Stocks Inside Feedback

Stock & flow diagramsPart III · Accumulation · Chapter 7 of 12 · the second of two chapters on stock & flow diagrams

Where do things wait on their way through a system? In stocks, between the flows that fill and drain them. A stock & flow diagram with loops shows which loops pass through each stock, where material waits along a chain of stocks, and which delays hold material and which hold news of it.

Print this chapter, with a sheet for each exercise and the answers at the back, from its PDF.

A flu season in a region

A new strain of flu reaches a region of a million people, none of whom has had it. Each day people who are ill meet people who have never had it, and some of those catch it. Each person who falls ill is ill for about a week, then recovers and doesn’t catch this strain again that season.

Reported cases reach the news a week after people fall ill. As the reports rise, people stay home and keep apart, and fewer fall ill.

The number of people ill rises for weeks, peaks and falls away. When the season ends, some people have never caught it.

What the notation expresses

Loops through stocks

A loop through a stock is a loop whose path runs along one of the stock’s flows: a signal from the stock reaches the flow’s valve, directly or through auxiliaries, and the flow changes the stock. The parity rule counts the flow as one step: + from the flow into the stock it fills, − from the flow out of the stock it drains.

Infectious contacts are meetings between someone ill and someone susceptible, so they rise with both stocks. Three loops run through falling ill:

R1, contagion: people ill → infectious contacts → falling ill, which fills people ill. No − step: reinforcing.
B1, depletion: people susceptible → infectious contacts → falling ill, which drains people susceptible. One − step: balancing.
B2, caution: people ill → reported cases → caution → infectious contacts (−) → falling ill, which fills people ill. One − step: balancing.

Falling ill counts + in R1 and − in B1, since it fills one stock and drains the other.

Loop dominance shifts as stocks fill and empty. Early in the season nearly everyone is susceptible, R1 dominates, and people ill grows exponentially. As people susceptible empties, each person ill meets fewer people who can catch flu; B1 dominates, falling ill drops below recovering, and people ill falls.

Conservation

Falling ill and recovering are transfers, and the diagram has no cloud, so everyone who leaves one stock arrives in the next. The three stock equations,

change in people susceptible = − falling ill

change in people ill = falling ill − recovering

change in people recovered = recovering

add up to zero: the three stocks always total the region’s million people.

Births, deaths and moves are left out. Drawn in, each would run from a source or to a sink, and people would cross the region’s boundary only along those flows. An external driver reaches a stock through a signal to an auxiliary or a valve, never to the stock: if school holidays cut contacts, ‹school holidays› → infectious contacts is −.

Evidence coding marks signals only. A flow is never dashed: that people move from susceptible to ill isn’t in question, only how fast, which the signals into its valve set.

Aging chains

An aging chain is a row of stocks joined by transfers, through which material passes in order: people susceptible, then ill, then recovered.

The time material spends in a stock is a delay. Someone who falls ill on a Monday is counted in people ill until about the next Monday, so a rise in falling ill shows in recovering about a week later, on average. People ill → recovering is +: with each person ill for about a week, about a seventh of those ill recover each day. Recovering carries no delay: the stock holds the week, and a delay on the flow would count it twice.

Material and signal delays

A delay in a stock & flow diagram, the two strokes of chapter 4’s delays, sits on a flow or on a signal. A material delay, on a flow, holds material in transit, in neither stock: grain at sea between a port and a mill. A signal delay, on a signal, holds news: the people are already ill, and the reading of how many arrives late. People ill → reported cases carries a signal delay of a week.

Caution is set by reported cases, a reading of people ill a week old, so after people ill peaks, reported cases and caution go on rising for about a week, and caution is highest once fewer people are ill.

Check your understandingAn office orders printer paper by the box. A box arrives five days after it is ordered, and the office manager counts the boxes in the cupboard only on Fridays, then orders from that count. Which of these is a signal delay?

the five days between ordering a box and its arrival

Not quite. That is a material delay: for those five days the box is in transit, in neither the supplier's stock nor the cupboard. It is marked on the flow of deliveries.

the days between a box leaving the cupboard and the Friday count

Yes. The box has already left the cupboard; only the count of it is late. The delay is marked on the signal from the boxes in the cupboard to orders.

the time a box spends in the cupboard before it is used

Not quite. That is the time spent in a stock. The cupboard holds the box for that time, so no delay is drawn for it.

Capacity limits

A stock’s capacity is the most it can hold. As the stock nears it, the flow into it slows sharply: a nonlinear effect on a signal from the stock to its own inflow, its threshold an amount the stock holds. If the flu filled the region’s hospital beds, people in hospital → admissions would be − and nonlinear: weak while beds are free, strong as the last ones fill.

