Don Woodlock · YouTube · 6:25
This 120-second clip explains how to add a construction delay to a housing stock-and-flow model. The lecturer states that houses do not appear instantly and uses a one-year building time as the model assumption. He introduces a work-in-progress stock, House WIP, and describes delay as a chain of stocks, here a two-stock chain of unfinished and finished houses. On the whiteboard he keeps the goal-gap-builders control structure, relabels the original Houses stock as House WIP, and draws a new outflow labeled Completing houses to represent completion after 12 months. This segment demonstrates how to model production delays in System Dynamics by introducing a 'Work In Progress' (WIP) stock. The instructor adds a 'Finished Houses' stock and rewires the 'Gap' calculation to depend on finished supply rather than WIP. He defines the completion rate as the WIP stock divided by the average completion time (12 months), illustrating the standard first-order delay formulation. This segment extends a system dynamics model of the housing market by introducing a decay mechanism for finished houses. The instructor explains how to model the 'scrap/decay' flow using a time constant derived from the average lifetime of a house (36 months). He demonstrates that dividing the stock of finished houses by 36 yields the monthly decay rate, equivalent to th of the houses decaying per month. This reinforces the general principle of using average delay times to formulate flow rates in first-order delays. This introductory segment features a lecturer presenting a hand-drawn stock-and-flow diagram on a whiteboard. The model represents a housing market with two primary stocks: 'House WIP' (work-in-progress) and 'Finished Houses'. Flows include 'Building rate', 'Completion rate', and 'Sales rate'. Crucially, the diagram annotates significant time delays: 3 months for construction and 30 months for sales. A feedback loop involves a 'GOAL' of 10,000 houses and a calculated 'Gap'. The speaker explains that this structure will be used to demonstrate how delays influence the system's attempt to reach its target, setting the stage for analyzing potential oscillations.
Use the learning inspector for key ideas and moments, or open the reading tabs for the complete notes.
Generated from the video's visuals and explanation; not verbatim speech.
The lecturer begins by saying the model will be made more interesting by including the delay discussed earlier. The visible whiteboard already contains a stock-and-flow structure with GOAL (Population), Gap (Land for houses), Builders, Smooth Adj Time, and a stock labeled Houses.
He states the key modeling issue: houses do not simply appear when builders act, because construction takes time. In this simplified model the delay is set to one year from start to finish, though he notes real construction could last longer.
To represent that delay, he introduces a work-in-progress stock. Instead of treating started construction as immediate output, the model first accumulates houses that are under construction but not yet complete.
He then generalizes the mechanism: a delay can be handled as a chain of stocks. For this example the chain has only two links, House WIP followed by finished houses, which he says is adequate for the present model.
Turning to the board, he preserves the upstream control logic from goal to gap to builders. The change happens at the destination of the Builders inflow: the old Houses stock is relabeled House WIP, making it the stock of unfinished construction.
As he explains, once builders start a house it does not become a finished house immediately; it becomes a house work in progress. This verbal point matches the board edit where the first stock is renamed WIP.
Finally he draws a new outflow from House WIP and labels it Completing houses, corresponding to the statement that after 12 months the houses are completed. The clip ends while this revised delay structure is being drawn.
The instructor begins by drawing a new stock box labeled 'Finished Houses' to the right of the 'House WIP' box. This visually separates the concept of houses currently under construction from those that are fully completed and ready for occupancy.
Next, the instructor performs a 'rewiring' operation. He draws an arrow from the 'Finished Houses' stock to the 'Gap' variable. He explains that the 'Gap'—the difference between demand and supply—must be calculated based on the number of *finished* houses available, not the work-in-progress. He provides a numerical example: if the goal is 10,000 families and there are 1,000 finished houses, the gap is 9,000.
The focus shifts to the flow valve labeled 'Completing houses'. The instructor writes 'Completion Time' next to it and states it is 12 months. He explains the mathematical relationship governing this flow: the rate at which houses leave the WIP stock and enter the Finished stock is equal to the current level of the WIP stock divided by the completion time. Thus, .
He generalizes this principle, stating that in System Dynamics, delays are modeled by dividing the stock level by the average delay time to determine the outflow rate. This creates a first-order delay structure where the 'House WIP' acts as a buffer accumulating items before they are processed and moved to the next stage.
