Robust scheduling to minimize the weighted number of late jobs with interval due-date uncertainty

TL;DR

This paper addresses robust scheduling on a single machine to minimize weighted late jobs under uncertain due-date intervals, proposing algorithms and formulations for both equal and general weights, with computational validation.

Contribution

It introduces a polynomial algorithm for equal weights and a mixed-integer programming model for the general case, advancing robust scheduling under due-date uncertainty.

Findings

Polynomial algorithm for equal weights case

Mixed-integer programming formulation for general case

Computational experiments demonstrating effectiveness

Abstract

We consider the class of single machine scheduling problems with the objective to minimize the weighted number of late jobs, under the assumption that completion due-dates are not known precisely at the time when decision-maker must provide a schedule. It is assumed that only the intervals to which the due-dates belong are known. The concept of maximum regret is used to define robust solution. A polynomial time algorithm is given for the case when weights of jobs are all equal. A mixed-integer linear programming formulation is provided for the general case, and computational experiments are reported.