A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by \"Ozg\"uven, \"Ozbakir, and Yavuz (Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Applied Mathematical Modelling, 34:1539--1548, 2010), using instances from the literature and instances inspired by real data from the printing industry.Comment: 15 pages, 2 figures, 4 tables. Optimization Letters, 201

Abstract. In 2006, Barát and Thomassen posed the following conjecture: for each tree T , there exists a natural number k T such that, if G is a k T -edge-connected graph and |E(G)| is divisible by |E(T )|, then G admits a decomposition into copies of T . This conjecture was verified for stars, some bistars, paths of length 3, 5, and 2 r for every positive integer r. We prove that this conjecture holds for paths of any fixed length.

No abstract

No abstract

No abstract