# POM Prof. Tempelmeier GmbH

## Production and Operations Management Consulting.

## Production line balancing

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

- positional weight (the sum of the task times of all successors)
- total number of successors
- longest task time

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

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.

Symbols:

i | task index |

D(i) | processing time of task i |

AE-i | task i |

Assumptions:

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

- Krajewski/Ritzman (1996), Chapter 10

- Nahmias (1997), Chapter 3

- Hopp/Spearman (1996), Chapter 18