The bad diagram

What’s wrong with this diagram of a town library’s books, lent from the shelves, returned to a trolley and reshelved?

The books on the shelves, on loan and in the returns trolley are three stocks, but lending runs from the shelves to a cloud, borrowing from a cloud into the books on loan, returning to a cloud and dropping off from a cloud. Between each stage and the next the same books leave the model and come back into it, so the three stocks’ total can rise or fall with no book bought or lost. The lab’s check for at least three transfers reports:

No transfers. Brief: at least 3. A transfer runs from one stock straight into another, with no cloud between them.

The corrected diagram

Corrected, lending, returning and reshelving are transfers around the three stocks; purchases arrive from a source and lost books leave to a sink, so each book is counted in one stock from the day it is bought until it is lost.

Bad diagram

Corrected diagram

Labels unchanged. Flows: 3 added, 2 removed, lending now ends at books on loan instead of a cloud, returning now ends at books in the returns trolley instead of a cloud.

Notation moves

Notation move	When	What it shows	Example
Declare a loop through a flow	A signal from a stock reaches the valve of one of its own flows	Which loops change the stock, and through which flow	R1 contagion, through falling ill

Chain stocks with transfers	Material passes through stages in order	Where it waits, with none lost between stages	people susceptible → people ill → people recovered

Mark a signal delay	A reading arrives well after what it reads	News running behind a stock	people ill → reported cases

Mark a material delay	Material is in transit between stocks	Material in neither stock	grain shipped to a mill

Mark a nonlinear signal from a stock to its inflow	A stock nears the most it can hold	Where the capacity lies	people in hospital → admissions

Graph a stock in a loop		The shape the shifts in dominance produce	people ill, overshoot and collapse

Common misreading

Reading a stock’s graph as the shape of its inflow, the stock highest when the inflow is fastest, is the correlation heuristic (Cronin, Gonzalez and Sterman, 2009). Falling ill peaks first. At its peak more people still fall ill each day than recover, so people ill goes on rising; it peaks later, on the day falling ill has dropped to equal recovering.

Shown graphs of people entering and leaving a department store each minute, 96 percent of 173 graduate students in a business simulation course at MIT found the minute the most people entered, and 44 percent the minute the most people were in the store; 29 percent chose the minute of the largest net flow into the store.

The strongest objection

Without equations and simulation, a stock & flow diagram is a causal loop diagram with boxes: when loops trade dominance, and how far a stock overshoots, depend on numbers the diagram doesn’t hold. Homer and Oliva (2001), answering Coyle (2000), argue that simulation lets a modeler draw behavioral inferences reliably “in a way that is rarely possible with maps alone”.

A behavior-over-time graph drawn from the structure is a hypothesis until the model is simulated or the system measured: the graph of people ill shows an overshoot and collapse, not how high it peaks or in which week.

Units and conservation are checked on the drawing, before any number. The lab’s checks catch a transfer between stocks in different units, books that vanish between the shelves and the loans, and a signal drawn into a stock; a causal loop diagram has no mark they could catch.

Check your understanding

Check your understandingSkiers join the queue for a chairlift at 10 a minute at 8:30, at 60 a minute at 9:30, and at 10 a minute again by 11:00. The lift carries 30 skiers a minute all morning. When is the queue longest?

at 9:30, when skiers join fastest

Not quite. That reads the queue's graph as the shape of its inflow. At 9:30, 60 skiers join a minute and 30 leave, so the queue is still growing by 30 a minute.

after 9:30, when joining has fallen back to 30 a minute

Yes. The queue grows while more skiers join than the lift carries, and shrinks once fewer do, so it is longest when joining equals the lift's 30 a minute.

at 11:00, when joining is slowest

Not quite. By 11:00, 10 skiers join a minute and 30 leave, so the queue has been shrinking since joining fell below 30 a minute.

Waits for heart attack care, redrawn

Redrawn from Luciano de Andrade, Catherine Lynch, Elias Carvalho, Clarissa Garcia Rodrigues, João Ricardo Nickenig Vissoci, Guttenberg Ferreira Passos, Ricardo Pietrobon, Oscar Kenji Nihei and Maria Dalva de Barros Carvalho, “System Dynamics Modeling in the Evaluation of Delays of Care in ST-Segment Elevation Myocardial Infarction Patients within a Tiered Health System”, PLOS ONE 9(7): e103577 (2014), Figure 4. CC BY 4.0.

