QUANTITATIVE SCHEDULE RISK ANALYSIS · AACE RP 57R-09 · OPRA-COMPATIBLE

MONTE CARLO
SCHEDULE RISK

PROJECT SUMMIT TOWER · 41 FLOORS · 489 FT · NEWARK NJ

STRUCTURAL ENGINEERING · FOUNDATION DESIGN
GABE KAFKA · STRUCTURAL ENGINEERING TECHNOLOGIES (S.E.T)

Three-point triangular duration distributions over a 43-activity CPM network. Sampled durations propagate through a forward pass; the maximum early-finish defines the project completion for each iteration.

Iterations10,000

Activities43

WBS Groups9

Risks15

Baseline T—

PRESS → TO ADVANCE · SPACE TO PLAY · F FULLSCREEN · 1-8 JUMP

Summit Tower — 41-story residential tower, Newark NJ

SUMMIT TOWER · NEWARK NJ RENDERING

— —

SCHEDULE · ACTIVITY NETWORK (44)

RISK PARAMETERS · THREE-POINT FACTORS (44)

DEFAULTS LOADED · SUMMIT TOWER

RISK REGISTER · SUMMIT TOWER · 15 IDENTIFIED RISKS SORTED BY PID DESC

01 · WHAT IS A RISK REGISTER?

A structured log of identified threats to the project, each with an owner, a category, a probability estimate, and an impact estimate. It is the bridge between qualitative risk workshops and the quantitative model.

02 · THE PID SCORE

PID = Probability × Impact (days). A single scalar used to rank risks and to govern how wide the pessimistic tail $\beta_i$ of an affected activity's triangular distribution should be.

$$\mathrm{PID}_r = \Pr(r) \cdot \mathrm{Impact}_r$$

e.g. SKD-02 Groundwater: $0.80 \times 80\,\text{days} = 64$ — the highest-scoring risk in the register.

03 · REGISTER → DISTRIBUTION

Each activity's $\beta_i$ is inflated by the sum of PID scores for the risks it is exposed to. Activities exposed to multiple high-PID risks receive the widest tails.

A402 Pile Install carries 5 risks (PID 36+28+28+28+18 = 138) → $\beta = 2.20$.

04 · WHY NO DISCRETE EVENTS

Per AACE RP 57R-09, discrete probability/impact events are not modeled separately. All risk is folded into duration width — trading event-level fidelity for parameter transparency and auditability.

→ NEXT: THE DETERMINISTIC BASELINE

DETERMINISTIC BASELINE GANTT · CPM FORWARD PASS T_DET = — DAYS

01 · THE SETUP

The project is a directed acyclic graph of $n$ activities with finish-to-start, zero-lag precedence. Each activity has a baseline duration $d_i$ and a set of predecessors $P(i)$.

02 · THE FORWARD PASS

Given a topological ordering, CPM computes early start ($ES_i$) and early finish ($EF_i$) recursively:

$$ES_i = \max_{j \in P(i)} EF_j \qquad EF_i = ES_i + d_i$$ $$T^{\text{det}} = \max_{i} EF_i$$

03 · WHY DETERMINISTIC ISN'T ENOUGH

The baseline tells us what would happen if every activity took exactly its estimated duration. But durations are uncertain — weather, labor, permits, groundwater, design changes. We need a probabilistic view.

→ NEXT: HOW WE MODEL THAT UNCERTAINTY

TRIANGULAR DURATION DISTRIBUTIONS · ONE PER ACTIVITY FILL = PDF · DASHED = MODE

01 · THREE-POINT ESTIMATES

Each activity receives three multiplicative factors from the risk register — optimistic ($\alpha$), most-likely ($\mu$), pessimistic ($\beta$):

$$(a_i, m_i, b_i) = (\alpha_i d_i,\; \mu_i d_i,\; \beta_i d_i)$$

02 · THE TRIANGULAR DENSITY

Activity duration $D_i$ is modeled as a triangular random variable $D_i \sim \mathrm{Tri}(a_i, m_i, b_i)$ with density:

$$f_{D_i}(x) = \begin{cases} \dfrac{2(x-a_i)}{(b_i-a_i)(m_i-a_i)} & a_i \le x \le m_i \\[0.4em] \dfrac{2(b_i-x)}{(b_i-a_i)(b_i-m_i)} & m_i \lt x \le b_i \\[0.4em] 0 & \text{otherwise} \end{cases}$$

03 · RISK REGISTER → DISTRIBUTION

Identified risks are encoded into the distribution width: activities exposed to multiple risks get wider pessimistic tails (higher $\beta_i$). No discrete risk events are modeled separately.

e.g. A402 Pile Installation: $\alpha=0.60$, $\beta=2.20$ (5 risks)

→ NEXT: SAMPLE 10,000 TIMES

Iterations0/ 10,000

Current T—working days

T deterministic—baseline

Mean—days

Std Dev—days

P50—median

P80—80% conf

P90—90% conf

LIVE GANTT · EACH ITERATION RESAMPLES DURATIONS, RE-RUNS FORWARD PASS DET (DASH) · CURRENT (SOLID) · GHOSTS (FAINT)

HISTOGRAM OF T N=0

S-CURVE (CDF) P50 / P80 / P90

HOVERED ACTIVITY — hover —

Iterations—total

T deterministic—days

Det Confidence—percentile