Algorithms for minimizing maximum lateness with unit length tasks and resource constraints
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Uniform machine scheduling of unit-time jobs subject to resource constraints
Discrete Applied Mathematics
Parallel machine scheduling with earliness-tardiness penalties and additional resource constraints
Computers and Operations Research
Scheduling problems for parallel dedicated machines under multiple resource constraints
Discrete Applied Mathematics - International symposium on combinatorial optimisation
IEA/AIE '08 Proceedings of the 21st international conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems: New Frontiers in Applied Artificial Intelligence
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This study deals with an unrelated parallel machine scheduling problem with one additional resource type (e.g., machine operators). The objective is to minimize the total completion time. After giving the integer programming model of the problem, a Lagrangian relaxation problem (LRP) is introduced by relaxing the constraint set concerning the additional resource. A general subgradient optimization procedure is applied to a series of LRPs to maximize the lower bound for the original problem. To generate efficient upper bounds for the original problem, a constraint programming (CP) model is applied by taking the LRP solutions as input regarding the machine assignments. For the problem, a pure CP model is also developed to evaluate its performance. All the solution approaches are evaluated through a range of test problems. The initial computational results show that Lagrangian-based CP approach produces promising results especially for larger problem sizes.