PRICE-----------FINAL;

SETS:
  TASK/ FIRST, FCAST, SURVEY, PRICE,
        SCHED, COSTOUT, FINAL/:
              TIME,  ! Normal time for task;
              TMIN,  ! Min time at max crash;
              CCOST, ! Crash cost/unit time;
                 EF, ! Earliest finish;
              CRASH; ! Amount of crashing;

 ! Here are the precedence relations;
  PRED( TASK, TASK)/  FIRST,FCAST   FIRST,SURVEY,
   FCAST,PRICE   FCAST,SCHED   SURVEY,PRICE,
   SCHED,COSTOUT   PRICE,FINAL   COSTOUT,FINAL/;
 ENDSETS

DATA:
  TIME = 0 14 3 3 7 4 10; ! Normal times;
  TMIN = 0  8 2 1 6 3  8; ! Crash times;
  CCOST = 0 4 1 2 4 5  3; ! Cost/unit to crash;
  DUEDATE = 31;           ! Project due date;
ENDDATA

! The crashing LP model;
! Define earliest finish, each predecessor of a task
  constrains when the earliest time the task can be
  completed. The earliest the preceding task can be
  finished plus the time required for the task minus
  any time that could be reduced by crashing this
  task.;
  @FOR( PRED( I, J):
    EF( J) >= EF( I) + TIME( J) - CRASH( J)
  );

! For each task, the most it can be crashed is the
  regular time of that task minus minimum time for
  that task;
  @FOR( TASK( J):
    CRASH( J) <= TIME( J) - TMIN( J)
  );

! Meet the due date;
! This assumes that there is a single last task;
  EF( @SIZE( TASK)) <= DUEDATE;

! Minimize the sum of crash costs;
  MIN = @SUM( TASK: CCOST * CRASH);

END