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Decision Lab 01 · Assortment
When less shelf space makes more revenue.
Build a small product assortment. Synthetic buyers arrive with a first choice, then move through a Markov chain when that product is missing. The best decision is not necessarily to offer everything—or even to fill every available slot.
Live decision
Design the shelf.
Click products to offer or withhold. The model recomputes where every buyer eventually purchases—or leaves—using exactly the same inputs for each policy.
Buyer flow
Where visitors end up
Model mechanics
A choice is a path
- 1
Arrive with a first product in mind.
- 2
Substitute if that product is not offered.
- 3
Absorb at an offered product or no purchase.
All positive transition percentages are disclosed on the product cards; self-transition weights are zero. 10.0% of visitors begin at no purchase. These are illustrative inputs, not estimates from customer data.
Policy comparison
Same buyers. Different shelf.
15 feasible subsets checked by exhaustive enumeration.
The tradeoff is visible: the revenue leader accepts more no-purchase outcomes, but redirects many Entry visitors toward higher-value products. Revenue rises by $25.28 versus offering all four in this synthetic world.
The M2W map
One decision, traced from model to transfer.
The current lab completes the first three stages in a transparent synthetic world. The transfer stage defines the next research program: learn behavior from data, validate out of sample, experiment, and monitor performance.
- 01 · Model
Customer substitution
Products and no purchase form a Markov chain with disclosed initial and transition probabilities.
- 02 · Simulate / evaluate
Buyer destinations
Because the state space is small, exact absorption probabilities make every assortment comparison transparent and free of simulation error.
- 03 · Decide
Choose the shelf
Every capacity-feasible subset is compared on the same modeled buyers using expected revenue and conversion.
- 04 · Transfer
Learn and test
Estimate behavior from retailer data, validate decisions out of sample, run controlled experiments, and monitor performance and drift.
Evidence passport
What the prototype establishes—and what comes next.
- Build status
- Interactive prototype connecting a Markov-chain choice model to an assortment decision
- Evidence
- Synthetic inputs make the substitution mechanism transparent and fully inspectable
- Computation
- Exact linear-system solution with exhaustive comparison of every feasible assortment
- Reproducibility
- Deterministic results from fully disclosed model inputs
- Next validation
- Estimate behavior from retailer data, validate decisions out of sample, then test them experimentally before deployment
From theory to a testable object
The model supplies a world. The interface exposes a decision.
This prototype starts from the Markov-chain choice representation developed by José Blanchet, Guillermo Gallego, and Vineet Goyal. Offered products are absorbing purchase states; an unavailable first choice sends the buyer to another product or to no purchase.
Here, exhaustive enumeration is deliberately used for a four-product teaching example. Later increments can replace the known synthetic world with learned behavior, robust decisions, experiments, and closed-loop diagnosis.
Read the research foundationWhat goes next?