Robust unrelated parallel machine scheduling problem with interval release dates

TL;DR

This paper investigates a robust job scheduling problem on unrelated machines with uncertain release dates, proposing algorithms to minimize worst-case makespan under interval uncertainty and analyzing their effectiveness.

Contribution

Introduces a mixed-integer nonlinear programming model and three greedy algorithms for robust scheduling with interval release dates, including polynomial-time solvable cases.

Findings

Decomposition strategy yields competitive robust schedules.

Algorithms effectively handle worst-case scenario optimization.

Computational results validate the proposed methods' efficiency.

Abstract

This paper presents a profound analysis of the robust job scheduling problem with uncertain release dates on unrelated machines. Our model involves minimizing the worst-case makespan and interval uncertainty where each release date belongs to a well-defined interval. Robust optimization requires scenario-based decision-making. A finite subset of feasible scenarios to determine the worst-case regret (a deviation from the optimal makespan) for a particular schedule is indicated. We formulate a mixed-integer nonlinear programming model to solve the underlying problem via three (constructive) greedy algorithms. Polynomial-time solvable cases are also discussed in detail. The algorithms solve the robust combinatorial problem using the makespan criterion and its non-deterministic counterpart. Computational testing compares both robust solutions and different decomposition strategies. Finally, the results confirm that a decomposition strategy applied to the makespan criterion is enough to create a competitive robust schedule.