To the Bedrock
Interdependence & Coordination

Cost of mismatch

When a retractive conflict waits for a periodic review, work continues against a commitment that will later change. The eventual adjustment reaches more completed work and may trigger another round of rework.

This is a two-activity rework model with a Design Structure Matrix dependency structure, indexed to planned effort of 100. The equations are illustrative. They are informed by the cited literature, but they are neither a published forecasting formula nor a calibrated budget model.

80% of work is coupled across the boundary
45% of exposed work is invalidated
6 weeks before a contextual decision
20 index units of work under the unresolved commitment each week
70% of a revision reopens its counterpart activity
6 rework-propagation rounds are modelled
3 index units of explicit coordination per round

Scenario reading

Direct plan · B
100
Short loop · Cshort
—
Delayed adjustment · Cdelayed
—

Chart unavailable. The scenario reading above remains available.

How the three curves relate

At Discovery, the horizontal axis is k = 0 and all three curves begin at the same direct plan: B = 100. Each subsequent point is one rework-propagation round, k, across the reciprocal boundary.

Direct plan · B

Cplan(k) = B

The slate line stays flat at 100. It represents planned coordination through a pre-specified interface, work breakdown, schedule, acceptance criteria, and stage gate. Its implied work type is sequential and non-retractive: an upstream decision remains valid when the downstream team starts.

ExampleA payments team publishes a settled API contract; the mobile team implements it against that contract; both sides test against fixed acceptance criteria. The handoff may be late, but it does not make completed mobile work wrong. The line excludes normal planning and review effort because it is the conventional direct-work estimate against which the other two cases are compared.

Short loop · Cshort

Cshort(k) = B + 1TRk(q(1)) + kh

The sage line represents mutual adjustment: the coordination mechanism Thompson associates with reciprocal work. Its implied work type is reciprocal and retractive. The mechanism places an empowered integrator or cross-functional team at the boundary, gives it shared evidence and decision rights, records changed commitments, and meets before dependent work hardens.

ExampleA battery constraint changes a device's thermal envelope. Hardware, firmware, product, and support review the trade-off in the same working loop; they choose a new charging behaviour while only a small amount of dependent work has been committed. The line rises for propagated rework, 1TRk, and for visible coordination effort, kh.

Delayed adjustment · Cdelayed

Cdelayed(k) = B + 1TRk(q(L))

The rust line is the same reciprocal-retractive work governed as though it were sequential and non-retractive. The deployed mechanism is a document handoff, a delivery plan, local functional decisions, and periodic escalation to a programme board or steering review. That mechanism can coordinate a true sequential handoff; here it discovers the contradiction too late.

ExampleThe same battery constraint is documented as a risk and waits for the monthly programme review. In the meantime, firmware completes charging logic, product commits the customer promise, support writes operating guidance, and test automation encodes the old threshold. When the board resolves the constraint, q(L) = dr min(B, vL) is larger because six weeks of work accumulated. The same matrix A then propagates that larger rework seed between the activities.

The comparison is narrow. Cshort pays for early coordination and uses q(1). Cdelayed uses the larger q(L) in the same reciprocal loop. Ordinary planning and periodic-review effort sit outside both curves; h represents the additional recurring effort of the short loop.

The rework-loop formulation

The model contains two activities. A revision to either can reopen the other. The structure is deliberately small so that the reciprocal loop can be inspected. A real programme would require a larger activity network.

A = [ 0   g ; g   0 ]

The matrix A describes propagation after a revision. The zeroes say an activity does not reopen itself in this simplified model. Each g says what fraction of rework in one activity creates rework in the other in the next propagation round. The Reciprocal feedback gain slider sets g directly.

q(L) = d r min(B, vL)

q(L) is the initial rework seed, not the programme's full cost. While the decision waits, work under the unresolved commitment accumulates at rate v. The share d crosses the boundary; the share r of that work is invalidated. The cap min(B, vL) keeps accumulated work within the planned-work index B.

B
Direct planned work, fixed at 100 index units.
d
Dimensionless share of accumulated work coupled across the boundary. Reciprocal dependence slider.
r
Dimensionless share of coupled work invalidated at discovery. Retraction at discovery slider.
L
Decision latency in weeks. Decision latency slider.
v
Work-release rate in index units per week. Work release rate slider.
g
Dimensionless share of one activity's rework that creates counterpart rework in the next round; both off-diagonal entries of A. Reciprocal feedback gain slider.
N
Number of rework-propagation rounds examined. Revision rounds slider.
h
Additional coordination effort in one short-loop round, in index units. Short-loop coordination effort slider.

RN(q) = Σj=0N-1 Aj · (q / 2) [1, 1]T

RN(q) is rework propagated through N rounds from seed q. The vector divides the seed equally between the two activities. The first term is the discovered rework; later terms are the next-round rework it produces. At N = 0, the empty sum is zero, so every chart line starts at B.

Cdelayed = B + 1TRN(q(L))

Cshort = B + 1TRN(q(1)) + Nh

The delayed path uses the selected L. The short-loop path sets the interval to one week, uses q(1), and adds Nh. One week is a modelling choice, not a general prescription. Ordinary planning and periodic review are held constant, so the model does not treat delayed governance as cost-free.

The chart is a direct rendering of these equations. Its horizontal axis is the rework-propagation round k; Discovery at zero is the direct-work baseline before rework propagates. Its vertical axis is cumulative effort indexed to B = 100, so it is neither currency nor elapsed time. The slate line holds the traditional plan at 100. The rust line is Cdelayed. The sage line is Cshort, including the coordination effort you set.

For an infinite horizon, the rework series converges only when the spectral radius ρ(A) is below one. With this symmetric matrix, ρ(A) = g, so the condition is g < 1. For the finite N shown in the chart, the sum is always finite; as g approaches one, each extra round retains more of the preceding rework.

Related work