Tropical approximation to finish time of activity networks

TL;DR

This paper introduces a tropical algebraic approach to estimate project finish times in activity networks, accounting for delays and their propagation, providing explicit distribution formulas based on network structure and delay distributions.

Contribution

It develops a novel tropical algebraic framework for modeling and analyzing finish times in activity networks, incorporating delay cascades and network topology.

Findings

Derived a tropical algebraic equation for finish time

Explicit distribution formulas based on delays and network structure

Provides a new analytical tool for project time estimation

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.