Its four stages, first medical contact (FMC), ECG and diagnosis (ECG), the ECG sent by fax to the PCI center, where the blocked artery is opened, and its reply (TXF), and the wait for transfer there (TWT), named for the patients at each; each Retained stock named for the patients held there, and its retain and back flows renamed retaining and returning; each output named for where its patients go, the last door out; its auxiliaries and their signals left out; its B1 to B4, each labeled inside a stage’s path of retaining and returning, which carries no signal, each drawn as the loop through the signal from its stage’s patients to their outflow, which it draws, and named moving on; the chain drawn downward.

Question 1 of 3A patient reaches the first hospital at two o’clock and leaves for the PCI center at four. Where in the diagram are those two hours spent?

In the flows, since a flow is the patient moving from one stage to the next.

Not quite. A flow is a rate, patients a minute, and holds no one at an instant. Every patient counted at an instant is in one of the eight stocks.

In the loops B1 to B4, since each loop keeps patients until they move on.

Not quite. A loop is a closed path, here a signal and a flow: it sets how fast patients leave a stage, and holds no one. Patients wait only in stocks.

In the stocks: at each stage in turn, and in a held stock wherever the patient is held.

Yes. A stock is where material waits between the flows that fill and drain it. The four stages are an aging chain, passed through in order, and a stay in a held stock adds to the time at its stage until returning brings the patient back.

Question 2 of 3B2 runs from patients at the ECG to the valve of to fax, the flow that drains them. What does B2 do to patients at the ECG?

The more patients at the ECG, the faster they leave for the fax, so a rise in that stock comes back against itself.

Yes. The signal is +, and to fax counts − from the flow into the stock it drains: one − step, so B2 is balancing. The stock settles where its outflows run as fast as its inflows.

It holds the patients’ wait at the guidelines’ optimal time, the value the authors compare each wait with.

Not quite. No target is drawn: no variable holds a chosen time, and nothing compares one with the wait. B2 drains the stock faster the fuller it is, and no more.

It makes patients at the ECG grow, since more of them send more on to the fax.

Not quite. More patients sent on is a faster outflow from patients at the ECG, which lowers it. The rise is in patients at the fax, the next stock along.

Question 3 of 3At the fax stage, 76% of the patients the authors followed waited longer than the optimal time. Where does a patient’s wait at that stage appear in the diagram?

As a material delay on to transfer, for patients between the two stages.

Not quite. A material delay holds material in neither stock, as grain at sea is. These patients wait at the fax stage, counted in its stocks; moving on to transfer takes no time of its own.

As the time a patient spends in patients at the fax and in patients held at the fax, with no delay drawn.

Yes. The time material spends in a stock is a delay already, so a delay drawn on to transfer would count the wait twice. A patient held adds the time in the held stock.

As a signal delay on patients at the fax → to transfer, since the reply from the PCI center arrives late.

Not quite. A signal delay holds news of a quantity. The reply is what the patients wait for, and the patients themselves sit in the stock, counted there until they move on.

Exercises

Passing the checks means meeting the brief, not being right.

SF 06Players of an online game

Stocks embedded in feedback

Reasoning3 of 5
Polish4 of 5

Players around the world join an online puzzle game only by invitation: each day about one player in fifty invites a friend, who joins. Matches run on a fixed number of servers, so the more players there are, the longer each waits for a match, and the longer the wait, the more players quit each day. Count the stock in players, and time in days.

The brief

Draw two flows: players joining, and players quitting. checked by the lab
Declare one reinforcing loop. checked by the lab
Declare one balancing loop. checked by the lab
Run each loop through a flow, so that it passes through the stock. checked by the lab
Each loop is named for what goes around it, such as word of mouth or queue frustration. you check this

Your palette

stock
flow
cloud
auxiliary
signal
polarity
loop
reinforcing loop
balancing loop

To draw in the lab, use a tablet or a larger screen. Everything else reads normally here.

Press an empty spot to add an auxiliary and type its name. Drag a stock, an auxiliary, a cloud or a graph to move it. Select anything drawn to change it. Double-click or double-tap a stock's name or units, an auxiliary, a flow's name or a loop's label or name to edit its words in place, or select it and use Rename or the fields under the canvas.

Nothing selected. Select a stock, an auxiliary, a flow, a signal, a cloud or a loop label on the canvas, and what you can change shows here.

The tools

Auxiliaries V: add an auxiliary (press an empty spot), move a stock, an auxiliary, a cloud or a graph (drag it), rename one (double-click it, or Rename under the canvas), or select anything.
Stocks S: add a stock (press an empty spot) and name it.
Flows M: draw a flow by dragging from a stock or an empty spot to a stock or an empty spot, and name it; clouds appear at empty ends.
Signals E: draw a signal by dragging from a stock, an auxiliary or a flow's valve to an auxiliary or a flow's valve.
Loop L: declare a loop by selecting its signals and flows in order, then label and name it.

