Model. Understand. Improve.
Three steps. The first takes days rather than months, because the model needs the shape of the factory, not every transaction in it.
Model your factory
Products are grouped into families that share routing behaviour. Resources are modelled as pools, including pools of unlike machines. Demand is modelled as a mix with its real variability, not a smooth annual figure. Labour that moves between machines is modelled as a shared resource, because that is how it behaves.
What it needs: routings and operation times, resource and shift data, downtime, setup and batch policy, and a demand mix. Most of it already exists in an ERP export and a few weeks of shop-floor observation.
See where flow breaks
The model is solved forward. For every resource: projected utilisation, projected queue time, work in process and its contribution to lead time. For every product family: manufacturing critical-path time, decomposed into processing and waiting.
The output states which resource becomes the constraint, when, and what is driving it. Not a colour-coded grid to interpret.
Test what changes
A scenario is a change to the model: a shift pattern, a machine, a routing, a transfer lot, a cell, a demand mix. It is solved the same way, and the two results are compared on the same measures. The comparison includes what the change costs — setups added, capacity committed, utilisation moved elsewhere.
What the model is made of
Eight quantities, and the relationships between them. Everything the product says is expressed in these terms, because they are the terms a plant already uses.
- Demand
- The order mix and its variability — not a smoothed annual volume. A plant that averages steadily and arrives in bursts is two different factories.
- Routing
- The sequence of operations a product actually takes, and where different products collide on the same resource.
- Resources
- Machines, pools of unlike machines, and the people who run them. Labour that moves between machines is modelled as shared, because it behaves that way.
- Utilisation
- The fraction of available time a resource is committed. A diagnostic, not a verdict: high utilisation is only a problem in the presence of variability, and queue time does not rise in proportion to it — it multiplies.
- Variability
- How unevenly work arrives and how unevenly it takes to process. Setup, breakdown, rework and adhoc jobs all enter here, and all of it propagates downstream.
- Queue
- Time a job spends waiting for a resource that is busy. In most high-mix plants this is the majority of lead time, and it is invisible in a capacity calculation.
- WIP
- Work released into the factory but not finished. Little’s Law ties it to throughput and lead time, and does not negotiate: at a given throughput, more WIP is more lead time.
- Lead time · MCT
- Manufacturing critical-path time: the calendar time from order to completion along the path that actually governs it, decomposed into processing, waiting, batching and move time.
The mathematics underneath
For the industrial engineer in the room. Nothing below is needed to use the product, and nothing above depends on it.
An open queueing network
The factory is solved as an open queueing network. Each resource is a general-arrival, general-service, multi-server station, approximated with Allen–Cunneen. Arrival and service variability are propagated between stations rather than assumed away, so variability introduced at Milling is still present when it reaches Assembly.
Wq ≈ ( ρ√(2(m+1))−1 / m(1 − ρ) ) · ( (Ca² + Cs²) / 2 ) · te
What else is carried
- Labour interference
- Operators shared across machines are resolved by fixed-point iteration, so a resource is not credited with capacity that has no one to run it.
- Transfer batching
- Process and transfer lots are modelled separately, which is where a large share of lead time in high-mix plants actually lives.
- Rework and scrap
- Rework loops and yield loss are propagated through the network, raising both the load and the variability at the operations that absorb them.
- Assembly convergence
- Where components meet, critical-path time is taken through the indented bill of materials — an assembly waits for its slowest branch.
- Effective process time
- Setup, downtime and availability are folded into effective process time and its variability, rather than treated as a separate efficiency percentage.
Where it comes from
The approach is Quick Response Manufacturing: lead time as the organising measure, manufacturing critical-path time as the way to see it, and queueing theory as the explanation for why capacity utilisation and delivery performance keep disagreeing. Little’s Law connects the three quantities the plant argues about every week — work in process, throughput and lead time — and it does not negotiate.
What it is not
It is not a scheduler and it does not sequence your orders. It is not an MES and it does not collect shop-floor transactions. It is not a discrete-event simulation you have to maintain as a second factory. It is an analytical model of flow behaviour, built to answer questions in minutes and be re-run when something changes.
Where confidence is low, the output says so. A model that implies precision it does not have will be found out by this audience within a week.
Start with one product family.
A Flow Analysis models a slice of your factory and returns where the queues form and what moves them.