Core methods | about 55 minutes | free
Distinguish causal-loop reasoning from an executable stock-flow model and verify a small model by hand.
An original discrete-time stock-flow rehearsal with a deliberately simple boundary. It is not a prediction of a real service and does not validate a model merely because it runs.
This is original learning material, not a reproduced official course. Mechanical checks have determinate answers within the stated case. Worked comparisons for open judgements show defensible reasoning, not the only possible model. Specialist pedagogical review is not recorded.
Fictional case: a service starts week 1 with a backlog of 40 cases. Exactly 12 new cases arrive at the start of each week. Staff can complete at most 10 cases per week in weeks 1 and 2. Additional trained capacity is available from the start of week 3, raising the limit to 16. All cases are identical in this toy model. Completions during a week cannot exceed that week's starting backlog plus arrivals. There are no withdrawals or reopens in the first model.
Use paper, your own drawing tool or the notes below. Attempt each step before opening its comparison. Describe a diagram in words when that is more accessible.
Produce: One stock, two flows and an explicit time step.
Stock: backlog in cases. Inflow: arrivals in cases/week. Outflow: completions in cases/week. Capacity is a limit on the outflow, not another stock of cases. For a one-week step: end backlog = start backlog + arrivals - completions; completions = min(capacity, start backlog + arrivals). The minimum prevents negative backlog. Changing the time step would require rates and event timing to be handled consistently.
Produce: A four-row calculation table.
Week 1: 40 + 12 - 10 = 42. Week 2: 42 + 12 - 10 = 44. Week 3: 44 + 12 - 16 = 40. Week 4: 40 + 12 - 16 = 36. Backlog rises before the extra capacity arrives, then falls by four cases per week while enough cases remain. A drop in arrivals is not needed to explain this change.
Produce: A signed loop and its delay.
Backlog (+) increases perceived capacity gap; gap (+) increases training commissions; commissions (+), after a training delay, increase effective completion capacity; capacity (+) increases completions; completions (-) reduce backlog. The single negative causal link makes this proposed loop balancing. The fixed capacity schedule in the numerical exercise is externally specified: the loop is not yet implemented in its equations. Do not claim a two-flow stock model already simulates the decision feedback.
Produce: Results for zero arrivals and for an almost empty queue.
With zero arrivals and backlog 40, capacity 10 yields backlog 30 after one week. With starting backlog 2, arrivals 0 and capacity 16, completions are 2 and ending backlog 0, not -14. These are necessary accounting checks, not evidence that the real service behaves like the model.
Produce: One boundary extension and data needed to assess it.
Rushed work might reopen cases, making nominal completions overstate resolved need. Add a reopen inflow with an explicit timing rule and measure its rate. Alternatively, training may temporarily reduce experienced staff availability. A model boundary that omits these effects may overstate the improvement from additional capacity.
Calculate the four backlogs before using this check. It tests the supplied accounting model, not a real service.
These checks test the supplied case, not your overall competence. Open answers and model variants still need your judgement.
Backlog = arrivals / completions. It is labelled 'cases', and managers say its fall proves a balancing feedback loop.
The ratio of two rates is dimensionless and is not an accumulation. Use the stock accounting equation with an initial condition. A changing ratio does not identify a closed causal mechanism. State and test the decision rules and delays separately.
From week 3, let 25% of each week's 16 completions return as new backlog at the end of that same week. Calculate end backlogs for weeks 3 and 4.
Each week four cases reopen. Week 3 ends at 44+12-16+4=44; week 4 also ends at 44. Gross completion capacity increased but net resolution is only 12 cases/week. This timing is stipulated for the exercise; a real reopen delay must be investigated rather than assumed.
A different model can be defensible when its purpose, assumptions and reasoning are explicit. A contradiction, incorrect unit, invented fact or unacknowledged change of purpose needs repair. Keep both your first attempt and revision.
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The complete original case above is free. Links below distinguish exercises from explanations, recordings, software and paid study. Reading a page or drawing in a tool is not itself a model check.
Start with the early assignments and their paired solutions. Predict behaviour, calculate it, then compare. Do not confuse this course with MIT courses that publish assignments without solutions.
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