Keys

R reverse the selected signal or flow
+− the selected signal's polarity
Delete delete what's selected
Ctrl+Z undo
Ctrl+Shift+Z redo
Esc clear the selection
Enter finish the words you're writing
Esc cancel them

Keys act on the lab you last used, or on the open lab view, and never while you type.

0 of 11 checks passed; 11 pending.

Draw two flows: players joining, and players quitting. (Not started)No flows yet. Brief: exactly 2.
Declare one reinforcing loop. (Not started)No loop declared yet. Brief: exactly 1 reinforcing loop.
Declare one balancing loop. (Not started)No loop declared yet. Brief: exactly 1 balancing loop.
Run each loop through a flow, so that it passes through the stock. (Not started)No loop declared yet. Brief: every loop through a stock.
Each loop is named for what goes around it, such as word of mouth or queue frustration. You check this.

Always checked

Each loop's kind matches its − effects (Not started)No loop declared yet.
Loop labels are unique and match their kind (Not started)No loop declared yet.
Every stock has units (Not started)No stock drawn yet.
The time unit is given (Not started)No flow drawn yet.
Every stock has a flow in or out (Not started)No stock drawn yet.
Every flow has a name (Not started)No flow drawn yet.
No variable's name breaks the more test's three rules (Not started)No variable drawn yet.

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SF 07Dogs at a rescue shelter

Capacity and nonlinear rates

Reasoning4 of 5
Polish4 of 5

A town's dog rescue shelter has 40 places. Owners and the council refer about eight dogs a week to its waiting list, and owners withdraw about one a week after finding a home elsewhere. Staff take dogs in from the list, but intake slows sharply as the places fill: about six dogs a week while 30 are in care, almost none at 38. Crowding lengthens stays: a dog waits about four weeks for adoption while the shelter is half full, seven while it is full. The manager proposes recruiting foster homes, each adding a place. Count both stocks in dogs, and time in weeks.

The brief

Draw two stocks: dogs on the waiting list, and dogs in care. checked by the lab
Join them with intake, a transfer. checked by the lab
Mark the signal by which filling places slow intake as nonlinear. checked by the lab
Mark what foster homes would add to as the one leverage point. checked by the lab
The nonlinear signal reaches intake through occupancy. you check this

Your palette

stock
flow
cloud
auxiliary
signal
polarity
nonlinear effect
leverage point

To draw in the lab, use a tablet or a larger screen. Everything else reads normally here.

Press an empty spot to add an auxiliary and type its name. Drag a stock, an auxiliary, a cloud or a graph to move it. Select anything drawn to change it. Double-click or double-tap a stock's name or units, an auxiliary or a flow's name to edit its words in place, or select it and use Rename or the fields under the canvas.

Nothing selected. Select a stock, an auxiliary, a flow, a signal or a cloud on the canvas, and what you can change shows here.

The tools

Auxiliaries V: add an auxiliary (press an empty spot), move a stock, an auxiliary, a cloud or a graph (drag it), rename one (double-click it, or Rename under the canvas), or select anything.
Stocks S: add a stock (press an empty spot) and name it.
Flows M: draw a flow by dragging from a stock or an empty spot to a stock or an empty spot, and name it; clouds appear at empty ends.
Signals E: draw a signal by dragging from a stock, an auxiliary or a flow's valve to an auxiliary or a flow's valve.

Keys

R reverse the selected signal or flow
+− the selected signal's polarity
Delete delete what's selected
Ctrl+Z undo
Ctrl+Shift+Z redo
Esc clear the selection
Enter finish the words you're writing
Esc cancel them

Keys act on the lab you last used, or on the open lab view, and never while you type.

0 of 10 checks passed; 10 pending.

Draw two stocks: dogs on the waiting list, and dogs in care. (Not started)No stocks yet. Brief: at least 2.
Join them with intake, a transfer. (Not started)No flows yet. Brief: at least 1 transfer.
Mark the signal by which filling places slow intake as nonlinear. (Not started)No signals yet. Brief: at least 1 nonlinear signal.
Mark what foster homes would add to as the one leverage point. (Not started)No variables yet. Brief: exactly 1 leverage point.
The nonlinear signal reaches intake through occupancy. You check this.

