Modeling The Capacity-Inventory Relationship

X_(n+1)=rX_(n)(1-X_(n))

gives rise to highly complex and chaotic behavior. This equation and its lessons will be the a future topic topic.

To study capacity-inventory-variability relationships in production systems, the simple model illustrated above, was constructed using Simul8 software. These are the important features:

• They system is a simple, straight-through production line with 10 sequential stations.

• Each workstation has an average cycle time of 1.0 minute. Hence, the line is perfectly balanced (on average).

• The capacity of this system, based on this average cycle time, is 60 units per hour. This is a production rate corresponding to 100% utilization.

• Workpieces enter the system at regular intervals corresponding to particular production rates from 0% to 100%.

• Workpieces may queue at the head of the line (labeled "Backlog"), if station #1 is not empty.

• Workpieces may queue between stations if the downstream station cannot accept a workpiece when the upstream station releases it.

• The investigator introduces variation by increasing or decreasing the standard deviation of the work times for all stations.

• The independent variable is output rate. The dependent variable is average inventory in the system.

The system was operated with six different values for the work time standard deviation and through a range of workpiece input rates. When inventory stabilized, the results were recorded.