A MILP model for an extended version of the Flexible Job Shop Problem

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

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Woodall’s conjecture

Woodall’s conjecture asserts the following about every directed graph: if every directed cut of the graph has k or more edges then the graph has k or more mutually disjoint dijoins. Here, a dijoin is a set J of arcs such that any vertex is connected to any other by a path all of whose forward-directed arcs are in J. This talk is a little survey of the counterexamples to a generalized version of the conjecture

A Note on Johnson, Minkoff and Phillips ’ Algorithm for the Prize-Collecting Steiner Tree Problem

The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2 − 1)-approximation for the Prize-Collecting Steiner Tree Problem n−1 that runs in O(n 3 log n) time—it applies the primal-dual scheme once for each of the n vertices of the graph. Johnson, Minkoff and Phillips proposed a faster implementation of Goemans and Williamson’s algorithm. We present a proof that the approximation ratio of this implementation is exactly 2.