Always checked

Every stock has units (Not started)No stock drawn yet.
The time unit is given (Not started)No flow drawn yet.
Every stock has a flow in or out (Not started)No stock drawn yet.
Every flow has a name (Not started)No flow drawn yet.
Each transfer joins stocks in the same units (Not started)No transfer drawn yet: a flow from one stock straight into another.
No variable's name breaks the more test's three rules (Not started)No variable drawn yet.

Written feedback

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SF 08Seedlings raised on a windowsill

Aging chain

Reasoning4 of 5
Polish4 of 5

Amira raises tomatoes and peppers from seed on her kitchen windowsill. Each spring she sows about 60 seeds in trays; about one in five fails to sprout, and the rest come up within two weeks. Seedlings grow on the sill for about five weeks, and a few die of damping off. Before going into the garden, each seedling spends exactly ten days in a cold frame, hardening off, and cold nights kill a few there. The cold frame holds 24, so seedlings wait on the sill until it has room. Count every stage in seedlings, a seed counted from the day it is sown, and time in days.

The brief

Draw a stock for each stage: sown in trays, seedlings on the sill, in the cold frame, planted out. checked by the lab
Chain the stages with transfers, so a seedling leaving one arrives in the next. checked by the lab
Mark the ten days in the cold frame as a material delay. checked by the lab
Add a behavior note. checked by the lab
Where seedlings pile up, and why, is in the note. you check this

Your palette

stock
flow
cloud
delay
behavior note

To draw in the lab, use a tablet or a larger screen. Everything else reads normally here.

Drag a stock, a cloud or a graph to move it. Select a stock, a flow, a cloud or a graph to change it. Pressing an empty spot adds nothing. Drag a behavior note to move it. Double-click or double-tap a stock's name or units, a flow's name or a behavior note to edit its words in place, or select it and use Rename or the fields under the canvas.

Nothing selected. Select a stock, a flow, a cloud or a behavior note on the canvas, and what you can change shows here.

The tools

Arrange V: move a stock, a cloud or a graph (drag it), rename a stock (double-click it, or Rename under the canvas), or select anything.
Stocks S: add a stock (press an empty spot) and name it.
Flows M: draw a flow by dragging from a stock or an empty spot to a stock or an empty spot, and name it; clouds appear at empty ends.
Note N: place a behavior note (press where it goes).

Keys

R reverse the selected flow
Delete delete what's selected
Ctrl+Z undo
Ctrl+Shift+Z redo
Esc clear the selection
Enter finish the words you're writing
Esc cancel them

Keys act on the lab you last used, or on the open lab view, and never while you type.

0 of 9 checks passed; 9 pending.

Draw a stock for each stage: sown in trays, seedlings on the sill, in the cold frame, planted out. (Not started)No stocks yet. Brief: at least 4.
Chain the stages with transfers, so a seedling leaving one arrives in the next. (Not started)No transfer yet. Brief: at least 4 stocks in the longest chain.
Mark the ten days in the cold frame as a material delay. (Not started)No flows yet. Brief: exactly 1 material delay.
Add a behavior note. (Not started)No flow drawn yet. Once one is, add a behavior note naming how the stocks change over time.
Where seedlings pile up, and why, is in the note. You check this.

Always checked

Every stock has units (Not started)No stock drawn yet.
The time unit is given (Not started)No flow drawn yet.
Every stock has a flow in or out (Not started)No stock drawn yet.
Every flow has a name (Not started)No flow drawn yet.
No variable's name breaks the more test's three rules (Not started)No variable drawn yet.

Written feedback

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SF 09A city's bike-share fleet

Multiple stocks, a boundary and evidence

Reasoning5 of 5
Polish5 of 5

A city's bike-share scheme has docks on a hilltop and by the river. Riders seldom pedal uphill, so rides between the two run downhill and bikes collect at the riverside docks; on rainy days about a third fewer bikes are ridden. Vans collect bikes from the riverside docks and bring them to the scheme's workshop, where mechanics check and repair them; the vans then deliver them to the hilltop docks. Bikes beyond repair are scrapped. Staff record rides, collections and deliveries each day. They believe the vans deliver more bikes the lower the hilltop docks run, but nobody has checked. Rain, and scrapped bikes once they leave, lie outside the scheme. Count every stock in bikes, and time in days.

The brief

Draw a stock for each place bikes wait: the hilltop docks, the riverside docks, the workshop. checked by the lab
Join the stocks with transfers, so no bike appears or vanishes between them. checked by the lab
Declare a balancing loop through the vans' deliveries. checked by the lab
Draw the scheme's boundary, with rain outside it as an external driver. checked by the lab
Code the signal you judge less supported as a hypothesis. checked by the lab
Rain's signal rests on ride counts and is solid; the vans' response, a belief, is the hypothesis, and the legend shows the coding. you check this

Your palette

stock
flow
cloud
auxiliary
signal
polarity
loop
balancing loop
boundary
external driver
evidence coding

To draw in the lab, use a tablet or a larger screen. Everything else reads normally here.