The instructor begins by reviewing the calculation for the completion rate of houses. He points to the 'House WIP' stock and explains that the outflow is determined by dividing the current stock by the average build time, which is 12 months. This results in a completion rate of of the WIP per month.
Next, he introduces a new element to the model: a decay rate for finished houses. He draws a valve exiting the 'Finished Houses' stock, labeling it 'Scrap/decay'. He explains that houses do not last forever; in this simplified model, they have an average lifetime of three years, or 36 months.
Applying the same logic used for construction, he formulates the decay rate. He states that the number of houses decaying per month is found by dividing the 'Finished Houses' stock by the average lifetime of 36 months. Mathematically, this means of the existing houses decay each month.
He addresses a potential confusion, noting that while treating a fixed lifetime as a fractional monthly decay might seem counter-intuitive, it is mathematically equivalent in continuous system dynamics models. He summarizes the three time constants in the model: 3 months for the builder's response delay, 12 months for the construction delay, and 36 months for the housing decay delay.
The lecturer stands before a whiteboard displaying a system dynamics model. He concludes a previous thought about monthly rates.
He identifies the drawing as a 'stock-and-flow diagram,' acknowledging that new elements have been added which might cause confusion. The diagram clearly shows rectangles for stocks ('House WIP', 'Finished Houses') and arrows for flows ('Building rate', 'Completion rate', 'Sales rate').
The speaker proposes enhancing the model using this specific diagram. He points out the annotations indicating delays: '3 months Avg Time' for construction and '30 months (sales)' for selling. He also highlights the feedback mechanism involving a 'GOAL (10,000)' and the resulting 'Gap'.
He explains the purpose of this setup: to observe how the system behaves as it attempts to reach the target of 10,000 houses, implying that the delays will play a critical role in this dynamic process.
The lecture adds realism by recognizing that houses are not created instantaneously. In the model, starting construction and finishing construction are separated by one year, although the lecturer notes actual building times may be longer.
A work-in-progress stock stores items that have entered the production process but are not yet finished. Here House WIP represents houses under construction, so the Builders inflow adds to unfinished inventory rather than directly to completed houses.
The lecturer explains that time delays can be modeled by chaining stocks so that units move through successive stages before reaching the final stock. This example uses a two-stock chain: House WIP and then finished houses.
On the board, the existing goal-gap-builders feedback path is kept, but the original Houses stock is relabeled House WIP. A new outflow labeled Completing houses is drawn from that stock to represent completion after the one-year delay.
In System Dynamics, processes that take time (like building a house) are modeled by inserting a 'Work In Progress' (WIP) stock. This stock accumulates items as they enter the process and depletes as they finish. It acts as a buffer between the start and end of the activity.
The rate at which items leave a delay stock (e.g., 'Completing houses') is calculated by dividing the current stock level by the average time it takes to complete the process. Formula: .
The 'Gap' represents the discrepancy between a target goal and current performance. In this housing model, it is crucial to calculate the gap using 'Finished Houses' (actual supply) rather than 'House WIP', as only completed houses satisfy demand. .
In system dynamics, a first-order delay is modeled by dividing the stock level by the average delay time (time constant). For example, if the average build time is 12 months, the completion rate is .
To model the removal of items from a stock (like houses decaying), use the average lifetime as the time constant. If the average lifetime is 36 months, the decay rate is , meaning of the stock decays per month.
It is a common misconception that a fixed lifetime (e.g., 36 months) cannot be represented by a fractional decay rate ( per month). In continuous exponential decay models, these two formulations are mathematically equivalent.
A modeling tool where rectangles represent accumulations (stocks like 'House WIP'), thick arrows represent rates of change (flows like 'Building rate'), and thin lines represent information links. Valves on flow arrows indicate control points.
Explicit lags between cause and effect. In this housing model, there is a 3-month delay for construction and a 30-month delay for sales. These delays prevent instantaneous adjustment to changes in demand or supply.
A regulatory mechanism where the system compares its current state against a target ('GOAL = 10,000'). The difference ('Gap') drives adjustments in inflow rates (like 'Building rate') to reduce the discrepancy over time.
