Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs

• Published in: Omega (Oxford) Vol. 84; pp. 18 - 30
• Main Authors: Arbib, Claudio, Felici, Giovanni, Servilio, Mara
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2019
• Subjects: Constrained submodular maximization; Cover inequalities; Integer linear programming; Pattern sequencing; Scheduling; Pattern sequencing; Cover inequalities; Integer linear programming; Scheduling; Constrained submodular maximization
• ISSN: 0305-0483; 1873-5274; 1873-5274
• DOI: 10.1016/j.omega.2018.04.002

•Operation sharing among jobs is quite common in important applications and calls for a special scheduling paradigm, whose relation to ordinary precedence-constrained scheduling is explicated.•A general formulation of common operation scheduling to minimize the weighted number of tardy jobs is provided.•The formulation, in the shape of set covering, has exponentially many inequalities; the complexity of their recognition and separation is investigated.•A branch-and-cut algorithm is devised and tested, features of difficult problems are identified, a comparison with the state-of-the-art algorithm for this problem is discussed. Common operation scheduling (COS) problems arise in real-world applications, such as industrial processes of material cutting or component dismantling. In COS, distinct jobs may share operations, and when an operation is done, it is done for all the jobs that share it. We here propose a 0-1 LP formulation with exponentially many inequalities to minimize the weighted number of tardy jobs. Separation of inequalities is in NP, provided that an ordinary min Lmax scheduling problem is in P. We develop a branch-and-cut algorithm for two cases: one machine with precedence relation; identical parallel machines with unit operation times. In these cases separation is the constrained maximization of a submodular set function. A previous method is modified to tackle the two cases, and compared to our algorithm. We report on tests conducted on both industrial and artificial instances. For single machine and general processing times the new method definitely outperforms the other, extending in this way the range of COS applications.