Press an empty spot to add an auxiliary and type its name. Drag a stock, an auxiliary, a cloud or a graph to move it. Select anything drawn to change it. Drag a boundary by its outline or its name to move it, and by the square at its corner to resize it. Double-click or double-tap a stock's name or units, an auxiliary, a flow's name, a loop's label or name or a boundary's name to edit its words in place, or select it and use Rename or the fields under the canvas.

Nothing selected. Select a stock, an auxiliary, a flow, a signal, a cloud, a loop label or a boundary on the canvas, and what you can change shows here.

The tools

Auxiliaries V: add an auxiliary (press an empty spot), move a stock, an auxiliary, a cloud or a graph (drag it), rename one (double-click it, or Rename under the canvas), or select anything.
Stocks S: add a stock (press an empty spot) and name it.
Flows M: draw a flow by dragging from a stock or an empty spot to a stock or an empty spot, and name it; clouds appear at empty ends.
Signals E: draw a signal by dragging from a stock, an auxiliary or a flow's valve to an auxiliary or a flow's valve.
Loop L: declare a loop by selecting its signals and flows in order, then label and name it.
Boundary B: drag out a boundary around the system, and name it.

Keys

G legend on or off
R reverse the selected signal or flow
+− the selected signal's polarity
Delete delete what's selected
Ctrl+Z undo
Ctrl+Shift+Z redo
Esc clear the selection
Enter finish the words you're writing
Esc cancel them

Keys act on the lab you last used, or on the open lab view, and never while you type.

0 of 17 checks passed; 17 pending.

Draw a stock for each place bikes wait: the hilltop docks, the riverside docks, the workshop. (Not started)No stocks yet. Brief: at least 3.
Join the stocks with transfers, so no bike appears or vanishes between them. (Not started)No flows yet. Brief: at least 3 transfers.
Declare a balancing loop through the vans' deliveries. (Not started)No loop declared yet. Brief: at least 1 balancing loop.
Draw the scheme's boundary, with rain outside it as an external driver. (Not started)No boundary drawn yet. Draw one and name the system it holds. Brief: at least 1 external driver outside it.
Code the signal you judge less supported as a hypothesis. (Not started)No signals yet.
Rain's signal rests on ride counts and is solid; the vans' response, a belief, is the hypothesis, and the legend shows the coding. You check this.

Always checked

Each loop's kind matches its − effects (Not started)No loop declared yet.
Loop labels are unique and match their kind (Not started)No loop declared yet.
No effect runs into an external driver (Not started)No variable is marked as an external driver yet.
External drivers sit outside every boundary (Not started)No variable is marked as an external driver yet.
The legend is on when effects are coded or tagged (Not started)No signal is coded as a hypothesis yet, so the legend has nothing to declare.
Every stock has units (Not started)No stock drawn yet.
The time unit is given (Not started)No flow drawn yet.
Every stock has a flow in or out (Not started)No stock drawn yet.
Every flow has a name (Not started)No flow drawn yet.
Each transfer joins stocks in the same units (Not started)No transfer drawn yet: a flow from one stock straight into another.
Clouds sit outside every boundary (Not started)No cloud drawn yet.
No variable's name breaks the more test's three rules (Not started)No variable drawn yet.

Written feedback

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SF 10Teachers in a country's schools

A complete model

Reasoning5 of 5
Polish5 of 5

Student teachers take a one-year course; about one in ten drops out. Newly qualified teachers count as experienced after three years, and about one in eight leaves each year before then; about one experienced teacher in fourteen leaves each year. Pupil numbers are rising, and the fewer experienced teachers there are, the heavier each one's workload. In exit surveys, teachers name workload as their main reason for leaving, and resignations rise a year or two after workload does. Head teachers believe that mentoring by experienced teachers keeps new teachers from leaving, but nobody has measured it. The education ministry proposes funding more training places; whether they would fill is untested. Pupil numbers lie outside the schools. Count every stage in teachers, student teachers included, and time in years.

