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Production line balancing

The line balancing problem is solved with a heuristic procedure based on sorting the work elements (tasks) with respect to the following criteria:

  • cumulated rank value (the task time + the sum of the cumulated rank values of all immediate successors)
  • rank positional weight (the sum of the task times of all successors)
  • total number of successors
  • longest task time

First, the precedence graph must be defined with the graphical editor. Note that the nodes (tasks) must be numbered from left to right.

Next, the cycle time or the planned production quantity per period must be entered. The period length is assumed to be 480 time units. If the cycle time is entered, production quantity is adapted and vice versa.

The procedure works as follows: Beginning with station 1 all tasks in the set of candiate tasks are checked whether they could be assigned to the current station. If no further task can be assigned, the next station is opened. If a task is assigned to a station, all arcs leaving the tasks in the precedence graph are deleted. The set of candidate tasks is identified as those tasks with no incoming arc.

During the procedure two kinds of pictures may be displayed.

The workload graph shows the assignment of tasks to the stations generated. The coloured bar segments show the tasks (task number/task time).

Workload graph:

The precedence graph shows the different sets of tasks (green - assignable; white - not assignable; other - station identification)

Precedence graph:


i task index
D(i) processing time of task i
AE-i task i


  • deterministic processing times
  • known precedence graph sorted in topological order

Tip: Move the mouse over the nodes in the precedence graph. Then further informations will be displayed.


- Krajewski/Ritzman (1996), Chapter 10
- Nahmias (1997), Chapter 3
- Hopp/Spearman (1996), Chapter 18

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