Formulating the single machine sequencing problem with release dates as a mixed integer program
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
An Implementation of Shor's r-Algorithm
Computational Optimization and Applications
PERT scheduling with convex cost functions
Theoretical Computer Science
The One-Machine Problem with Earliness and Tardiness Penalties
Journal of Scheduling
Solving Project Scheduling Problems by Minimum Cut Computations
Management Science
Optimal Real-Time Traffic Control in Metro Stations
Operations Research
Genetic algorithm and local search for just-in-time job-shop scheduling
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
LION'10 Proceedings of the 4th international conference on Learning and intelligent optimization
Models and strategies for variants of the job shop scheduling problem
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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We study the job-shop scheduling problem with earliness and tardiness penalties. We describe two Lagrangian relaxations of the problem. The first one is based on the relaxation of precedence constraints while the second one is based on the relaxation of machine constraints. We introduce dedicated algorithms to solve the corresponding dual problems. The second one is solved by a simple dynamic programming algorithm while the first one requires the resolution of an NP-hard problem by branch and bound. In both cases, the relaxations allow us to derive lower bounds as well as heuristic solutions. We finally introduce a simple local search algorithm to improve the best solution found. Computational results are reported.