Deterministic model of throughput in a (single tread) production line

Question

I am looking for a simple and canonical model of throughput (number of batches per unit of time) of a sequential and deterministic production line. For this simple model, I am searching for theorems relating throughput to the throughput of the slowest step and lead time (time to transform inputs into the final product).

The production line (P) is sequential and single threaded, comprises S steps. Each step, s, comprises a throughput per worker and a number of workers. The throughput per worker in each step is deterministic.

Is there a canonical model for this?

I found references for Jackson networks in this Operations Research textbook, such as this, but these seem much more complex and flexible than I am looking for (every node can connect to any other node, the productivity of each step is stochastic). I suppose this is related to work on queues, but I was neve exposed to such theories.

This is for a research project. Any references will be appreciated.

Answer 1

In a linear production line, the throughput of the slowest step will be the throughput of the entire line. Every other step must adjust its throughput to match the slowest.

• If the steps before the slowest run faster, then their output will back up at the slowest step until there is no more room to store it, or inventory is lost.
• The steps after the slowest are unable to run faster, as they run out of the input produced by that set.