Business Inventory
A stock-and-flow model of inventory management that demonstrates how delays in perception, response, and delivery can cause oscillations in inventory levels and ordering behavior, illustrating the dynamics of supply chains.
THE IDEA
This model describes a business inventory system using system dynamics. The core structure is a stock (inventory of cars on the lot) with inflows (deliveries) and outflows (sales). The ordering decision is based on perceived sales, desired inventory, and a discrepancy term. Different delays (perception, response, delivery) are introduced to show how they affect system stability.
Model Equations
Stock:
- inventory of cars on the lot(t) = inventory of cars on the lot(t - dt) + (deliveries - sales) × dt
- Initial stock: 200 cars
Inflows:
- deliveries = 20 for time 0 to 5; orders to factory (t - delivery delay) for time 6 to 100
Outflows:
- sales = minimum of inventory of cars on the lot or customer demand
Converters:
- customer demand = 20 cars per day for time 0 to 25; 22 cars per day for time 26 to 100
- perceived sales = sales averaged over perception delay (smoothing)
- desired inventory = perceived sales × 10
- discrepancy = desired inventory - inventory of cars on the lot
- orders to factory = maximum of (perceived sales + discrepancy) or 0 (Figure 32); maximum of (perceived sales + discrepancy/response delay) or 0 (Figures 34–36)
Delay Scenarios
- Figure 30: perception delay = 0, response delay = 0, delivery delay = 0 (ideal, no delays)
- Figure 32: perception delay = 5 days, response delay = 3 days, delivery delay = 5 days
- Figure 34: perception delay = 2 days, response delay = 3 days, delivery delay = 5 days
- Figure 35: perception delay = 5 days, response delay = 2 days, delivery delay = 5 days
- Figure 36: perception delay = 5 days, response delay = 6 days, delivery delay = 5 days
The scenarios compare how perception, ordering adjustments, and delivery delays affect inventory. Their full response curves are not included in this excerpt.
When to use it
Designing inventory replenishment policies in manufacturing or retail.
Simulating the impact of information delays (e.g., slow sales data) on ordering decisions.
Teaching system dynamics to business students to illustrate feedback and delays.
Analyzing and mitigating oscillations in supply chains during demand fluctuations.
FROM THEORY TO EVERYDAY LIFE
In practice
Zero Delays (Figure 30)
The no-delay case provides an idealized comparison: demand information and deliveries are available without a lag. Compare it with the delayed cases to see how those lags affect adjustment.
Large Delays (Figure 32)
The scenario combines a perception delay of 5 days, a response delay of 3 days, and a delivery delay of 5 days. Demand information, ordering adjustments, and arriving stock therefore change on different schedules.
Reduced Perception Delay (Figure 34)
Lowering perception delay to 2 days while keeping the other delays fixed isolates the effect of receiving sales information sooner. Compare the resulting inventory curve with the original scenario.
Short Response Delay (Figure 35)
A response delay of 2 days rather than 3, with perception delay of 5 days, makes orders respond more quickly to the inventory discrepancy. The resulting oscillation pattern needs to be assessed from the model output.
Long Response Delay (Figure 36)
Increasing response delay to 6 days spreads the inventory correction over more time. Compare the resulting curve with the shorter-response cases rather than assuming that faster adjustment is always more stable.
A MOMENT TO REFLECT
Put it to work.
Why does increasing the perception delay make inventory oscillations worse? How does this relate to real-world supply chains?
If you were a manager, what combination of delays would you prioritize reducing first to stabilize inventory?
How can an understanding of this model help prevent the bullwhip effect in a multi-echelon supply chain?
Often confused with
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Source texts
- Thinking in Systems A Primer