A new optimization algorithm for the vehicle routing problem with time windows
Operations Research
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Solving Parallel Machine Scheduling Problems by Column Generation
INFORMS Journal on Computing
Time-Indexed Formulations for Machine Scheduling Problems: Column Generation
INFORMS Journal on Computing
Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems
INFORMS Journal on Computing
Engine Routing and Scheduling at Industrial In-Plant Railroads
Transportation Science
An efficient optimal solution to the coil sequencing problem in electro-galvanizing line
Computers and Operations Research
A branch-and-price algorithm for the multi-activity multi-task shift scheduling problem
Journal of Scheduling
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The molten iron allocation problem (MIAP) is to allocate molten iron from blast furnaces to steel-making furnaces. The allocation needs to observe the release times of the molten iron defined by the draining plan of the blast furnaces and the transport time between the iron-making and steel-making stages. Time window constraints for processing the molten iron must be satisfied to avoid freezing. The objective is to find a schedule with minimum total weighted completion time. This objective reflects the practical consideration of improving steel-making efficiency and reducing operation cost caused by the need for reheating. Such a problem can be viewed as a parallel machine scheduling problem with time windows which is known to be NP-hard. In this paper, we first formulate the molten iron allocation problem as an integer programming model and then reformulate it as a set partitioning model by applying the Dantzig-Wolfe decomposition. We solve the problem using a column generation-based branch-and-price algorithm. Since the subproblem of column generation is still NP-hard, we propose a state-space relaxation-based dynamic programming algorithm for the subproblem. Computational experiments demonstrate that the proposed algorithm is capable of solving problems with up to 100 jobs to optimality within a reasonable computation time.