The brief

Draw a stock for each stage: student teachers, newly qualified teachers, experienced teachers. checked by the lab
Join the stages with transfers. checked by the lab
Declare two or more loops. checked by the lab
Run every loop through a stock. checked by the lab
Code each signal you judge less supported as a hypothesis. checked by the lab
Mark what the ministry proposes to change as the one leverage point. checked by the lab
Mark the year or two between heavier workload and more resignations as a signal delay. checked by the lab
The leverage point's signal is a hypothesis, as mentoring's is; the legend shows the coding, and every other signal is solid. you check this

Your palette

stock
flow
cloud
auxiliary
signal
stock equation
polarity
delay
loop
reinforcing loop
balancing loop
boundary
external driver
nonlinear effect
evidence coding
leverage point
behavior note
behavior-over-time graph

To draw in the lab, use a tablet or a larger screen. Everything else reads normally here.

Press an empty spot to add an auxiliary and type its name. Drag a stock, an auxiliary, a cloud or a graph to move it. Select anything drawn to change it. Drag a boundary by its outline or its name to move it, and by the square at its corner to resize it. Drag a behavior note to move it. Double-click or double-tap a stock's name or units, an auxiliary, a flow's name, a loop's label or name, a boundary's name or a behavior note to edit its words in place, or select it and use Rename or the fields under the canvas.

Nothing selected. Select a stock, an auxiliary, a flow, a signal, a cloud, a behavior-over-time graph, a loop label, a boundary or a behavior note on the canvas, and what you can change shows here.

The tools

Auxiliaries V: add an auxiliary (press an empty spot), move a stock, an auxiliary, a cloud or a graph (drag it), rename one (double-click it, or Rename under the canvas), or select anything.
Stocks S: add a stock (press an empty spot) and name it.
Flows M: draw a flow by dragging from a stock or an empty spot to a stock or an empty spot, and name it; clouds appear at empty ends.
Signals E: draw a signal by dragging from a stock, an auxiliary or a flow's valve to an auxiliary or a flow's valve.
Loop L: declare a loop by selecting its signals and flows in order, then label and name it.
Boundary B: drag out a boundary around the system, and name it.
Note N: place a behavior note (press where it goes).
Behavior-over-time graphs H: select a stock, an auxiliary or a flow, then press an empty spot, to add its behavior-over-time graph there.

Keys

G legend on or off
R reverse the selected signal or flow
Q the selected stock's equation, on or off
+− the selected signal's polarity
Delete delete what's selected
Ctrl+Z undo
Ctrl+Shift+Z redo
Esc clear the selection
Enter finish the words you're writing
Esc cancel them

Keys act on the lab you last used, or on the open lab view, and never while you type.

0 of 19 checks passed; 19 pending.

Draw a stock for each stage: student teachers, newly qualified teachers, experienced teachers. (Not started)No stocks yet. Brief: at least 3.
Join the stages with transfers. (Not started)No flows yet. Brief: at least 2 transfers.
Declare two or more loops. (Not started)No loop declared yet. Brief: at least 2 loops.
Run every loop through a stock. (Not started)No loop declared yet. Brief: every loop through a stock.
Code each signal you judge less supported as a hypothesis. (Not started)No signals yet.
Mark what the ministry proposes to change as the one leverage point. (Not started)No variables yet. Brief: exactly 1 leverage point.
Mark the year or two between heavier workload and more resignations as a signal delay. (Not started)No signals yet. Brief: at least 1 signal delay.
The leverage point's signal is a hypothesis, as mentoring's is; the legend shows the coding, and every other signal is solid. You check this.

Always checked

Each loop's kind matches its − effects (Not started)No loop declared yet.
Loop labels are unique and match their kind (Not started)No loop declared yet.
No effect runs into an external driver (Not started)No variable is marked as an external driver yet.
External drivers sit outside every boundary (Not started)No variable is marked as an external driver yet.
The legend is on when effects are coded or tagged (Not started)No signal is coded as a hypothesis yet, so the legend has nothing to declare.
Every stock has units (Not started)No stock drawn yet.
The time unit is given (Not started)No flow drawn yet.
Every stock has a flow in or out (Not started)No stock drawn yet.
Every flow has a name (Not started)No flow drawn yet.
Each transfer joins stocks in the same units (Not started)No transfer drawn yet: a flow from one stock straight into another.
Clouds sit outside every boundary (Not started)No cloud drawn yet.
No variable's name breaks the more test's three rules (Not started)No variable drawn yet.

Written feedback

Turn on written feedback

Export

One defensible answer

It opens here once you've drawn at least one stock in the lab above. Your attempt saves as you draw.

