---
title: "Stock-Flow Models | Intro to Industrial Engineering"
description: "Stock-flow models track how quantities build up and change over time in Industrial Engineering, from inventory and capacity to demand, delay, and output."
canonical: "https://fiveable.me/introduction-industrial-engineering/key-terms/stock-flow-models"
type: "key-term"
subject: "Intro to Industrial Engineering"
unit: "Unit 1"
---

# Stock-Flow Models | Intro to Industrial Engineering

## Definition

Stock-flow models are diagrams and equations that show how a stock changes as flows add to it or remove from it. In Intro to Industrial Engineering, they help you track inventory, capacity, labor, or other system quantities over time.

## What It Is

Stock-flow models are a way to describe how a system changes over time in Intro to Industrial Engineering. A stock is the amount you have at a specific moment, while a flow is the rate that adds to or subtracts from that amount. Think of stock as the water in a tank and flow as the faucet and drain rates.

That time distinction matters. Stocks are measured at a point in time, such as units in inventory, machines available, or people in a queue. Flows are measured over time, such as production per hour, sales per day, arrivals per minute, or defect removal per shift. If you confuse the two, you end up comparing a total with a rate, which makes the model stop making sense.

In industrial engineering, stock-flow models are used to see how a process behaves when something changes upstream or downstream. For example, if production increases but shipping stays the same, finished goods inventory grows. If demand spikes and production does not catch up, inventory drops and shortages can appear. The model lets you trace that movement instead of guessing from a snapshot.

These models are often drawn as boxes and arrows, or turned into equations that update a stock from one time period to the next. A simple structure looks like this: new stock equals old stock plus inflow minus outflow. If a stock starts at 500 units, production adds 80 units per day, and customer orders remove 60 units per day, then the stock rises by 20 units per day, unless one of those rates changes.

Delays are where stock-flow models get more realistic. In real factory or supply chain settings, a change in flow does not always show up immediately in the stock. An order today may not arrive for days, and a decision to hire workers may not raise output right away. That lag is one reason industrial engineers use stock-flow models to test policies before applying them in a real process.

You will also see these models when a system has feedback. A growing stock can trigger a response, like more inventory causing a manager to cut production, or too many defects causing rework and inspection changes. That feedback makes the model more than a spreadsheet of totals, because it shows how the system reacts to its own state.

## Why It Matters

Stock-flow models give you a clean way to analyze process behavior instead of just looking at one moment in time. In Intro to Industrial Engineering, that matters whenever a system changes gradually, like inventory in a warehouse, work-in-process on a line, staffing levels in a service system, or parts moving through supply chain stages.

They also connect directly to systems engineering thinking. You are not just asking, “How much is there right now?” You are asking, “What rates are feeding this stock, what rates are draining it, and what happens if one of those rates changes?” That shift from snapshot thinking to dynamic thinking shows up in production planning, quality control, and resource planning.

A stock-flow model can also reveal bottlenecks and policy side effects. For example, if a factory keeps increasing order releases to avoid shortages, the model may show the work-in-process stock climbing faster than the line can clear it. That is the kind of result industrial engineers use to explain why a local fix can create a larger problem elsewhere in the system.

The concept is a good bridge between diagrams and decisions. Once you can read the stock, identify the flows, and track delays, you can test what happens under different policies, rather than relying on guesswork.

## Connections

### System Dynamics

Stock-flow models are one of the core building blocks of system dynamics. System dynamics uses stocks, flows, feedback, and time delays to study how complex systems behave over time, especially when changes in one part affect the rest of the system later.

### Feedback Loop

Feedback loops often drive the behavior inside a stock-flow model. A rising stock can trigger a balancing response, or a growing problem can reinforce itself, so the model shows not just movement but the system's reaction to that movement.

### Equilibrium

Equilibrium is the point where inflows and outflows balance, so a stock stays steady. In industrial engineering, this helps you see whether a process is stable, growing, or shrinking, and what has to change to keep it at a target level.

### [Causal Loop Diagrams](/introduction-industrial-engineering/key-terms/causal-loop-diagrams)

Causal loop diagrams show the direction of influence between variables, while stock-flow models add the actual quantities and rates. If a causal loop explains why inventory rises, the stock-flow model shows how fast it rises and where the delay comes in.

## On the AP Exam

A problem set question may give you a process like an inventory system, patient queue, or production line and ask you to identify the stock, the inflows, and the outflows. You may also need to predict how the stock changes after a rate change, such as higher production or delayed deliveries. A strong answer names the stock as the quantity at a moment in time, then follows the net flow over the time period.

On a quiz or in-class case discussion, you might explain why two processes with the same starting stock behave differently because their flows or delays are different. If a graph or diagram is included, you should trace arrows carefully and check whether each label is a rate or a total. The most common mistake is treating a flow like a stock, or forgetting that a delay can keep the visible stock from changing right away.

## stock-flow models vs Causal Loop Diagrams

Causal loop diagrams and stock-flow models both describe system behavior, but they are not the same tool. Causal loop diagrams show relationships and feedback directions, while stock-flow models track actual levels and rates over time. If you need to calculate how inventory changes, stock-flow is the better fit.

## Key Takeaways

- A stock is the amount you have at a point in time, while a flow is a rate that changes that amount over an interval.
- In Intro to Industrial Engineering, stock-flow models are used for inventory, work-in-process, staffing, capacity, and other changing system quantities.
- The basic logic is simple: stock goes up with inflows and down with outflows, but delays can make the behavior less obvious.
- These models help you see bottlenecks, shortages, buildup, and feedback effects instead of only looking at one snapshot.
- The biggest mistake is mixing up totals and rates, especially when a problem gives you numbers with different time units.

## FAQs

### What is stock-flow models in Intro to Industrial Engineering?

Stock-flow models are tools for tracking how a system quantity changes over time. The stock is the current amount, and the flows are the rates that increase or decrease it. In industrial engineering, this shows up in inventory, production, staffing, and queue systems.

### What is the difference between a stock and a flow?

A stock is measured at a single moment, like 300 units in inventory right now. A flow is measured over time, like 50 units shipped per day or 20 units produced per hour. If you mix them up, your model will not balance correctly.

### How do stock-flow models help with inventory problems?

They show whether inventory is building up, staying steady, or being depleted based on production and demand rates. That makes it easier to spot when a policy is causing overstock, shortages, or delays. You can also see the effect of lead times instead of assuming everything changes instantly.

### Are stock-flow models the same as system dynamics?

No, but they are closely related. System dynamics is the broader approach to studying behavior over time, and stock-flow models are one of its main tools. A stock-flow model is more specific because it focuses on quantities, rates, and how they change.

## Related Study Guides

- [1.2 Fundamentals of Systems Engineering](/introduction-industrial-engineering/unit-1/fundamentals-systems-engineering/study-guide/h2ZcGuEIrQDxv2qf)

## About This Document

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