players
speed1× is two weeks a second
each station: red box, its backlog · big box, its inventory · orders flow up the chain (amber: 2 weeks in the mail) · beer flows down it (blue: 2 weeks on the road) · dashed: each order depends on the station's stock and supply line

How every player orders

The world they order in

orders placed (cases a week) · ◆ real teams' average peak (Sterman 1989)

net stock: inventory minus backlog (cases)

cost so far: $0.50 a case in stock, $1 a case in backlog, per week

team cost for 36 weeks against β, every other setting as it is now

The model: the Beer Game as stocks and flows

Every box on the board is a stock. A delay box empties at its content divided by its time, so a 2-week delay is two 1-week boxes in series. The orders rule is Sterman's: start from the demand you expect, then correct part of the gap in your stock and part of the gap in your supply line. For the first 4 weeks every player orders 4, as in the game.

INVᵢ, BLᵢinventory and backlog of station i; net stock is INV − BL
SLᵢsupply line: orders in the mail, the supplier's backlog, and beer on the road (the factory: requests and brewing)
θhow fast the expected demand Eᵢ follows incoming orders, per week
αSthe share of the stock gap ordered each week
βthe share of the supply line the player counts: 1 counts everything already ordered, 0 ignores it
S*the stock the player wants on hand
λ̂the lead time the player believes, so the supply line wanted is λ̂ Eᵢ; the true lead time is mail + shipping (the factory: 1 week + brewing)
τf1/8 week: a station ships what it has almost at once

Sterman fitted the rule to 44 players; their average was θ = 0.36, αS = 0.26, β = 0.34, and a stock target and pipeline that split as S* = 13.9 and λ̂ = 2.1 weeks. The best rule found here is the cheapest of 7,200 combinations, computed once.