Explore conditions, steps and evidence. Supplementary explanations are labeled separately from content shown in the video.
Whiteboard shows a rectangular stock labeled "Houses".
Houses
Stock of finished houses in the system dynamics model.
Count of completed houses.
Whiteboard shows a valve/flow labeled "Builders" entering the Houses stock.
Builders
Inflow rate representing builders starting construction.
Whiteboard shows "Smooth Adj Time" connected to the Builders flow.
Smooth Adj Time
Adjustment time parameter controlling how quickly builders respond to the gap.
Whiteboard shows "Gap (Land for houses)" feeding into the Builders flow.
Gap
Difference between desired housing/land and current stock, driving construction.
Whiteboard shows "GOAL (Population)" pointing toward the Gap.
Goal
Target population or housing requirement used to compute the gap.
Lecturer writes "House WIP" inside the former Houses box.
Lecturer says it becomes a house work in progress, WIP.
House WIP
Stock of houses under construction, introduced to represent building delay.
Count of unfinished houses.
Lecturer draws an outflow from House WIP and labels it "Completing houses".
Lecturer says after 12 months they are completing the houses.
Completing houses
Outflow rate from House WIP to finished houses.
Rectangular box labeled 'House WIP'
House WIP
Stock representing the number of houses currently under construction (Work In Progress).
Non-negative integer count of houses.
Rectangular box labeled 'Finished Houses'
Finished Houses
Stock representing the cumulative number of completed houses.
Non-negative integer count of houses.
Text label 'Gap' with an arrow pointing to it from 'Goal (Population)' and 'Finished Houses'
Gap
Difference between the target population (goal) and the current number of finished houses.
Number of households/families.
Text label 'Goal (Population)'
Goal (Population)
Target number of households or families that need housing.
Number of households/families.
Text label '3 months Adj Time'
3 months Adj Time
Adjustment time parameter for the builders' goal closing rate.
Time in months.
Lecturer says houses do not just appear; they take time to be built, with one year as the building time in the model.
The model includes a delay because construction is not instantaneous. In this simplified version, one year passes between starting a house and finishing it.
Model assumes a fixed building time of one year.
Real-world construction could take longer.
Lecturer explains handling delay by doing a work in progress notion, with a stock of houses being built but not yet finished.
Later whiteboard edit labels the first stock as House WIP.
A work-in-progress stock holds items that have entered the process but have not yet become final output. Here it represents houses under construction.
Used when a flow does not immediately produce the final stock.
Lecturer says the delay is almost a chain of stocks, in this case just a two chain: house in progress and finished house.
Delays can be represented by chaining stocks so material moves from one stock to the next over time. This example uses a two-stock chain.
At least one intermediate stock is needed before the final stock.
Speaker explains adding stocks for Work in Progress and Finished Houses.
Whiteboard shows boxes for 'House WIP' and 'Finished Houses' connected by flows.
The system is modeled using stocks (accumulations) and flows (rates of change). 'House WIP' accumulates via 'Building houses' and depletes via 'Completing houses'. 'Finished Houses' accumulates via 'Completing houses'.
Stocks represent quantities at a point in time.
Flows represent rates of change over time.
Speaker states 'once you're up and running, you're going to complete one twelfth of this inventory... each month.'
Valve symbol labeled 'Completing houses' with 'Completion Time' parameter.
Delays in processes (like building a house) are represented by inserting a stock (Work In Progress) between the inflow and outflow. The outflow rate is calculated as the stock level divided by the average delay time.
Assumes a first-order delay or exponential distribution of completion times.
Applicable when the process has a significant duration.
Whiteboard diagram showing boxes (stocks), valves (flows), and arrows (information links).
A system dynamics model uses stocks (boxes) to represent accumulations, flows (valves) to represent rates of change, and information links (arrows) to show how variables influence decisions.
Stocks accumulate over time.
Flows change the level of stocks.
Information links transmit values without material flow.
Speaker explains dividing the stock by the average time to find the monthly rate, e.g., per month.
In first-order delays, the outflow rate is calculated by dividing the current stock level by the average delay time (time constant). This represents the fraction of the stock that turns over per unit time.
Assumes exponential aging or a first-order linear delay approximation.
Time must be expressed in the same units as the desired rate (e.g., months).
