1Demonstration 1 of 4
One station's order, with and without the supply line
How much of an order is a reaction to goods that are already on their way?
The order is the expected demand plus a correction: the gap between target and effective stock, spread over the adjustment time. A weight of 0 leaves the supply line out of effective stock, so the gap looks large and the correction is large.
Cases are the unit. The station expects 8 cases a week, holds 6 in inventory, owes 4 in backlog, has 24 cases ordered or in transit (the supply line) and wants 12 on hand. supply_line_weight is how much of the supply line it credits.
Predict first. With a weight of 0 and an adjustment time of 4 weeks, does the station order more or less than the 8 cases it expects to sell?
Choose an example
Constructed example: the chapter's ordering rule applied to a station state defined for this reader.
Calculated values
- Effective stock (cases)
- 2.0
- Gap (cases)
- 10.0
- Order before the floor (cases)
- 10.5
- Order placed (cases)
- 10.5
Effective stock = 6 - 4 + 0.0 x 24 = 2.0. Gap = 12 - 2.0 = 10.0. Order = 8 + 10.0 / 4 = 10.5. Ignoring the supply line leaves a large gap, so the station orders again for goods already on their way.
Use the idea
When a rule orders, hires or builds to close a gap, ask whether the gap already counts what has been committed but has not arrived.
Where the conclusion applies
One station in one week with the state defined above. The rule floors the order at zero; a station that also returns goods would need a different rule.
Check your understanding: With a weight of 0.5 and an adjustment time of 4 weeks, what does the station order?
Chapter 5 source: section "Four stations and what each can see". Demonstration C05-D01.
2Demonstration 2 of 4
Expected demand lags a step in orders
How long does a station take to believe that demand has really changed?
Each week the belief moves 1 / smoothing_time of the way to what was observed. The gap shrinks by the same fraction each week, so the belief approaches the new level but never jumps to it unless the smoothing time is 1.
expected is the station's belief about weekly demand, observed is the order it just saw, and smoothing_time is how many weeks of the gap to close at once. Cases per week.
Predict first. With a smoothing time of 8 weeks and orders jumping from 4 to 8, is the belief above 6 after 4 weeks?
Choose an example
Constructed example: the chapter's smoothing rule with its four-week default, started at 4 cases a week and stepped to 8 or 12.
Calculated values
- Smoothing time (weeks)
- 4
- Expected demand after week 1
- 5.00
- Expected demand after week 4
- 6.73
- Expected demand after week 20
- 7.99
- First week within 1 case of the orders seen
- 5
Week 1: 4 + (8 - 4) / 4 = 4 + 1.00 = 5.00. Each later week closes 1 / 4 of the remaining gap. The belief first comes within 1 case of the orders seen in week 5, so a step in demand takes weeks to register.
Use the idea
A forecast that is updated gradually is a delay. Treat its smoothing time as a delay length when you reason about stability.
Where the conclusion applies
The belief starts at 4 and the orders seen stay constant after the step. If orders keep changing, the belief trails them.
Check your understanding: With a smoothing time of 2 and orders of 8 after a start of 4, what is the belief after week 2?
Chapter 5 source: section "Four stations and what each can see". Demonstration C05-D02.
3Demonstration 3 of 4
A four-case step grows at every station upstream
How much larger is each station's order swing than the customer's, and what does delay length do to it?
Each station's order stream is the next station's demand signal, and each station adds its own correction on top. Longer pipelines mean each correction lands later, so the swing grows steeply with delay length.
The customer orders 4 cases a week for 5 weeks, then 8 for 45 weeks. A station's swing is its highest weekly order minus its lowest. The ratio divides that by the customer's swing of 4. pipeline_weeks is the delay in each direction.
Predict first. With two weeks of delay each way, does the factory's swing exceed 30 times the customer's?
Choose an example
Constructed example: the chapter's four-station chain and its 4-to-8 step, run with one to four weeks of delay.
Calculated values
- Weeks of delay each way
- 2
- Retailer order swing (x customer)
- 5.7
- Wholesaler order swing (x customer)
- 14.9
- Distributor order swing (x customer)
- 28.3
- Factory order swing (x customer)
- 34.3
- Factory peak order (cases)
- 137
The customer's swing is 8 - 4 = 4 cases. The factory's orders range from 0.00 to 137.36, a swing of 137.36 - 0.00 = 137.36, so the ratio is 137.36 / 4 = 34.3. The ratio grows from 5.7 at the retailer to 34.3 at the factory with 2 week(s) of delay each way, because each station's orders are the next station's demand signal.
Use the idea
A chain's exposure is mostly a property of its delays. Measure the delay before blaming the people who order.
Where the conclusion applies
Identical stations, a single step in demand, the supply line ignored, orders floored at zero and a 50 week run. With four weeks of delay the factory is still ordering heavily at week 50, so its swing is measured on that window. A chain with different policies at each station would give different ratios.
Check your understanding: If the factory's orders ranged from 0 to 140 cases and the customer's swing is 4, what would the ratio be?
Chapter 5 source: section "What the reconstruction produces". Demonstration C05-D03.
4Demonstration 4 of 4
The supply-line fix lands three stations away
If every station credits what it has already ordered, who benefits?
Counting the supply line removes the repeat orders that cause the later stations to overshoot, which shrinks swings far upstream. At the retailer the same change costs a little, so a local experiment would reject it.
supply_line_weight runs from 0 (ignore the supply line) to 1 (credit it in full). The inventory adjustment time is how many weeks a station takes to close its inventory gap. Swing ratios are as in the previous demonstration.
Predict first. At weight 1 and an adjustment time of 4 weeks, does the retailer's swing fall or rise?
Choose an example
Constructed example: the chapter's weight 0 and weight 1 runs, plus a weight of 0.5 and a one-week adjustment time defined for this reader.
Calculated values
- Supply line weight
- 1.0
- Inventory adjustment time (weeks)
- 4
- Retailer swing, ignored then chosen
- 5.7 then 6.0
- Factory swing, ignored then chosen
- 34.3 then 18.6
- Factory peak order (cases)
- 74
Effective stock = inventory - backlog + 1.0 x supply line. Factory swing: 18.6 - 34.3 = (-15.7). Retailer swing: 6.0 - 5.7 = 0.4. The retailer's swing moves by 0.4 and the factory's by (-15.7). The retailer sees no gain from the change while the factory three stations away does.
Use the idea
A change can look unhelpful from every seat inside a system and still be right for the system. That is the case for modelling the whole chain.
Where the conclusion applies
Two-week delays, a 4-to-8 step and identical policies at every station. Whether the retailer's loss is real in a given chain depends on the delays and rules in that chain.
Check your understanding: If the factory's swing falls from 34.3 to 18.6, by how much does it fall?
Chapter 5 source: section "The fix, and why nobody finds it". Demonstration C05-D04.