# Twinworks Line Capacity Calculator

> Takt time, bottleneck, OEE, throughput and Little’s law lead time of a production line. Analytic capacity of a serial production line: takt time from demand and available time, theoretical and effective capacity of every station with parallel machines and batch sizes, OEE = availability × performance × quality with downstream scrap, the bottleneck with and without losses, load at demand, Little’s law lead time for your work in process and the Factory Physics best-case, practical-worst-case and worst-case benchmarks. Enter stations or read them from a Twinworks model.

Part of usefulweb.app (https://usefulweb.app/). Part of [Twinworks](https://twinworks.usefulweb.app/) (ownerApp: twinworks). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://twinworkslinecapacity.usefulweb.app/ (interactive tool at https://twinworkslinecapacity.usefulweb.app/tool)
- JSON API: POST https://twinworkslinecapacity.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://twinworkslinecapacity.usefulweb.app/api/v1/tool)
- OpenAPI: https://twinworkslinecapacity.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://twinworkslinecapacity.usefulweb.app/mcp - tool `twinworks_line_capacity`

## Inputs
- stations (table): Stations in flow order - Cycle time per unit and machine (for a batch station: per batch). Availability, performance and quality in percent (empty = 100 %).
- template (select): Or read the stations from a template
- model (textarea): Or a Twinworks model JSON - A .twinworks.json project or model; the serial line from its source to its sink is read (mean cycle times, servers, MTBF/MTTR availability, ideal cycle time, scrap).
- availableMinutes (number): Available time per period - Net production time, e.g. a 8 h shift minus 30 min breaks = 450 min.
- demand (number): Demand per period - Optional: gives the takt time and the load at demand.
- wip (number): Work in process - Optional: units in the line for Little’s law (lead time = WIP ÷ throughput).

## Method
- Takt time = available time ÷ demand; demand rate = demand × 3600 ÷ available seconds.
- Theoretical station capacity = parallel machines × units per cycle × 3600 ÷ cycle time (units/h). The slowest station is the theoretical bottleneck; its rate rb is the line’s theoretical throughput (the same rule as the Twinworks analytic check of a deterministic serial line).
- OEE per station = availability × performance × quality (availability = run time ÷ planned time, performance = ideal cycle × units ÷ run time, quality = good ÷ processed). Effective processed rate = theoretical × A × P. Rejected units leave the line, so a station supports only (its processed rate × the product of its own and all downstream quality rates) good finished units per hour. The smallest of these is the effective throughput and the effective bottleneck.
- Little’s law: WIP = throughput × lead time, so lead time = WIP ÷ effective throughput (long-run averages, any distributions).
- Benchmarks for a given WIP w (Factory Physics): raw process time T0 = Σ cycle ÷ units per cycle, critical WIP W0 = rb × T0; best case TH = min(w ÷ T0, rb), practical worst case TH = rb × w ÷ (W0 + w − 1), worst case TH = 1 ÷ T0. A real line between best case and practical worst case is doing well; below practical worst case it has more variability than exponential.
- From a Twinworks model: stations are the machine, assembly and quality nodes from the source to the sink in flow order; cycle = mean of the cycle distribution (or the ideal cycle time with performance = ideal ÷ mean), servers = parallel machines, availability = MTBF ÷ (MTBF + MTTR) with mean times, quality = 1 − scrap %.

## Limits
- Analytic averages for a steady line without starvation and blocking from variability; buffers, setups, shifts and random breakdowns can lower the real output — simulate the line in Twinworks to see those effects.