Speaker states: 'So that is a stock and flow diagram...'
Whiteboard displays boxes (stocks), arrows (flows), valves, and information links.
A visual representation used in system dynamics to model accumulations (stocks) and the rates of change (flows) between them. Stocks are depicted as rectangles, flows as thick arrows with valves, and auxiliary variables or goals as circles or text annotations connected by thin information links.
Used to represent dynamic systems over time.
Annotations '3 months Avg Time' and '30 months (sales)' indicate time delays in the processes.
The elapsed time between an action (e.g., starting construction) and its result (e.g., completing a house). In the diagram, delays are explicitly annotated on the stocks, affecting how quickly the system responds to changes in flow rates.
Delays cause lagged responses in the system state.
Speaker mentions: 'as the system tries to reach 10,000 houses.'
Diagram includes 'GOAL (10,000)' and 'Gap' feeding into decision logic.
A control mechanism where the system adjusts its inflow rates based on the discrepancy (gap) between a desired target (goal) and the current state. Here, the building rate is influenced by the gap between the goal of 10,000 houses and the actual number of finished houses.
Requires a defined target and a measurable current state.
Lecturer states that for this model the delay can be handled as a two-chain of stocks.
For this housing model, a two-stock chain consisting of House WIP and finished houses is adequate to represent the one-year building delay.
Building time is modeled as one year.
Only a simple delay representation is required.
For the model under discussion.
Speaker states: 'mathematically that is equivalent... might sound funny, but that's been proven to be equivalent.'
The specific mathematical proof is not shown, only asserted.
Modeling a stock with an average lifetime of T months is mathematically equivalent to applying a fractional decay rate of per month.
The system is modeled using continuous first-order differential equations.
For any stock with a defined average lifetime T.
Lecturer says once builders start building, it does not become a house; it becomes a house work in progress, then after 12 months they are completing the houses.
Lecturer edits the diagram: changes Houses to House WIP, draws an outflow, and labels it Completing houses.
The finished-house stock itself is not fully drawn before the clip ends.
Keep the existing goal-to-gap-to-builders control structure unchanged.
Lecturer says the rest of this is okay: you have a goal, a gap to the goal, and that drives builders to build.
Change the destination of the Builders inflow from finished houses to a work-in-progress stock.
Lecturer says once they start building, it does not become a house; it becomes a house work in progress, WIP.
Add an outflow from House WIP labeled Completing houses.
Lecturer says after 12 months they are completing the houses.
The delayed construction process is represented by moving new starts into House WIP and then transferring completed units out through a completion flow.
Speaker derives the completion rate: 'complete one twelfth of this inventory... each month' and 'stock divided by the time is the amount you're going to complete'.
Arrow from 'House WIP' to 'Completing houses' valve.
The average time to complete a house is given as 12 months.
Stated by speaker and written on board.
The rate at which houses are completed is the current inventory of work-in-progress divided by the average completion time.
Standard system dynamics formulation for a first-order delay.
Substituting the value, the rate is th of the WIP stock per month.
Arithmetic substitution.
The flow 'Completing houses' is determined by dividing the 'House WIP' stock by the 'Completion Time' (12 months).
Speaker derives the decay rate: 'take the stock divided by the 36 months... one thirty-sixth of those houses are going to decay each month.'
Divide the current stock of finished houses by the average lifetime of 36 months.
Definition of average delay/time constant.
This implies that th of the existing houses decay every month.
Algebraic rearrangement of the rate equation.
The scrap/decay flow is proportional to the Finished Houses stock with a coefficient of .
Lecturer uses the housing model with one-year building time as the example throughout.
Whiteboard contains Goal, Gap, Builders, Smooth Adj Time, Houses/House WIP, and Completing houses.
No numerical values are shown for goal, gap, or rates.
Modify a stock-and-flow housing model so that construction delay is explicitly represented.
There is a goal related to population.
There is a gap driving builders.
Builders form an inflow.
Construction takes one year in the model.
Introduce a work-in-progress stock and completion flow to represent delayed house construction.
Recognize that houses do not appear instantly when builders start them.
Stated directly by the lecturer.
Create a stock for houses under construction, labeled House WIP.
This is the work-in-progress notion introduced for delays.
