La Bourse / Volume IV / Nº IV.07 / Ten concept briefs

A woman reading in a rattan chair beside a tall white window, light falling across her and the floor. — Plate IV.07 · Ten concept briefsThe Second Room.Everyone draws a supply chain as a line because a line fits on a page. The thing itself is a population, and it is lit from a room you have not entered.

TEN CONCEPT BRIEFS · Chapter IV.07 — Supply Chains as Ecologies

One page each. A reader who reads only these ten pages has the chapter.

BRIEF 1 — The Population, Not the Chain

The idea. A supply chain is drawn as a line because a line fits on a page. What is actually upstream of you is a population that multiplies at every step.

        N_n  =  N₁ · b^(n-1)

  N₁ = your direct suppliers      b = suppliers behind each supplier

Worked example. Sixty part families, four qualified sources each, gives 240 direct suppliers. With a branching factor of five:

  tier 1        240 firms
  tier 2      1,200
  tier 3      6,000
  tier 4     30,000
  tier 5    150,000

By the second tier you have more counterparties than you have employees, and by the third you have more than you could telephone in a year. Nothing about your contracts changed; only the arithmetic of the word chain.

Why it matters. Populations are governed by distributions, not by contracts. Every management technique built for a line — negotiate, specify, audit, penalise — scales linearly at best, and the thing it is pointed at scales geometrically. That gap is the whole of this chapter.

You already know this because you have been stopped by a company whose name you learned on the day it stopped you, and you had no contract with them, and nobody in your building had ever written their name down.

BRIEF 2 — Tier-n Visibility, and What It Costs

The idea. Seeing your upstream is not free and not impossible. It is a priced service with a known unit cost and a known decay.

Worked example. At $1,200 to identify and verify one node, and a disclosure rate of sixty percent per tier — because you can only ask tier three through tier two:

  tier   firms    gross cost/yr    visible    cost per node FOUND
   1       240        288,000      100.00%              1,200
   2     1,200      1,440,000       60.00%              2,000
   3     6,000      7,200,000       36.00%              3,333
   4    30,000     36,000,000       21.60%              5,556

Tiers one to three: $8,928,000 a year, 2.48 percent of external spend, for thirty-six percent of the third tier. Tiers one to four: $44,928,000, or 12.48 percent of spend.

Why it matters. "Full supply chain transparency" is a sentence with a price tag, and once the price tag is visible the conversation improves immediately: you stop arguing about whether to have visibility and start choosing which families deserve it. The answer is the top decile by exposure ratio (Brief 5).

You already know this because you have asked a supplier who their supplier is and received either a polite deflection or a spreadsheet three months later, and you understood in that moment that the information costs somebody something.

BRIEF 3 — Recruitability, Not Redundancy

The idea. There are two ways to survive losing a node. Hold a spare (redundancy) or be able to reassemble the lost function out of neighbours (recruitability). Ecologies mostly run on the second.

Worked example. The Aisin fire, 1 February 1997. Toyota's sole source for the brake P-valve burned down. There was no spare and no second source. Within days the blueprints were circulating laterally through more than two hundred firms; sixty-two of them produced valves; line output resumed in about five days and was near normal within two weeks. Compare a four-sourced commodity that took a year to recover from the 2011 Thai floods, because all four sources sat on the same flood plain.

Why it matters. Redundancy is bought with money and consumes leverage. Recruitability is bought with relationship density and consumes almost nothing — but it cannot be procured in a quarter, and it does not appear on any balance sheet. It is the single largest asset most industrial groups hold and do not count.

You already know this because the last genuine emergency you were in was solved by people phoning people they already trusted, and the contract was signed afterwards, if at all.

BRIEF 4 — The Transmission Coefficient

The idea. When a place that makes a share of the world's output goes down, some fraction of that share becomes world shortfall. That fraction is measurable, and it is not one.

        T  =  world output shortfall  /  the failed region's share

Worked example. Thailand assembled about forty-five percent of the world's hard drives. After the 2011 floods, global shipments fell from 176.6 million units in Q3 to 120.0 million in Q4 — a fall of 32.05 percent.

  T  =  32.05%  /  45%  =  0.712

Seventy-one percent of one flood plain's share became world shortfall in a single quarter. Average drive prices rose eighty to a hundred percent and took about a year to return.

Why it matters. T tells you how much substitution and inventory the rest of the world actually had. A T near zero means the system absorbed the loss; a T near one means there was nothing behind it. Measured after the fact, it is the cheapest empirical test of whether a market is genuinely diversified — cheaper and more honest than counting suppliers.

You already know this because you have watched a price double for a part that was made in four countries, and understood that three of those countries were not really making it.

BRIEF 5 — The Exposure Ratio

The idea. Criticality is close to the inverse of spend share.

        E  =  value of downstream output the node gates
              ------------------------------------------
                    the node's own revenue from it

Worked example.

  all chips in a car      $500 gates $35,000           70 x
  one automotive MCU      $3.50 gates $35,000       10,000 x
  one hard drive          $50 gates a $700 machine      14 x
  one Aisin P-valve       $10 gates a $15,000 car    1,500 x

A single microcontroller is one hundredth of one percent of a vehicle's price and stops the vehicle completely.

