268. Stock Management
The generic structure for inventory / stock control in system dynamics: order based on expected loss + inventory gap + supply-line gap.
268.1. The classical formula
where:
- : current stock
- : target stock
- : current supply line (on-order, not yet received)
- : target supply line
- : time to correct stock gap
- : time to correct supply-line gap
- : supply-line weighting (how much you account for orders already placed)
- Expected loss: replacement for expected demand
268.2. The supply-line neglect parameter
is critical:
- : fully account for on-order inventory → stable, no over-ordering
- : ignore the supply line entirely → over-order while waiting → oscillation
Sterman’s beer-game experiments find on average — most subjects substantially neglect the supply line.
268.3. Anchoring and adjustment
Generic decision-rule structure:
- Anchor: the default level (e.g., expected demand)
- Cue: corrective signal (e.g., inventory gap)
- : partial-adjustment coefficient
This is the anchoring-and-adjustment heuristic (Tversky-Kahneman) operationalized as a formula. Captures bounded rationality.
268.4. Why this generates bullwhip
The chain of reasoning that produces bullwhip:
- Retailer sees demand spike → expected demand rises
- Inventory gap grows → orders bigger (anchor + correction)
- Supply-line neglect → keeps ordering even though previous orders are in transit
- Wholesaler sees retailer’s amplified orders → repeats the pattern
- Manufacturer sees wholesaler’s even more amplified orders → repeats
Each echelon amplifies the variance. The math: see Bullwhip in SD.
268.5. Real-world example
A factory targets 100 units of inventory (). Currently has 60 (). On-order 50 units (). Expected demand 20 units/period.
Settings: periods, , (an order-of-magnitude approximation: target supply-line equal to target stock).
268.6. See also
- Feedback Loops
- Smoothing — for expected demand
- Bullwhip in SD
- Beer Game
- Bullwhip Effect (Supply Chain)