Tropical approximation to finish time of activity networks

Abstract

We breakdown complex projects into activities and their logical dependencies. We estimate the project finish time based on the activity durations and relations. However, adverse events trigger delay cascades shifting the finish time. Here I derive a tropical algebraic equation for the finish time of activity networks, encapsulating the principle of linear superposition of exogenous perturbations in the tropical sense. From the tropical algebraic equation I derive the finish time distribution with explicit reference to the distribution of exogenous delays and the network topology and geometry.

5 pages, 4 figures. The figures for simulated projects have an error in v1. The code to calculate the free floats was using w_ij = y_j - x_i instead of the correct expression w_ij = x_j - x_i$ (see Eq. (3)). This error is the actual cause of the anomalies observed in the small sigma region in Figs. 2 and 3. After correcting this coding error, the new Figs. 1, and 3 are shown here

References in corpus (2)

• Critical phenomena in complex networks
• Stochastic Earned Value Analysis using Monte Carlo Simulation and Statistical Learning Techniques