Why it matters. Every procurement system in the world ranks suppliers by spend, and spend sorts your exposures in almost exactly the wrong order. Kraljic named this in 1983 as the bottleneck quadrant; E gives you the same insight as a number you can sort a spreadsheet by, which means it survives being handed to someone who was not in the room.

You already know this because the part that has hurt you most was never the part you spent most on.

BRIEF 6 — The Common-Mode Floor

The idea. Multi-sourcing works against independent failures and does nothing against correlated ones. Model both.

        P(all m fail)  =  q  +  (1 - q)·p^m

  p = each source fails independently    q = all fail together

q is the shared region, port, sub-tier supplier, certification body, sanctions regime, or mode of transport.

Worked example. With p = 0.05 and q = 0.015:

  m = 1   P = 0.064250
  m = 2   P = 0.017462
  m = 3   P = 0.015123
  m = 4   P = 0.015006
  m = 8   P = 0.015000

The second source buys 4.68 percentage points. The eighth buys effectively nothing, because q is a floor and no number of suppliers passes it.

Why it matters. It converts "how many suppliers should we have" from a temperament question into a computation, and it explains the otherwise puzzling fact that heavily multi-sourced industries still stop.

You already know this because you have seen three independent suppliers all fail in the same week, and afterwards somebody discovered they all bought from the same factory two tiers up.

BRIEF 7 — The Source Count, Priced

The idea. Each additional source has an exact event cost above which it pays for itself. Compute it and the argument ends.

        breakeven event cost  =  extra annual admin  /  ΔP

Worked example. At $18,000 a year to keep one supplier qualified and audited, sixty families:

  1 -> 2   ΔP 0.046788   extra admin 1,080,000   pays above      $23,083,088
  2 -> 3   ΔP 0.002339   extra admin 1,080,000   pays above     $461,661,769
  3 -> 4   ΔP 0.000117   extra admin 1,080,000   pays above   $9,233,235,373

With a $28 million stoppage, total cost is minimised at two sources ($2,648,950 a year against $2,879,000 for one and $4,740,172 for four).

Why it matters. It defends both directions. The same line of arithmetic justifies single sourcing where a stoppage is cheap and quad sourcing where a stoppage costs half a billion, which means it is a genuine decision rule rather than an argument for a preference.

You already know this because you have already made this trade informally every time you decided a part was "not worth a second supplier."

BRIEF 8 — Leverage Attenuation

The idea. Your influence over a supplier's conduct is roughly your share of its revenue, and that share divides by the number of sources you split a family across. Influence also decays as it travels upstream, because you are asking someone to ask someone.

        λ  ≈  0.60 / m        leverage retained per tier

Worked example. Single-sourced, you might hold sixty percent of the influence one tier up. Split the family four ways and you hold fifteen percent. Split it eight ways and you hold seven and a half. The supplier has not become less cooperative; you have become less important to it.

Why it matters. This is the invisible price of diversification. Nobody records it, no system reports it, and it is the reason a firm can add suppliers for years and find its code of conduct means steadily less. It is also recoverable — through share, contract length, joint engineering and being the customer a supplier would protect in a shortage — but only for a handful of relationships at a time.

You already know this because you know exactly which of your suppliers returns your call within the hour, and it is the one where you are a large fraction of their order book.

BRIEF 9 — Enforcement Depth, n\*

The idea. A standard's reach is a number of tiers, and you can compute it. Cost grows geometrically with depth; value falls geometrically with depth.

   C_n = c · N₁ · b^(n-1)        V_n = V₁ · λ^(n-1)

   n*  =  1  +  ln(V₁ / C₁) / ln(b / λ)

Worked example. $6,000 an audit, 240 direct suppliers, b = 5, λ = 0.15, value of full compliance $12 million a year:

  ln(V₁/C₁) = ln(8.3333)  = 2.1203
  ln(b/λ)   = ln(33.3333) = 3.5066
  n*        = 1 + 0.6047  = 1.605 tiers

Single-sourced, n* = 2.654. Quadrupling sources costs 1.049 tiers of reach. Shared audit across eight buyers gives 2.198; deep partnership gives 2.000; both together give 2.981.

Why it matters. It replaces "we require compliance throughout our supply chain" — a sentence with no truth value — with a depth you can state, defend and improve. And it says precisely which two things improve it, neither of which is another audit.

You already know this because you have signed a code of conduct that required flow-down to all sub-suppliers, and you knew as you signed it that nobody would ever check the fourth one.

BRIEF 10 — The Waist

The idea. Where a population narrows, enforcement is cheap. Audit the hourglass at its waist, not at its mouth.

Worked example. Tin, tantalum, tungsten and gold come from thousands of mine sites and pass through roughly three hundred smelters and refiners.

  audit at the source   8,000 sites x $6,000  =  $48 million a year
  audit at the waist      300 sites x $6,000  =  $1.8 million a year
  saving                                          96.25 %
  shared across 8 buyers                        $225,000 a year each
  value at tier 3 (V₁ · λ²)                     $270,000 a year
  net                                            +$45,000  — it PAYS

Why it matters. The geometric arithmetic of Brief 9 declares tier three unreachable, and at the waist it is reachable and profitable. The two statements are both true: reach is a property of where you stand in the network, not of how determined you are. The Responsible Minerals Initiative is not a compromise with the ideal; it is the ideal, correctly located.

You already know this because you know that the way to check what a hundred rivers carry is to stand at the one bridge they all pass under.