Route the Builders inflow into House WIP instead of directly into finished houses.
Starting construction adds to the unfinished stock.
Add a Completing houses outflow from House WIP after the one-year delay.
After 12 months, houses are completed.
The revised model uses a two-stock chain: House WIP followed by finished houses, linked by a completion flow.
The verbal explanation matches the whiteboard edits visible in the clip.
Speaker gives numbers: '1,000 houses finished... 10,000 people families that want it... gap is 9,000'.
Determine the 'Gap' given specific values for Goal and Finished Houses.
Goal (Population) = 10,000 families
Finished Houses = 1,000 houses
Calculate the Gap.
The gap is defined as the difference between the target population and the current supply.
Definition of Gap in the model.
Substitute the given values.
Arithmetic substitution.
Perform the subtraction.
Arithmetic calculation.
The Gap is 9,000 families.
Matches the speaker's verbal statement.
Complete whiteboard diagram of the housing market model.
Speaker walks through the parameters: 3 months avg time, 12 months build time, 36 months life.
Model the dynamics of house construction, completion, and decay over time.
Average time to attend to gap: 3 months
Average time to build a house: 12 months
Average lifetime of a house: 36 months
Define the flow rates based on stock levels and time constants.
Calculate the rate at which houses finish construction.
First-order delay formulation using the 12-month build time.
Calculate the rate at which houses are scrapped.
First-order delay formulation using the 36-month lifetime.
The model uses fractional turnover rates ( and per month) applied to their respective stocks to determine flow speeds.
Consistent with the speaker's explanation of dividing stock by average time.
Complete whiteboard drawing showing House WIP, Finished Houses, rates, delays, and goal.
Speaker refers to 'this particular stock and flow diagram' and 'reach 10,000 houses'.
Model the dynamics of a housing market where construction takes time and sales take time, aiming for a specific inventory level.
Stocks: House WIP, Finished Houses
Flows: Building rate, Completion rate, Sales rate
Delays: 3 months for construction, 30 months for sales
Goal: 10,000 finished houses
Understand how the system behaves when trying to reach the goal given the delays.
Identify stocks and flows in the diagram.
Visual inspection of whiteboard.
Note the time delays associated with each stock.
Annotations '3 months' and '30 months' visible on board.
Observe the feedback loop involving the Goal and Gap.
Arrows connect GOAL and Gap to the Building rate.
The system exhibits delayed response due to construction and sales times, potentially leading to oscillations around the 10,000 house goal.
Consistent with video title 'Delays and Oscillation' and speaker's intent to enhance the model.
Initial whiteboard shows a stock labeled Houses with inflow Builders, plus Smooth Adj Time, Gap (Land for houses), and GOAL (Population).
Houses stock
Builders inflow
Smooth Adj Time
Gap (Land for houses)
GOAL (Population)
The control path from goal to gap to builders remains visible.
The original stock label is Houses before revision.
This is the pre-revision model in which construction appears to feed directly into the Houses stock.
Lecturer turns to the board, erases part of the Houses label, writes House WIP, draws a rightward outflow, and labels it Completing houses.
The downstream finished-house stock is not fully drawn within this clip.
House WIP stock
Builders inflow
Completing houses outflow
Gap
GOAL (Population)
Houses is relabeled as House WIP.
A new outflow arrow is added from the WIP stock.
The outflow is labeled Completing houses.
The upstream goal-gap-builders structure stays in place.
Builders still enters the first stock.
The visual edit implements the delay by separating construction start from completion.
Speaker draws a new rectangular box labeled 'Finished Houses' to the right of the existing diagram.
Speaker says 'move from a work in progress house to a finished house'.
Whiteboard marker
'Finished Houses' box
New stock box is drawn.
Arrow connects 'Completing houses' flow to the new box.
Existing 'House WIP' stock remains unchanged.
This visual step introduces the final accumulation point in the production chain, separating the concept of 'in progress' from 'completed'.
Speaker erases part of the previous connection to 'Gap' and draws a new arrow from 'Finished Houses' to 'Gap'.
Speaker says 'The gap is really identified from the number of finished houses relative to the population'.
Eraser
Arrows
'Gap' label
'Finished Houses' box
Connection source for 'Gap' changes from 'House WIP' (implied previously) to 'Finished Houses'.
