MODEL:

! Assembly line balancing model;

  ! This model involves assigning tasks to stations

    in an assembly line so bottlenecks are avoided.

    Ideally, each station would be assigned an

    equal amount of work.;

SETS:

  ! The set of tasks to be assigned are A through

    K, and each task has a time to complete, T;

  TASK/ A B C D E F G H I J K/: T;

 

  ! Some predecessor,successor pairings must be

    observed(e.g. A must be done before B, B

    before C, etc.);

  PRED( TASK, TASK)/ A,B  B,C  C,F  C,G  F,J  G,J

    J,K  D,E  E,H  E,I  H,J  I,J /;

 

  ! There are 4 workstations;

  STATION/1..4/;

 

  TXS( TASK, STATION): X;

  ! X is the attribute from the derived set TXS

    that represents the assignment. X(I,K) = 1

    if task I is assigned to station K;

ENDSETS

 

DATA:

  ! Data taken from Chase and Aquilano, POM;

  ! There is an estimated time required for each

    task:

       A  B  C  D  E  F  G  H  I  J  K;

  T = 45 11  9 50 15 12 12 12 12  8  9;

ENDDATA

 

 ! The model;

 ! *Warning* may be slow for more than 15 tasks;

 

 ! For each task, there must be one assigned

   station;

 @FOR( TASK( I): @SUM( STATION( K): X( I, K)) = 1);

 

 ! Precedence constraints;

 ! For each precedence pair, the predecessor task

   I cannot be assigned to a later station than its

   successor task J;

 @FOR( PRED( I, J):

  @SUM( STATION( K):

   K * X( J, K) - K * X( I, K)) >= 0);

 

 ! For each station, the total time for the

   assigned tasks must be less than the maximum

   cycle time, CYCTIME;

 @FOR( STATION( K):

  @SUM( TXS( I, K): T( I) * X( I, K)) <= CYCTIME);

 

 ! Minimize the maximum cycle time;

 MIN = CYCTIME;

 

 ! The X(I,J) assignment variables are

   binary integers;

 @FOR( TXS: @BIN( X));

 

END

Model: ASLBAL