New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources

Aurélien Froger (1, 2) , Ruslan Sadykov (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Realopt - Reformulations based algorithms for Combinatorial Optimization

We study the prize-collecting job sequencing problem with one common and multiple secondary resources. In this problem, a set of jobs is given, each with a profit, multiple time windows for its execution, and a duration during which it requires the main resource. Each job also requires one of the secondary resources before, during, and after its use of the main resource. The goal is to select and schedule the subset of jobs that maximize the total profit. We present a new mixed integer linear programming formulation of the problem and a branch-cut-and-price algorithm as exact solution methods. We also introduce a heuristic algorithm to tackle larger instances. Extensive numerical experiments show that our exact algorithms can solve to optimality literature instances with up to 500 jobs for a particular dataset and up to 250 jobs for another dataset with different characteristics. Our heuristic builds high-quality solutions in a small computational time. It computes new best-known solutions for most of the larger instances.

Mots clés: Scheduling; Sequencing; Labeling algorithm; Branch-cut-and-price; Iterated local search

Domaines: Recherche opérationnelle [math.OC]

Aurélien Froger, Ruslan Sadykov. New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources. 2021. ⟨hal-03287769v1⟩