INCpotential

INCpotential is a theoretical measure used in optimization and decision science to quantify the potential incremental gain in a system’s performance from a set of upgrades or interventions, normalized by their cost. It is intended to compare the efficiency of different upgrade paths and to guide resource allocation in technology development, operations, and project planning.

Mathematically, consider a system S with current state s0 and a finite set U of upgrade options. Each option u ∈ U has a cost c(u) > 0 and a performance gain g(u) ≥ 0 when applied to S. For a subset Δ ⊆ U, let G(Δ) denote the total performance gain from applying Δ (accounting for interactions if specified). The total cost is C(Δ) = ∑_{u∈Δ} c(u). The incremental potential of Δ is IP(Δ) = G(Δ) / C(Δ). The INCpotential of S under a budget B is the maximum IP(Δ) over all Δ with C(Δ) ≤ B. In continuous settings, upgrade intensity or dosage can be modeled similarly, yielding a comparable ratio.

Computation often relies on a performance model to estimate G(Δ). If gains exhibit submodularity, greedy algorithms can provide near-optimal plans with provable bounds. INCpotential is particularly useful in portfolio optimization, technology roadmapping, and operations management, where it helps identify high-impact, cost-efficient upgrades.

Example: base performance 100. Upgrade A: cost 40, gain 25 (IP = 0.625). Upgrade B: cost 20, gain 15 (IP = 0.75). For a budget of 60, the option {B} yields IP 0.75, while {A,B} yields IP 40/60 ≈ 0.667, making {B} the more efficient choice under this budget.

Limitations include reliance on the accuracy of the performance model and potential non-additivity of gains.