The shifting bottleneck procedure for job shop scheduling
Management Science
Insertion techniques for the heuristic solution of the job shop problem
Proceedings of the workshop on Discrete algorithms
A lower bound for the job insertion problem
Discrete Applied Mathematics
A fast hybrid tabu search algorithm for the no-wait job shop problem
Computers and Industrial Engineering
A new neighborhood and tabu search for the Blocking Job Shop
Discrete Applied Mathematics
| Hi-index | 0.00 |
The no-wait job shop (NWJS) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is given. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The NWJS problem consists in finding a schedule that minimizes the makespan.We address here the so-called optimal job insertion problem (OJI) in the NWJS. While the OJI is NP-hard in the classical job shop, it was shown by Gröflin & Klinkert to be solvable in polynomial time in the NWJS. We present a highly efficient algorithm with running time $\mathcal {O}(n^{2}\cdot\max\{n,m\})$ for this problem. The algorithm is based on a compact formulation of the NWJS problem and a characterization of all feasible insertions as the stable sets (of prescribed cardinality) in a derived comparability graph.As an application of our algorithm, we propose a heuristic for the NWJS problem based on optimal job insertion and present numerical results that compare favorably with current benchmarks.