The Digital Twin Transition Model

In This Component

The transition function is the mathematical heart of the system. It defines precisely how the world changes as a consequence of each decision and each exogenous event. Without a correct transition model, any optimization is operating on a fantasy.

Implementation: DigitalTwinTransitionModel

The transition model is implemented as a Protocol-conforming class using Python 3.14’s match/case structural pattern matching to cleanly discriminate between event types.

Three-step process per epoch:

Step 1 — Process the decision $x_t$: If the action is accept_order=True, the system computes $\text{live\_mass}=\frac{\text{requested\_kg}}{\text{yield\_pct}}$ and deducts the corresponding birds and biomass from the physical state. The quoted price is locked into the information state.

Step 2 — Process exogenous information $W_{t+1}$:

match event:
    case B2BMarketEvent() if not action.accept_order:
        # Rejection penalty: churn +0.15, CLV × 0.90
    case IoTEdgeEvent(mortality_count=mort, cv_avg_weight_kg=cv_w, ammonia_spike=spike):
        # Biological update: count -= mort, biomass = count × cv_w
        # Ammonia spike: yield_pct × 0.85
    case _:
        pass

Step 3 — Return immutable $S_{t+1}$: Every state object uses @dataclass(frozen=True, slots=True). Transitions use dataclasses.replace() — no mutation, no shared mutable state, full reproducibility.

The Objective Function: MarginObjectiveFunction

The contribution margin $C(S_t,x_t,W_{t+1})$ implements Robert Phillips’ incremental-cost logic:

$C=(p\cdot q)-(c_{\text{feed}}\cdot q)-\text{SLA\_penalty}-(p\cdot q\cdot {\theta }_{\text{margin}})$

Feasibility is checked before scoring: sellable inventory must cover the order quantity, the schedule must not exceed the delivery offset, and the margin must be strictly positive. A reject action always returns $C=0$.