Beer Game

272. Beer Game

The Beer Distribution Game (MIT Sloan, 1960s) — a tabletop / simulation exercise demonstrating the bullwhip effect. The most-played management game ever.

272.1. Setup

Four-stage supply chain: Retailer → Wholesaler → Distributor → Factory. Each stage:

Receives orders from downstream
Ships goods to downstream
Places orders upstream
Carries inventory; pays holding cost and backorder cost

There’s a 2-week shipping delay between stages and 1-week order delay. Initially, demand is 4 cases/week (stable).

272.2. The shock

After 4 weeks, retail customer demand steps up to 8 cases/week and stays there.

272.3. The result (consistent across hundreds of plays)

Despite the step being small (4 → 8), upstream stages see:

Factory orders peak at 20-40 cases/week
All stages alternate between massive backorders and massive overstocks
Total system cost is 10-30× higher than the optimum

Even MIT students consistently exhibit this behavior. The bullwhip is structural, not a personal failure.

272.4. Sterman’s decision-rule estimate

Sterman (1989) fit each player’s order rule to:

{Order}_{𝑡} = max {0, {\hat{𝐷}}_{𝑡} + 𝛼_{𝑆} (𝑆^{*} - 𝑆_{𝑡}) + 𝛼_{𝑆 𝐿} (𝑆 𝐿^{*} - 𝑆 𝐿_{𝑡})}

where ${\hat{𝐷}}_{𝑡}$ is smoothed demand. He found:

$𝛼_{𝑆} \approx 0.36$ (modest correction speed)
$𝛼_{𝑆 𝐿} \approx 0.26$ — but more critically:
Players underweight the supply line (most attention on $𝑆$ , less on $𝑆 𝐿$ )

This supply-line neglect drives oscillation: players keep ordering even though previous orders are en route.

272.5. What works

After playing several rounds, players learn:

Slow down: smaller corrections per period
Pay attention to the supply line: full $𝛼_{𝑆 𝐿}$
Smooth demand: don’t react to every blip
Information sharing: when upstream sees end-customer demand (not just downstream orders), bullwhip largely vanishes

272.6. Mathematical structure

Each echelon is a 2nd-order delayed feedback system (here). Four cascaded → high-order oscillator. With shock input + supply-line neglect → sustained large oscillation.

272.7. Variations

Beer Game online: Powersim, Forio, MIT’s online version
Reduced-delay variant: shorter lead times → less bullwhip
Information-sharing variant: all stages see end-demand → bullwhip eliminated

272.8. Why it matters

The beer game is the empirical answer to “do real people exhibit bullwhip?” Answer: yes, robustly. It validates the SD theory and motivates:

Lead-time reduction
Information sharing (CPFR, VMI, EDI)
Order-policy training
Centralized planning

272.9. See also

Bullwhip in SD — closed-form analysis
Stock Management — the decision rule
Bullwhip Effect
Delays