CS 07Kelsham Primary School: four classes in a chain

A chain of stocks, and a loop through the flow that fills it

Reasoning4 of 5
Polish4 of 5

Since 2023 Kelsham Primary School has taught four classes: Reception, Years 1 and 2, Years 3 and 4, and Years 5 and 6. Children start in Reception each September; each September after that every pupil moves up a year, those finishing Reception, Year 2 and Year 4 into the next class, and Year 6 leaves for secondary school. Each October's count of every pupil sets the school's funding for the school year after it, at £4,800 a pupil. With less funding, Years 3 and 4 were taught as one class, and Priya Shah and other parents weigh mixed-age classes when they choose a school for a child about to start. Leave out pupils who move school during a school year. Count every class in pupils, and time in years.

The brief

Draw a stock for each class: Reception, Years 1 and 2, Years 3 and 4, Years 5 and 6. checked by the lab
Join the classes with transfers, as pupils move up each September. checked by the lab
Close one reinforcing loop from the classes through the school's funding to the flow of children starting. checked by the lab
Run the loop through a stock. checked by the lab
Mark the school year between the October count and the funding it sets as a signal delay. checked by the lab
The October count reads every class, not only Reception: the funding follows every pupil on roll. you check this

Your palette

stock
flow
cloud
auxiliary
signal
polarity
delay
loop
reinforcing loop

To draw in the lab, use a tablet or a larger screen. Everything else reads normally here.

Nothing selected. Select a stock, an auxiliary, a flow, a signal, a cloud or a loop label on the canvas, and what you can change shows here.

The tools

Auxiliaries V: add an auxiliary (press an empty spot), move a stock, an auxiliary, a cloud or a graph (drag it), rename one (double-click it, or Rename under the canvas), or select anything.
Stocks S: add a stock (press an empty spot) and name it.
Flows M: draw a flow by dragging from a stock or an empty spot to a stock or an empty spot, and name it; clouds appear at empty ends.
Signals E: draw a signal by dragging from a stock, an auxiliary or a flow's valve to an auxiliary or a flow's valve.
Loop L: declare a loop by selecting its signals and flows in order, then label and name it.

Keys

R reverse the selected signal or flow
+− the selected signal's polarity
Delete delete what's selected
Ctrl+Z undo
Ctrl+Shift+Z redo
Esc clear the selection
Enter finish the words you're writing
Esc cancel them

Keys act on the lab you last used, or on the open lab view, and never while you type.

0 of 13 checks passed; 13 pending.

Draw a stock for each class: Reception, Years 1 and 2, Years 3 and 4, Years 5 and 6. (Not started)No stocks yet. Brief: at least 4.
Join the classes with transfers, as pupils move up each September. (Not started)No flows yet. Brief: at least 3 transfers.
Close one reinforcing loop from the classes through the school's funding to the flow of children starting. (Not started)No loop declared yet. Brief: exactly 1 reinforcing loop.
Run the loop through a stock. (Not started)No loop declared yet. Brief: every loop through a stock.
Mark the school year between the October count and the funding it sets as a signal delay. (Not started)No signals yet. Brief: at least 1 signal delay.
The October count reads every class, not only Reception: the funding follows every pupil on roll. You check this.

Always checked

Each loop's kind matches its − effects (Not started)No loop declared yet.
Loop labels are unique and match their kind (Not started)No loop declared yet.
Every stock has units (Not started)No stock drawn yet.
The time unit is given (Not started)No flow drawn yet.
Every stock has a flow in or out (Not started)No stock drawn yet.
Every flow has a name (Not started)No flow drawn yet.
Each transfer joins stocks in the same units (Not started)No transfer drawn yet: a flow from one stock straight into another.
No variable's name breaks the more test's three rules (Not started)No variable drawn yet.

Written feedback

Turn on written feedback

Export

One defensible answer

It opens here once you've drawn at least one stock in the lab above. Your attempt saves as you draw.

Sources

Matthew A. Cronin, Cleotilde Gonzalez and John D. Sterman, “Why Don’t Well-Educated Adults Understand Accumulation? A Challenge to Researchers, Educators, and Citizens”, Organizational Behavior and Human Decision Processes 108, no. 1 (2009), on the correlation heuristic and the department store task.
John D. Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World (Irwin/McGraw-Hill, 2000), chapter 9, S-Shaped Growth: Epidemics, Innovation Diffusion, and the Growth of New Products, on epidemics; chapter 11, Delays, on delays in material and in information; and chapter 12, Co-Flows and Aging Chains.
Jack B. Homer and Rogelio Oliva, “Maps and Models in System Dynamics: A Response to Coyle”, System Dynamics Review 17, no. 4 (2001), on what simulation adds to maps.
Geoff Coyle, “Qualitative and Quantitative Modelling in System Dynamics: Some Research Questions”, System Dynamics Review 16, no. 3 (2000), the paper Homer and Oliva answer.