MIT OpenCourseWareSession 11: Student Projects (cont’d)
MIT OpenCourseWare
Project framing 0:00
The group begins by revisiting last week’s discussion of when system dynamics is useful. The focus is on problem formulation, on whether you start from stocks and flows or from feedback loops, and on what makes a problem dynamic enough to warrant this kind of modeling. Hazhir Rahmandad says there is no single right entry point, and that the choice depends on the problem.
Model scope and detail 6:02
The conversation then turns to how much detail a model should have. Rahmandad says the answer depends on purpose, audience, and empirical grounding. Simple models fit theory building and many business school audiences. More detailed models fit policy analysis or fields that expect complexity. He notes that many projects begin with a complex model and are later distilled into a smaller one, sometimes from 2,000 equations down to 20.
Make effects transparent 20:32
Keep each effect between 0 and 1 if you can. Multiplying several bounded factors makes the result hard to read, especially when another nonlinear step is involved. A weighted average can be easier to follow. The main point is to make the model easier for you to diagnose when it behaves badly.
Track prestige and demand 23:30
Accessibility can stay clean if you average sales to demand over time and let higher accessibility mean lower prestige. There is no need for extra nonlinearity there, because the later demand equation already has one. On demand, separate the price-sensitive group from the prestige-sensitive group, then decide whether you want fixed price sensitivity or a prestige-based adjustment to it.
Model structure 42:02
The reading model needs a tight link between books bought and books read. A simple split between high- and low-frequency readers is fine, but the flow between them should stay continuous. The buying side can be anchored to each group’s normal reading demand, then pushed upward by social prestige.
Social capital limits 59:34
The open question is how to build social capital in a simple, grounded way. One suggestion is to compare a person’s books bought with the average per person and let that gap raise their social value. But that kind of reinforcing loop can run away, so you also need bounding factors such as income.
Sentiment and inventory model 1:07:32
Serchin explains a model of instability in the economy. Firms face uncertainty, so they hold buffer stocks such as inventories and liquid assets. He links sentiment to recent demand growth and to volatility in that growth. When sentiment falls, firms change desired stocks and those changes feed back into demand and supply. That can create oscillations at business-cycle scale. Hazhir says the core idea is right, but the model should stay simple. He suggests using one clear sentiment index, a logistic form to keep it between 0 and 2, and a more direct adjustment rule rather than piling everything into one stock equation.
Tracing the oscillation loop 1:23:33
Rahmandad walks through the model that is producing oscillations and checks the standard deviation calculation, saying it is the usual variance formula: expected value of x squared minus the square of the expected value. He then traces the feedback path by following sentiment into effective growth, then into perceived average aggregate demand growth, real and nominal demand, household income, wages, labor demand, and production. To test the guess, he freezes household desired consumption at its base value. The oscillation disappears, which suggests the household demand loop is the main source of the behavior, not the volatility path the student had focused on.
Profit and congestion 1:46:03
A more structured profit function is set out for the location choice. Talent and infrastructure become inputs to a Cobb-Douglas production function, with tax added on the cost side. The result is expected profitability by location, and demand is split across locations with a sensitivity to profit. Congestion can stay as a modifier on attractiveness, or it can be folded into prices if you want congestion to appear through higher costs.
Data and flight protection 1:58:02
The model is checked against the LA production data in Vensim. The variable name must match the data column exactly, and the variable must be marked as a data equation and tied to the loaded dataset in simulation control. The last exchange turns to airline seat protection. A protection level keeps low-fare seats closed so higher-fare demand can be saved for later, and that level is used to shape future sales and forecasts.
Flight demand units 2:06:30
The discussion stays on the supply side of the airline model, but the main problem is the unit of demand. Hazhir Rahmandad keeps asking whether the forecast is for seats sold per month, seats per flight, or total demand over the life of one flight. The student says the forecast is for high-fare demand, but also admits the demand side is not fully formulated. Rahmandad says the model needs a clear flow variable, not a muddled mix of seats, sales, and protection levels. He explains that protection only makes sense if you know how many seats remain unsold, because sold seats are already out of the decision. The student then shifts the story from one flight to many flights, with a new flight born each day and protection reset overnight after bookings come in, so the feedback effect can run across flights.
Modeling smoking and nodules 2:26:32
Use simple smoking categories, not a co-flow, when people move from low to high smoking over time. Track how many people shift between categories, and let nodule growth depend on those stocks. If you need both smoking history and nodules, stratify the population by both dimensions, or use an agent-based approach. The same advice applies if the rates out of a state depend on nodules: build the model around the dimensions that actually drive movement.
Peer punishment strategy 2:33:00
Ali’s model also turned to peer punishment. The group kept the current ad hoc setup, but the better route was framed as a game between two actors. Each side can have a small strategy with parameters for when to punish, then optimize against the other side until the choices settle into a Nash-style equilibrium. The existing code can be pushed in that direction, but it needs iterative optimization and consistency checks.
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