M2W— Model-to-World LabBlanchet Research Group · Stanford MS&E
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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.

Interactive prototypeSynthetic evidenceReproducible model

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.

Shelf capacity

Use at most 3 of 4 positions. Leaving a position empty is allowed.

Products to offer
2 of 3 positions used

Where visitors end up

probability mass = 100%
Pro
38.1%
Plus
40.4%
Everyday
0.0%
Entry
0.0%
No purchase
21.6%

A choice is a path

  1. 1

    Arrive with a first product in mind.

  2. 2

    Substitute if that product is not offered.

  3. 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.

Same buyers. Different shelf.

15 feasible subsets checked by exhaustive enumeration.

PolicyAssortmentRevenuePurchaseNo purchase
Best ≤ 3Pro + Plus$79.9878.4%21.6%
Your assortmentPro + Plus$79.9878.4%21.6%
Offer all 4Unconstrained reference$54.7090.0%10.0%

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.

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.

  1. 01 · Model

    Customer substitution

    Products and no purchase form a Markov chain with disclosed initial and transition probabilities.

  2. 02 · Simulate / evaluate

    Buyer destinations

    Because the state space is small, exact absorption probabilities make every assortment comparison transparent and free of simulation error.

  3. 03 · Decide

    Choose the shelf

    Every capacity-feasible subset is compared on the same modeled buyers using expected revenue and conversion.

  4. 04 · Transfer

    Learn and test

    Estimate behavior from retailer data, validate decisions out of sample, run controlled experiments, and monitor performance and drift.

Audit the gapTransition estimates · population shift · strategic response · operational constraints · realized lift

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

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 foundation

The world is no longer known. Learn a decision from logged choices.

Continue the M2W sequenceDecision Lab 02 · Offline assortment learning