Minimizing maximum lateness in two-stage projects by tropical optimization

TL;DR

This paper addresses a two-stage scheduling problem aiming to minimize maximum lateness by formulating it as a tropical pseudoquadratic optimization problem, providing explicit solutions through tropical algebra techniques.

Contribution

It introduces a novel tropical optimization approach to solve a two-stage project scheduling problem with explicit solutions.

Findings

Explicit solution for the two-stage scheduling problem.

Application of tropical algebra yields full characterization of optimal schedules.

Demonstrates effectiveness of tropical optimization in complex scheduling scenarios.

Abstract

We are considering a two-stage optimal scheduling problem, which involves two similar projects with the same starting times for workers and the same deadlines for tasks. It is required that the starting times for workers and deadlines for tasks should be optimal for the first-stage project and, under this condition, also for the second-stage project. Optimality is measured with respect to the maximal lateness (or maximal delay) of tasks, which has to be minimized. We represent this problem as a problem of tropical pseudoquadratic optimization and show how the existing methods of tropical optimization and tropical linear algebra yield a full and explicit solution for this problem.