A branch and bound algorithm for the robust parall machine scheduling

TL;DR

This paper develops a branch and bound algorithm for robust parallel machine scheduling with uncertain processing times, introducing new bounds, a branch scheme, and dominance rules to improve efficiency and robustness verification.

Contribution

It presents a novel B&B algorithm with enhanced bounds and strategies specifically designed for stochastic processing times in parallel machine scheduling.

Findings

The new branch scheme improves algorithm efficiency.

The bounds and dominance rules enhance solution quality.

Robustness is verified through numerical experiments.

Abstract

This paper focuses on the identical parallel machine scheduling problem with sequence-dependent setup time, with special attention paid to the uncertainty of processing time. In this paper, a mathematical model of the parallel machine scheduling problem with stochastic processing time is constructed. Then a branch and bound (B&B) algorithm is proposed, and three methods for generating upper bounds and one heuristic for generating lower bound are developed to evaluate the performance of the B&B. In addition, a new branch scheme and two dominance rules are also devised to further improve the efficiency of the algorithm. In the numerical experiment analysis, the performance of the new branch scheme, the upper and lower bounds, and the dominance rule are tested, and the robustness of the stochastic parallel machine scheduling problem is verified by compared it with the deterministic version .