A time indexed formulation of non-preemptive single machine scheduling problems
Mathematical Programming: Series A and B
Modern heuristic techniques for combinatorial problems
Scheduling Computer and Manufacturing Processes
Scheduling Computer and Manufacturing Processes
Time-Indexed Formulations for Machine Scheduling Problems: Column Generation
INFORMS Journal on Computing
Scheduling unrelated parallel machines to minimize total weighted tardiness
Computers and Operations Research
Scheduling Algorithms
Computers and Operations Research
Hi-index | 0.01 |
Consider the problem of scheduling a set of jobs to be processed exactly once, on any machine of a set of unrelated parallel machines, without preemption. Each job has a due date, weight, and, for each machine, an associated processing time and sequence-dependent setup time. The objective function considered is to minimize the total weighted tardiness of the jobs. This work proposes a non-delayed relax-and-cut algorithm, based on a Lagrangean relaxation of a time indexed formulation of the problem. A Lagrangean heuristic is also developed to obtain approximate solutions. Using the proposed methods, it is possible to obtain optimal solutions within reasonable time for some instances with up to 180 jobs and six machines. For the solutions for which it is not possible to prove optimality, interesting gaps are obtained.