# Min-Max Regret Scheduling To Minimize the Total Weight of Late Jobs With Interval Uncertainty

## TL;DR

This paper addresses robust scheduling for a single machine to minimize total weighted lateness under uncertain processing times, proposing a min-max regret approach and a heuristic algorithm evaluated via computational experiments.

## Contribution

It introduces a novel min-max regret scheduling model for uncertain processing times and develops a heuristic algorithm based on mixed-integer linear programming.

## Key findings

- The heuristic performs well in computational tests.
- The min-max regret approach effectively handles processing time uncertainty.
- The method provides robust schedules minimizing worst-case regret.

## Abstract

We study the single machine scheduling problem with the objective to minimize the total weight of late jobs. It is assumed that the processing times of jobs are not exactly known at the time when a complete schedule must be dispatched. Instead, only interval bounds for these parameters are given. In contrast to the stochastic optimization approach, we consider the problem of finding a robust schedule, which minimizes the maximum regret of a solution. Heuristic algorithm based on mixed-integer linear programming is presented and examined through computational experiments.