Integer and combinatorial optimization
Integer and combinatorial optimization
Sequencing with earliness and tardiness penalties: a review
Operations Research
Formulating the single machine sequencing problem with release dates as a mixed integer program
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
Optimal pacing of trains in freight railroads: model formulation and solution
Operations Research
An efficient implementation of a scaling minimum-cost flow algorithm
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
PERT scheduling with convex cost functions
Theoretical Computer Science
Railway Timetabling Using Lagrangian Relaxation
Transportation Science
Modeling and Solving the Train Timetabling Problem
Operations Research
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
Lagrangian bounds for just-in-time job-shop scheduling
Computers and Operations Research
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Train movements across railway stations are still operated by human dispatchers. Motivated by an application provided by Azienda Trasporti Milanesi (ATM), the major Italian municipal transport company, we developed a real-time automated traffic control system to operate trains in metro stations. The system optimally controls the trains in a metro station by identifying a suitable routing and by establishing an optimum schedule of the performed operations. For each candidate routing an instance of the blocking, no-wait job-shop scheduling problem with convex costs is solved to optimality by branch and bound. A new, effective lower bound is developed to speed up the enumeration process. Computational testing in a real environment proved that the algorithm is able to solve relevant practical instances within the very tight time limit imposed by the application. The system has been in operation in the Milan metro since July 2007. To our knowledge, this is the first example of successful application of optimization methods to real-time traffic control in metro stations.