'Goal (Population)' remains a source for 'Gap'.
This corrects the model logic: the shortage (gap) should be measured against actual completed supply, not work-in-progress.
Speaker draws a valve exiting the 'Finished Houses' box and labels it 'Scrap/decay'.
Finished Houses box
Valve symbol
Sink cloud
A new outflow is added to the Finished Houses stock.
The structure of the previous stocks remains unchanged.
Introduces the concept that finished goods leave the system over time, creating a new demand gap.
Speaker writes '36 months (life)' next to the decay valve.
Text annotation
Numerical parameter 36 is assigned to the decay process.
The valve symbol itself does not change.
Defines the time constant for the decay flow.
Static shot of whiteboard with hand-drawn system dynamics model.
House WIP box
Finished Houses box
Building rate arrow
Completion rate arrow
Sales rate arrow
GOAL circle
Gap label
None; static image throughout the clip.
Relative positions of all diagram elements remain constant.
Provides the structural basis for discussing delays and goal-seeking behavior in the system.
Lecturer says houses do not just appear; they take time to be built.
One might think the Builders inflow immediately creates finished houses.
The lecture explicitly introduces a delay and a House WIP stock because started houses are not finished houses yet.
Speaker explicitly rewires the model, stating the gap comes from finished houses, implying a previous state or common error where it might come from WIP.
Thinking that the 'Gap' (shortage) should be calculated based on houses currently being built (WIP).
The 'Gap' represents unmet demand, so it must be calculated based on 'Finished Houses' (actual supply) versus the 'Goal'.
Speaker notes: 'might sound funny, but that's been proven to be equivalent.'
Learners may find it strange that a house lasting 36 months translates to exactly th of houses decaying each month, expecting a fixed number instead.
In continuous system dynamics models, exponential decay is the standard assumption for delays, making the fractional rate mathematically equivalent to the average lifetime.
Lecturer links the need to handle time delay to the work-in-progress notion.
The work-in-progress stock is the modeling device used to represent construction delay.
Lecturer describes the delay as almost a chain of stocks, here a two chain.
The housing example is a special case of delay modeling using a chain of stocks, here reduced to two stocks.
The board edit turns the single Houses stock into House WIP plus a completion outflow.
The abstract two-stock chain idea is applied concretely in the revised whiteboard diagram.
Discussion of 'work in progress bucket' and 'completion time'.
The method of representing delays (ki_delay_representation) is applied within the broader framework of Stock and Flow modeling (ki_stock_flow_model).
Speaker repeatedly refers to 'average time' as the divisor for stocks.
The time constant formula is the mechanism used to calculate flow rates within the stock and flow structure.
Delays are attached to stocks which mediate flows.
Speaker discusses enhancing the model to see changes as system reaches goal.
Time delays inherent in the construction and sales processes directly impact the effectiveness and stability of the goal-seeking feedback loop.
Lecturer defines the work in progress notion for houses being built but not finished.
Lecturer explains that delay is handled by a chain of stocks and then draws it.
Lecturer says once they start building, it does not become a house; it becomes a house work in progress.
Explanation of WIP and completion time.
Calculation of gap using 10,000 and 1,000.
Explanation of dividing stock by 36 months.
Statement about mathematical equivalence.
'So that is a stock and flow diagram...'
Annotations showing '3 months' and '30 months'.
'...as the system tries to reach 10,000 houses.'
Covered · Lecturer introduces the need to account for construction delay in the housing model.
Covered · Lecturer explains work in progress and the two-stock chain representation of delay.
Covered · Lecturer revises the whiteboard diagram by relabeling Houses as House WIP and adding Completing houses.
Covered · Full segment covers the addition of the Finished Houses stock, rewiring the Gap calculation, and defining the completion rate based on WIP and delay time.
Covered · Review of existing model components and completion rate calculation.
Covered · Introduction and drawing of the scrap/decay flow and its time parameter.
Covered · Mathematical derivation of the decay rate and discussion of its equivalence to average lifetime.
Covered · Entire clip presents a static whiteboard diagram while the speaker introduces the concept of using this stock-and-flow model to analyze delays and goal-seeking behavior.
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